Cellular Automata-Based Parallel Random Number Generators Using FPGAs
David H. K. Hoe
2012-01-01
Full Text Available Cellular computing represents a new paradigm for implementing high-speed massively parallel machines. Cellular automata (CA, which consist of an array of locally connected processing elements, are a basic form of a cellular-based architecture. The use of field programmable gate arrays (FPGAs for implementing CA accelerators has shown promising results. This paper investigates the design of CA-based pseudo-random number generators (PRNGs using an FPGA platform. To improve the quality of the random numbers that are generated, the basic CA structure is enhanced in two ways. First, the addition of a superrule to each CA cell is considered. The resulting self-programmable CA (SPCA uses the superrule to determine when to make a dynamic rule change in each CA cell. The superrule takes its inputs from neighboring cells and can be considered itself a second CA working in parallel with the main CA. When implemented on an FPGA, the use of lookup tables in each logic cell removes any restrictions on how the super-rules should be defined. Second, a hybrid configuration is formed by combining a CA with a linear feedback shift register (LFSR. This is advantageous for FPGA designs due to the compactness of the LFSR implementations. A standard software package for statistically evaluating the quality of random number sequences known as Diehard is used to validate the results. Both the SPCA and the hybrid CA/LFSR were found to pass all the Diehard tests.
An Asynchronous Cellular Automata-Based Adaptive Illumination Facility
Bandini, Stefania; Bonomi, Andrea; Vizzari, Giuseppe; Acconci, Vito
The term Ambient Intelligence refers to electronic environments that are sensitive and responsive to the presence of people; in the described scenario the environment itself is endowed with a set of sensors (to perceive humans or other physical entities such as dogs, bicycles, etc.), interacting with a set of actuators (lights) that choose their actions (i.e. state of illumination) in an attempt improve the overall experience of these users. The model for the interaction and action of sensors and actuators is an asynchronous Cellular Automata (CA) with memory, supporting a self-organization of the system as a response to the presence and movements of people inside it. The paper will introduce the model, as well as an ad hoc user interface for the specification of the relevant parameters of the CA transition rule that determines the overall system behaviour.
Cellular-automata-based learning network for pattern recognition
Tzionas, Panagiotis G.; Tsalides, Phillippos G.; Thanailakis, Adonios
1991-11-01
Most classification techniques either adopt an approach based directly on the statistical characteristics of the pattern classes involved, or they transform the patterns in a feature space and try to separate the point clusters in this space. An alternative approach based on memory networks has been presented, its novelty being that it can be implemented in parallel and it utilizes direct features of the patterns rather than statistical characteristics. This study presents a new approach for pattern classification using pseudo 2-D binary cellular automata (CA). This approach resembles the memory network classifier in the sense that it is based on an adaptive knowledge based formed during a training phase, and also in the fact that both methods utilize pattern features that are directly available. The main advantage of this approach is that the sensitivity of the pattern classifier can be controlled. The proposed pattern classifier has been designed using 1.5 micrometers design rules for an N-well CMOS process. Layout has been achieved using SOLO 1400. Binary pseudo 2-D hybrid additive CA (HACA) is described in the second section of this paper. The third section describes the operation of the pattern classifier and the fourth section presents some possible applications. The VLSI implementation of the pattern classifier is presented in the fifth section and, finally, the sixth section draws conclusions from the results obtained.
P. G. Klyucharev
2014-01-01
Full Text Available In the paper the author considers hardware implementation of the GRACE-H family general cellular automata based cryptographic hash functions. VHDL is used as a language and Altera FPGA as a platform for hardware implementation. Performance and effectiveness of the FPGA implementations of GRACE-H hash functions were compared with Keccak (SHA-3, SHA-256, BLAKE, Groestl, JH, Skein hash functions. According to the performed tests, performance of the hardware implementation of GRACE-H family hash functions significantly (up to 12 times exceeded performance of the hardware implementation of previously known hash functions, and effectiveness of that hardware implementation was also better (up to 4 times.
Phase transitions and hysteresis in a cellular automata-based model of opinion formation
Kacperski, K.; Holyst, J.A.
1996-01-01
A particular case of a cellular automata-based model of two-state opinion formation in social groups with a strong leader is studied. We consider a 2D Euclidian geometry of open-quotes social spaceclose quotes and mutual interactions ∝ 1/r n . The model shows an interesting dynamics which can be analytically calculated. There are two stable states of the system: a cluster around the leader and unification. Unstable clusters may also appear. A variation in parameters such as the leader's strength or the open-quotes social temperatureclose quotes can change the size of a cluster or, when they reach some critical values, make the system jump into another state. For a certain range of parameters the system exhibits bistability and hysteresis phenomena. We obtained explicit formulas for the cluster size, critical values, make the system jump into another state. For a certain range of parameters the system exhibits bistability and hysteresis phenomena. We obtained explicit formulas for the cluster size, critical leader's strength, and critical open-quotes social temperature.close quotes These analytical results are verified by computer simulations
A Cellular Automata-Based Simulation Tool for Real Fire Accident Prevention
Jacek M. Czerniak
2018-01-01
Full Text Available Many serious real-life problems could be simulated using cellular automata theory. There were a lot of fires in public places which kill many people. Proposed method, called Cellular Automata Evaluation (CAEva in short, is using cellular automata theory and could be used for checking buildings conditions for fire accident. The tests performed on real accident showed that an appropriately configured program allows obtaining a realistic simulation of human evacuation. The authors analyze some real accidents and proved that CAEva method appears as a very promising solution, especially in the cases of building renovations or temporary unavailability of escape routes.
Modeling cell adhesion and proliferation: a cellular-automata based approach.
Vivas, J; Garzón-Alvarado, D; Cerrolaza, M
Cell adhesion is a process that involves the interaction between the cell membrane and another surface, either a cell or a substrate. Unlike experimental tests, computer models can simulate processes and study the result of experiments in a shorter time and lower costs. One of the tools used to simulate biological processes is the cellular automata, which is a dynamic system that is discrete both in space and time. This work describes a computer model based on cellular automata for the adhesion process and cell proliferation to predict the behavior of a cell population in suspension and adhered to a substrate. The values of the simulated system were obtained through experimental tests on fibroblast monolayer cultures. The results allow us to estimate the cells settling time in culture as well as the adhesion and proliferation time. The change in the cells morphology as the adhesion over the contact surface progress was also observed. The formation of the initial link between cell and the substrate of the adhesion was observed after 100 min where the cell on the substrate retains its spherical morphology during the simulation. The cellular automata model developed is, however, a simplified representation of the steps in the adhesion process and the subsequent proliferation. A combined framework of experimental and computational simulation based on cellular automata was proposed to represent the fibroblast adhesion on substrates and changes in a macro-scale observed in the cell during the adhesion process. The approach showed to be simple and efficient.
A Cellular Automata-based Model for Simulating Restitution Property in a Single Heart Cell.
Sabzpoushan, Seyed Hojjat; Pourhasanzade, Fateme
2011-01-01
Ventricular fibrillation is the cause of the most sudden mortalities. Restitution is one of the specific properties of ventricular cell. The recent findings have clearly proved the correlation between the slope of restitution curve with ventricular fibrillation. This; therefore, mandates the modeling of cellular restitution to gain high importance. A cellular automaton is a powerful tool for simulating complex phenomena in a simple language. A cellular automaton is a lattice of cells where the behavior of each cell is determined by the behavior of its neighboring cells as well as the automata rule. In this paper, a simple model is depicted for the simulation of the property of restitution in a single cardiac cell using cellular automata. At first, two state variables; action potential and recovery are introduced in the automata model. In second, automata rule is determined and then recovery variable is defined in such a way so that the restitution is developed. In order to evaluate the proposed model, the generated restitution curve in our study is compared with the restitution curves from the experimental findings of valid sources. Our findings indicate that the presented model is not only capable of simulating restitution in cardiac cell, but also possesses the capability of regulating the restitution curve.
The Development of Design Tools for Fault Tolerant Quantum Dot Cellular Automata Based Logic
Armstrong, Curtis D.; Humphreys, William M.
2003-01-01
We are developing software to explore the fault tolerance of quantum dot cellular automata gate architectures in the presence of manufacturing variations and device defects. The Topology Optimization Methodology using Applied Statistics (TOMAS) framework extends the capabilities of the A Quantum Interconnected Network Array Simulator (AQUINAS) by adding front-end and back-end software and creating an environment that integrates all of these components. The front-end tools establish all simulation parameters, configure the simulation system, automate the Monte Carlo generation of simulation files, and execute the simulation of these files. The back-end tools perform automated data parsing, statistical analysis and report generation.
The Design of Fault Tolerant Quantum Dot Cellular Automata Based Logic
Armstrong, C. Duane; Humphreys, William M.; Fijany, Amir
2002-01-01
As transistor geometries are reduced, quantum effects begin to dominate device performance. At some point, transistors cease to have the properties that make them useful computational components. New computing elements must be developed in order to keep pace with Moore s Law. Quantum dot cellular automata (QCA) represent an alternative paradigm to transistor-based logic. QCA architectures that are robust to manufacturing tolerances and defects must be developed. We are developing software that allows the exploration of fault tolerant QCA gate architectures by automating the specification, simulation, analysis and documentation processes.
Cellular automata-based artificial life system of horizontal gene transfer
Ji-xin Liu
2016-02-01
Full Text Available Mutation and natural selection is the core of Darwin's idea about evolution. Many algorithms and models are based on this idea. However, in the evolution of prokaryotes, more and more researches have indicated that horizontal gene transfer (HGT would be much more important and universal than the authors had imagined. Owing to this mechanism, the prokaryotes not only become adaptable in nearly any environment on Earth, but also form a global genetic bank and a super communication network with all the genes of the prokaryotic world. Under this background, they present a novel cellular automata model general gene transfer to simulate and study the vertical gene transfer and HGT in the prokaryotes. At the same time, they use Schrodinger's life theory to formulate some evaluation indices and to discuss the intelligence and cognition of prokaryotes which is derived from HGT.
Adabi, Sepideh; Adabi, Sahar; Rezaee, Ali
According to the traditional definition of Wireless Sensor Networks (WSNs), static sensors have limited the feasibility of WSNs in some kind of approaches, so the mobility was introduced in WSN. Mobile nodes in a WSN come equipped with battery and from the point of deployment, this battery reserve becomes a valuable resource since it cannot be replenished. Hence, maximizing the network lifetime by minimizing the energy is an important challenge in Mobile WSN. Energy conservation can be accomplished by different approaches. In this paper, we presented an energy conservation solution based on Cellular Automata. The main objective of this solution is based on dynamically adjusting the transmission range and switching between operational states of the sensor nodes.
Vergara-Blanco, J. E.; Leboeuf-Pasquier, J.; Benavides-Solorio, J. D. D.
2017-12-01
A simulation software that reproduces rainfall infiltration and runoff for a storm event in a particular forest area is presented. A cellular automaton is utilized to represent space and time. On the time scale, the simulation is composed by a sequence of discrete time steps. On the space scale, the simulation is composed of forest surface cells. The software takes into consideration rain intensity and length, individual forest cell soil absorption capacity evolution, and surface angle of inclination. The software is developed with the C++ programming language. The simulation is executed on a 100 ha area within La Primavera Forest in Jalisco, Mexico. Real soil texture for unburned terrain and high severity wildfire affected terrain is employed to recreate the specific infiltration profile. Historical rainfall data of a 92 minute event is used. The Horton infiltration equation is utilized for infiltration capacity calculation. A Digital Elevation Model (DEM) is employed to reproduce the surface topography. The DEM is displayed with a 3D mesh graph where individual surface cells can be observed. The plot colouring renders water content development at the cell level throughout the storm event. The simulation shows that the cumulative infiltration and runoff which take place at the surface cell level depend on the specific storm intensity, fluctuation and length, overall terrain topography, cell slope, and soil texture. Rainfall cumulative infiltration for unburned and high severity wildfire terrain are compared: unburned terrain exhibits a significantly higher amount of rainfall infiltration.It is concluded that a cellular automaton can be utilized with a C++ program to reproduce rainfall infiltration and runoff under diverse soil texture, topographic and rainfall conditions in a forest setting. This simulation is geared for an optimization program to pinpoint the locations of a series of forest land remediation efforts to support reforestation or to minimize runoff.
Cellular Automata Based Modeling for Evaluating Different Bus Stop Designs in China
Haoyang Ding
2015-01-01
Full Text Available A cellular automaton model is proposed to simulate mixed traffic flow composed of motor vehicles and bicycles near bus stops. Three typical types of bus stops which are common in China are considered in the model, including two types of curbside bus stops and one type of bus bay stops. Passenger transport capacity of three types of bus stops, which is applied to evaluate the bus stop design, is calculated based on the corresponding traffic flow rate. According to the simulation results, the flow rates of both motor vehicles and bicycles exhibit phase transition from free flow to the saturation one at the critical point. The results also show that the larger the interaction between motor vehicle and bicycle flow is near curbside bus stops, the more the value of saturated flows drops. Curbside bus stops are more suitable when the conflicts between two flows are small and the inflow rate of motor vehicles is low. On the contrary, bus bay stops should be applied due to their ability to reduce traffic conflicts. Findings of this study can provide useful suggestions on bus stop selection considering different inflow rate of motor vehicles and bicycles simultaneously.
A cellular automata based FPGA realization of a new metaheuristic bat-inspired algorithm
Progias, Pavlos; Amanatiadis, Angelos A.; Spataro, William; Trunfio, Giuseppe A.; Sirakoulis, Georgios Ch.
2016-10-01
Optimization algorithms are often inspired by processes occuring in nature, such as animal behavioral patterns. The main concern with implementing such algorithms in software is the large amounts of processing power they require. In contrast to software code, that can only perform calculations in a serial manner, an implementation in hardware, exploiting the inherent parallelism of single-purpose processors, can prove to be much more efficient both in speed and energy consumption. Furthermore, the use of Cellular Automata (CA) in such an implementation would be efficient both as a model for natural processes, as well as a computational paradigm implemented well on hardware. In this paper, we propose a VHDL implementation of a metaheuristic algorithm inspired by the echolocation behavior of bats. More specifically, the CA model is inspired by the metaheuristic algorithm proposed earlier in the literature, which could be considered at least as efficient than other existing optimization algorithms. The function of the FPGA implementation of our algorithm is explained in full detail and results of our simulations are also demonstrated.
Sarkar, Chinmoy; Abbasi, S.A.
2006-01-01
The strategies to prevent accidents from occurring in a process industry, or to minimize the harm if an accident does take place, always revolve around forecasting the likely accidents and their impacts. Based on the likely frequency and severity of the accidents, resources are committed towards preventing the accidents. Nearly all techniques of ranking hazardous units, be it the hazard and operability studies, fault tree analysis, hazard indice, etc. - qualitative as well as quantitative - depend essentially on the assessment of the likely frequency and the likely harm accidents in different units may cause. This fact makes it exceedingly important that the forecasting the accidents and their likely impact is done as accurately as possible. In the present study we introduce a new approach to accident forecasting based on the discrete modeling paradigm of cellular automata. In this treatment an accident is modeled as a self-evolving phenomena, the impact of which is strongly influenced by the size, nature, and position of the environmental components which lie in the vicinity of the accident site. The outward propagation of the mass, energy and momentum from the accident epicenter is modeled as a fast diffusion process occurring in discrete space-time coordinates. The quantum of energy and material that would flow into each discrete space element (cell) due to the accidental release is evaluated and the degree of vulnerability posed to the receptors if present in the cell is measured at the end of each time element. This approach is able to effectively take into account the modifications in the flux of energy and material which occur as a result of the heterogeneous environment prevailing between the accident epicenter and the receptor. Consequently, more realistic accident scenarios are generated than possible with the prevailing techniques. The efficacy of the approach has been illustrated with case studies
Building mathematics cellular phone learning communities
Wajeeh M. Daher
2011-04-01
Full Text Available Researchers emphasize the importance of maintaining learning communities and environments. This article describes the building and nourishment of a learning community, one comprised of middle school students who learned mathematics out-of-class using the cellular phone. The building of the learning community was led by three third year pre-service teachers majoring in mathematics and computers. The pre-service teachers selected thirty 8th grade students to learn mathematics with the cellular phone and be part of a learning community experimenting with this learning. To analyze the building and development stages of the cellular phone learning community, two models of community building stages were used; first the team development model developed by Tuckman (1965, second the life cycle model of a virtual learning community developed by Garber (2004. The research findings indicate that a learning community which is centered on a new technology has five 'life' phases of development: Pre-birth, birth, formation, performing, and maturity. Further, the research finding indicate that the norms that were encouraged by the preservice teachers who initiated the cellular phone learning community resulted in a community which developed, nourished and matured to be similar to a community of experienced applied mathematicians who use mathematical formulae to study everyday phenomena.
Mathematical analysis of complex cellular activity
Bertram, Richard; Teka, Wondimu; Vo, Theodore; Wechselberger, Martin; Kirk, Vivien; Sneyd, James
2015-01-01
This book contains two review articles on mathematical physiology that deal with closely related topics but were written and can be read independently. The first article reviews the basic theory of calcium oscillations (common to almost all cell types), including spatio-temporal behaviors such as waves. The second article uses, and expands on, much of this basic theory to show how the interaction of cytosolic calcium oscillators with membrane ion channels can result in highly complex patterns of electrical spiking. Through these examples one can see clearly how multiple oscillatory processes interact within a cell, and how mathematical methods can be used to understand such interactions better. The two reviews provide excellent examples of how mathematics and physiology can learn from each other, and work jointly towards a better understanding of complex cellular processes. Review 1: Richard Bertram, Joel Tabak, Wondimu Teka, Theodore Vo, Martin Wechselberger: Geometric Singular Perturbation Analysis of Burst...
A Mathematical Model for Cisplatin Cellular Pharmacodynamics
Ardith W. El-Kareh
2003-03-01
Full Text Available A simple theoretical model for the cellular pharmacodynamics of cisplatin is presented. The model, which takes into account the kinetics of cisplatin uptake by cells and the intracellular binding of the drug, can be used to predict the dependence of survival (relative to controls on the time course of extracellular exposure. Cellular pharmacokinetic parameters are derived from uptake data for human ovarian and head and neck cancer cell lines. Survival relative to controls is assumed to depend on the peak concentration of DNA-bound intracellular platinum. Model predictions agree well with published data on cisplatin cytotoxicity for three different cancer cell lines, over a wide range of exposure times. In comparison with previously published mathematical models for anticancer drug pharmacodynamics, the present model provides a better fit to experimental data sets including long exposure times (∼100 hours. The model provides a possible explanation for the fact that cell kill correlates well with area under the extracellular concentration-time curve in some data sets, but not in others. The model may be useful for optimizing delivery schedules and for the dosing of cisplatin for cancer therapy.
Students’ Perceptions of Learning Mathematics With Cellular Phones and Applets
Wajeeh M. Daher
2009-03-01
Full Text Available This paper describes the perceptions of middle school students regarding learning mathematics with cellular phones and web applets, their perceptions regarding the differences between these two electronic devices and their preferences regarding using the devices in learning mathematics. To analyze these perceptions I used the grounded theory approach which involves: open coding, axial coding, and selective coding, where the unit of analysis was the sentence in each of the interviews. The research findings imply that the participants perceived different aspects of both of the electronic devices: the availability of the device, the collaboration aspect, the communication aspect, the size of the device, and the swiftness of working with the device. These aspects influenced the participants’ decisions when, where and how to use each of the devices for the learning of mathematics. More participants preferred the cellular phone over the applet primarily for its small size which makes easy its portability as well as for its communication facilities.
[Reparative and neoplastic spheroid cellular structures and their mathematical model].
Kogan, E A; Namiot, V A; Demura, T A; Faĭzullina, N M; Sukhikh, G T
2014-01-01
Spheroid cell structures in the cell cultures have been described and are used for studying cell-cell and cell- matrix interactions. At the same time, spheroid cell structure participation in the repair and development of cancer in vivo remains unexplored. The aim of this study was to investigate the cellular composition of spherical structures and their functional significance in the repair of squamous epithelium in human papilloma virus-associated cervical pathology--chronic cervicitis and cervical intraepithelial neoplasia 1-3 degree, and also construct a mathematical model to explain the development and behavior of such spheroid cell structure.
Performance of Сellular Automata-based Stream Ciphers in GPU Implementation
P. G. Klyucharev
2016-01-01
Full Text Available Earlier the author had developed methods to build high-performance generalized cellular automata-based symmetric ciphers, which allow obtaining the encryption algorithms that show extremely high performance in hardware implementation. However, their implementation based on the conventional microprocessors lacks high performance. The mere fact is quite common - it shows a scope of applications for these ciphers. Nevertheless, the use of graphic processors enables achieving an appropriate performance for a software implementation.The article is extension of a series of the articles, which study various aspects to construct and implement cryptographic algorithms based on the generalized cellular automata. The article is aimed at studying the capabilities to implement the GPU-based cryptographic algorithms under consideration.Representing a key generator, the implemented encryption algorithm comprises 2k generalized cellular automata. The cellular automata graphs are Ramanujan’s ones. The cells of produced k gamma streams alternate, thereby allowing the GPU capabilities to be better used.To implement was used OpenCL, as the most universal and platform-independent API. The software written in C ++ was designed so that the user could set various parameters, including the encryption key, the graph structure, the local communication function, various constants, etc. To test were used a variety of graphics processors (NVIDIA GTX 650; NVIDIA GTX 770; AMD R9 280X.Depending on operating conditions, and GPU used, a performance range is from 0.47 to 6.61 Gb / s, which is comparable to the performance of the countertypes.Thus, the article has demonstrated that using the GPU makes it is possible to provide efficient software implementation of stream ciphers based on the generalized cellular automata.This work was supported by the RFBR, the project №16-07-00542.
Daher, Wajeeh; Baya'a, Nimer
2012-01-01
Learning in the cellular phone environment enables utilizing the multiple functions of the cellular phone, such as mobility, availability, interactivity, verbal and voice communication, taking pictures or recording audio and video, measuring time and transferring information. These functions together with mathematics-designated cellular phone…
Cellular Automata-Based Application for Driver Assistance in Indoor Parking Areas
Cándido Caballero-Gil
2016-11-01
Full Text Available This work proposes an adaptive recommendation mechanism for smart parking that takes advantage of the popularity of smartphones and the rise of the Internet of Things. The proposal includes a centralized system to forecast available indoor parking spaces, and a low-cost mobile application to obtain data of actual and predicted parking occupancy. The described scheme uses data from both sources bidirectionally so that the centralized forecast system is fed with data obtained with the distributed system based on smartphones, and vice versa. The mobile application uses different wireless technologies to provide the forecast system with actual parking data and receive from the system useful recommendations about where to park. Thus, the proposal can be used by any driver to easily find available parking spaces in indoor facilities. The client software developed for smartphones is a lightweight Android application that supplies precise indoor positioning systems based on Quick Response codes or Near Field Communication tags, and semi-precise indoor positioning systems based on Bluetooth Low Energy beacons. The performance of the proposed approach has been evaluated by conducting computer simulations and real experimentation with a preliminary implementation. The results have shown the strengths of the proposal in the reduction of the time and energy costs to find available parking spaces.
Cellular Automata-Based Application for Driver Assistance in Indoor Parking Areas †
Caballero-Gil, Cándido; Caballero-Gil, Pino; Molina-Gil, Jezabel
2016-01-01
This work proposes an adaptive recommendation mechanism for smart parking that takes advantage of the popularity of smartphones and the rise of the Internet of Things. The proposal includes a centralized system to forecast available indoor parking spaces, and a low-cost mobile application to obtain data of actual and predicted parking occupancy. The described scheme uses data from both sources bidirectionally so that the centralized forecast system is fed with data obtained with the distributed system based on smartphones, and vice versa. The mobile application uses different wireless technologies to provide the forecast system with actual parking data and receive from the system useful recommendations about where to park. Thus, the proposal can be used by any driver to easily find available parking spaces in indoor facilities. The client software developed for smartphones is a lightweight Android application that supplies precise indoor positioning systems based on Quick Response codes or Near Field Communication tags, and semi-precise indoor positioning systems based on Bluetooth Low Energy beacons. The performance of the proposed approach has been evaluated by conducting computer simulations and real experimentation with a preliminary implementation. The results have shown the strengths of the proposal in the reduction of the time and energy costs to find available parking spaces. PMID:27854282
Cellular Automata-Based Application for Driver Assistance in Indoor Parking Areas.
Caballero-Gil, Cándido; Caballero-Gil, Pino; Molina-Gil, Jezabel
2016-11-15
This work proposes an adaptive recommendation mechanism for smart parking that takes advantage of the popularity of smartphones and the rise of the Internet of Things. The proposal includes a centralized system to forecast available indoor parking spaces, and a low-cost mobile application to obtain data of actual and predicted parking occupancy. The described scheme uses data from both sources bidirectionally so that the centralized forecast system is fed with data obtained with the distributed system based on smartphones, and vice versa. The mobile application uses different wireless technologies to provide the forecast system with actual parking data and receive from the system useful recommendations about where to park. Thus, the proposal can be used by any driver to easily find available parking spaces in indoor facilities. The client software developed for smartphones is a lightweight Android application that supplies precise indoor positioning systems based on Quick Response codes or Near Field Communication tags, and semi-precise indoor positioning systems based on Bluetooth Low Energy beacons. The performance of the proposed approach has been evaluated by conducting computer simulations and real experimentation with a preliminary implementation. The results have shown the strengths of the proposal in the reduction of the time and energy costs to find available parking spaces.
Horn clause verification with convex polyhedral abstraction and tree automata-based refinement
Kafle, Bishoksan; Gallagher, John Patrick
2017-01-01
In this paper we apply tree-automata techniques to refinement of abstract interpretation in Horn clause verification. We go beyond previous work on refining trace abstractions; firstly we handle tree automata rather than string automata and thereby can capture traces in any Horn clause derivations...... underlying the Horn clauses. Experiments using linear constraint problems and the abstract domain of convex polyhedra show that the refinement technique is practical and that iteration of abstract interpretation with tree automata-based refinement solves many challenging Horn clause verification problems. We...... compare the results with other state-of-the-art Horn clause verification tools....
Kadakia, Ekta; Shah, Lipa; Amiji, Mansoor M
2017-07-01
Nanoemulsions have shown potential in delivering drug across epithelial and endothelial cell barriers, which express efflux transporters. However, their transport mechanisms are not entirely understood. Our goal was to investigate the cellular permeability of nanoemulsion-encapsulated drugs and apply mathematical modeling to elucidate transport mechanisms and sensitive nanoemulsion attributes. Transport studies were performed in Caco-2 cells, using fish oil nanoemulsions and a model substrate, rhodamine-123. Permeability data was modeled using a semi-mechanistic approach, capturing the following cellular processes: endocytotic uptake of the nanoemulsion, release of rhodamine-123 from the nanoemulsion, efflux and passive permeability of rhodamine-123 in aqueous solution. Nanoemulsions not only improved the permeability of rhodamine-123, but were also less sensitive to efflux transporters. The model captured bidirectional permeability results and identified sensitive processes, such as the release of the nanoemulsion-encapsulated drug and cellular uptake of the nanoemulsion. Mathematical description of cellular processes, improved our understanding of transport mechanisms, such as nanoemulsions don't inhibit efflux to improve drug permeability. Instead, their endocytotic uptake, results in higher intracellular drug concentrations, thereby increasing the concentration gradient and transcellular permeability across biological barriers. Modeling results indicated optimizing nanoemulsion attributes like the droplet size and intracellular drug release rate, may further improve drug permeability.
Cantone, Martina; Santos, Guido; Wentker, Pia; Lai, Xin; Vera, Julio
2017-01-01
Even today two bacterial lung infections, namely pneumonia and tuberculosis, are among the 10 most frequent causes of death worldwide. These infections still lack effective treatments in many developing countries and in immunocompromised populations like infants, elderly people and transplanted patients. The interaction between bacteria and the host is a complex system of interlinked intercellular and the intracellular processes, enriched in regulatory structures like positive and negative feedback loops. Severe pathological condition can emerge when the immune system of the host fails to neutralize the infection. This failure can result in systemic spreading of pathogens or overwhelming immune response followed by a systemic inflammatory response. Mathematical modeling is a promising tool to dissect the complexity underlying pathogenesis of bacterial lung infection at the molecular, cellular and tissue levels, and also at the interfaces among levels. In this article, we introduce mathematical and computational modeling frameworks that can be used for investigating molecular and cellular mechanisms underlying bacterial lung infection. Then, we compile and discuss published results on the modeling of regulatory pathways and cell populations relevant for lung infection and inflammation. Finally, we discuss how to make use of this multiplicity of modeling approaches to open new avenues in the search of the molecular and cellular mechanisms underlying bacterial infection in the lung.
REDUNDANT ELECTRIC MOTOR DRIVE CONTROL UNIT DESIGN USING AUTOMATA-BASED APPROACH
Yuri Yu. Yankin
2014-11-01
Full Text Available Implementation of redundant unit for motor drive control based on programmable logic devices is discussed. Continuous redundancy method is used. As compared to segregated standby redundancy and whole system standby redundancy, such method provides preservation of all unit functions in case of redundancy and gives the possibility for continuous monitoring of major and redundant elements. Example of that unit is given. Electric motor drive control channel block diagram contains two control units – the major and redundant; it also contains four power supply units. Control units programming was carried out using automata-based approach. Electric motor drive control channel model was developed; it provides complex simulation of control state-machine and power converter. Through visibility and hierarchy of finite state machines debug time was shortened as compared to traditional programming. Control state-machine description using hardware description language is required for its synthesis with FPGA-devices vendor design software. This description was generated automatically by MATLAB software package. To verify results two prototype control units, two prototype power supply units, and device mock-up were developed and manufactured. Units were installed in the device mock-up. Prototype units were created in accordance with requirements claimed to deliverable hardware. Control channel simulation and tests results in the perfect state and during imitation of major element fault are presented. Automata-based approach made it possible to observe and debug control state-machine transitions during simulation of transient processes, occurring at imitation of faults. Results of this work can be used in development of fault tolerant electric motor drive control channels.
Lira, Matthew
This dissertation explores the Knowledge in Pieces (KiP) theory to account for how students learn to coordinate knowledge of mathematical and physical models in biology education. The KiP approach characterizes student knowledge as a fragmented collection of knowledge elements as opposed to stable and theory-like knowledge. This dissertation sought to use this theoretical lens to account for how students understand and learn with mathematical models and representations, such as equations. Cellular physiology provides a quantified discipline that leverages concepts from mathematics, physics, and chemistry to understand cellular functioning. Therefore, this discipline provides an exemplary context for assessing how biology students think and learn with mathematical models. In particular, the resting membrane potential provides an exemplary concept well defined by models of dynamic equilibrium borrowed from physics and chemistry. In brief, membrane potentials, or voltages, "rest" when the electrical and chemical driving forces for permeable ionic species are equal in magnitude but opposite in direction. To assess students' understandings of this concept, this dissertation employed three studies: the first study employed the cognitive clinical interview to assess student thinking in the absence and presence of equations. The second study employed an intervention to assess student learning and the affordances of an innovative assessment. The third student employed a human-computer-interaction paradigm to assess how students learn with a novel multi-representational technology. Study 1 revealed that students saw only one influence--the chemical gradient--and that students coordinated knowledge of only this gradient with the related equations. Study 2 revealed that students benefited from learning with the multi-representational technology and that the assessment detected performance gains across both calculation and explanation tasks. Last, Study 3 revealed how students
Aalaei, Amin; Davoudpour, Hamid
2012-11-01
This article presents designing a new mathematical model for integrating dynamic cellular manufacturing into supply chain system with an extensive coverage of important manufacturing features consideration of multiple plants location, multi-markets allocation, multi-period planning horizons with demand and part mix variation, machine capacity, and the main constraints are demand of markets satisfaction in each period, machine availability, machine time-capacity, worker assignment, available time of worker, production volume for each plant and the amounts allocated to each market. The aim of the proposed model is to minimize holding and outsourcing costs, inter-cell material handling cost, external transportation cost, procurement & maintenance and overhead cost of machines, setup cost, reconfiguration cost of machines installation and removal, hiring, firing and salary worker costs. Aimed to prove the potential benefits of such a design, presented an example is shown using a proposed model.
Kamran Forghani
2012-10-01
Full Text Available In this paper, a new mathematical model in cellular manufacturing systems (CMSs has been presented. In order to increase the performance of manufacturing system, the production quantity of parts has been considered as a decision variable, i.e. each part can be produced and outsourced, simultaneously. This extension would be minimized the unused capacity of machines. The exceptional elements (EEs are taken into account and would be totally outsourced to the external supplier in order to remove intercellular material handling cost. The problem has been formulated as a mixed-integer programming to minimize the sum of manufacturing variable costs under budget, machines capacity and demand constraints. Also, to evaluate advantages of the model, several illustrative numerical examples have been provided to compare the performance of the proposed model with the available classical approaches in the literature.
Bru, Antonio; Cardona, Pere-Joan
2010-01-01
Background Mycobacterium tuberculosis is a particularly aggressive microorganism and the host's defense is based on the induction of cellular immunity, in which the creation of a granulomatous structure has an important role. Methodology We present here a new 2D cellular automata model based on the concept of a multifunctional process that includes key factors such as the chemokine attraction of the cells; the role of innate immunity triggered by natural killers; the presence of neutrophils; apoptosis and necrosis of infected macrophages; the removal of dead cells by macrophages, which induces the production of foamy macrophages (FMs); the life cycle of the bacilli as a determinant for the evolution of infected macrophages; and the immune response. Results The results obtained after the inclusion of two degrees of tolerance to the inflammatory response triggered by the infection shows that the model can cover a wide spectrum, ranging from highly-tolerant (i.e. mice) to poorly-tolerant hosts (i.e. mini-pigs or humans). Conclusions This model suggest that stopping bacillary growth at the onset of the infection might be difficult and the important role played by FMs in bacillary drainage in poorly-tolerant hosts together with apoptosis and innate lymphocytes. It also shows the poor ability of the cellular immunity to control the infection, provides a clear protective character to the granuloma, due its ability to attract a sufficient number of cells, and explains why an already infected host can be constantly reinfected. PMID:20886087
Nguyen, Thanh Khuong; Khalloufi, Seddik; Mondor, Martin; Ratti, Cristina
2018-01-01
In the present work, the impact of glass transition on shrinkage of non-cellular food systems (NCFS) during air-drying will be assessed from experimental data and the interpretation of a 'shrinkage' function involved in a mathematical model. Two NCFS made from a mixture of water/maltodextrin/agar (w/w/w: 1/0.15/0.015) were created out of maltodextrins with dextrose equivalent 19 (MD19) or 36 (MD36). The NCFS made with MD19 had 30°C higher Tg than those with MD36. This information indicated that, during drying, the NCFS with MD19 would pass from rubbery to glassy state sooner than NCFS MD36, for which glass transition only happens close to the end of drying. For the two NCFS, porosity and volume reduction as a function of moisture content were captured with high accuracy when represented by the mathematical models previously developed. No significant differences in porosity and in maximum shrinkage between both samples during drying were observed. As well, no change in the slope of the shrinkage curve as a function of moisture content was perceived. These results indicate that glass transition alone is not a determinant factor in changes of porosity or volume during air-drying. Copyright © 2017 Elsevier Ltd. All rights reserved.
Meireles, Sincler P. de; Santos, Adriano M.; Grynberg, Suely Epsztein, E-mail: spm@cdtn.b, E-mail: amsantos@cdtn.b, E-mail: seg@cdtn.b [Centro de Desenvolvimento da Tecnologia Nuclear (CDTN/CNEN-MG), Belo Horizonte, MG (Brazil); Nunes, Maria Eugenia S., E-mail: mariaeugenia@iceb.ufop.b [Universidade Federal de Ouro Preto (UFOP), MG (Brazil)
2011-07-01
During recent years, there has been a shift from an approach focused entirely on DNA as the main target of ionizing radiation to a vision that considers complex signaling pathways in cells and among cells within tissues. Several newly recognized responses were classified as the so-called non-target responses in which the biological effects are not directly related to the amount of energy deposited in the DNA of cells that were traversed by radiation. In 1992 the bystander effect was described referring to a series of responses such as death, chromosomal instability or other abnormalities that occur in non-irradiated cells that came into contact with irradiated cells or medium from irradiated cells. In this work, we have developed a mathematical model via cellular automata, to quantify cell death induced by the bystander effect. The model is based on experiments with irradiated cells conditioned medium which suggests that irradiated cells secrete molecules in the medium that are capable of damaging other cells. The computational model consists of two-dimensional cellular automata which is able to simulate the transmission of bystander signals via extrinsic route and via Gap junctions. The model has been validated by experimental results in the literature. The time evolution of the effect and the dose-response curves were obtained in good accordance to them. Simulations were conducted for different values of bystander and irradiated cell densities with constant dose. From this work, we have obtained a relationship between cell density and effect. (author)
Meireles, Sincler P. de; Santos, Adriano M.; Grynberg, Suely Epsztein; Nunes, Maria Eugenia S.
2011-01-01
During recent years, there has been a shift from an approach focused entirely on DNA as the main target of ionizing radiation to a vision that considers complex signaling pathways in cells and among cells within tissues. Several newly recognized responses were classified as the so-called non-target responses in which the biological effects are not directly related to the amount of energy deposited in the DNA of cells that were traversed by radiation. In 1992 the bystander effect was described referring to a series of responses such as death, chromosomal instability or other abnormalities that occur in non-irradiated cells that came into contact with irradiated cells or medium from irradiated cells. In this work, we have developed a mathematical model via cellular automata, to quantify cell death induced by the bystander effect. The model is based on experiments with irradiated cells conditioned medium which suggests that irradiated cells secrete molecules in the medium that are capable of damaging other cells. The computational model consists of two-dimensional cellular automata which is able to simulate the transmission of bystander signals via extrinsic route and via Gap junctions. The model has been validated by experimental results in the literature. The time evolution of the effect and the dose-response curves were obtained in good accordance to them. Simulations were conducted for different values of bystander and irradiated cell densities with constant dose. From this work, we have obtained a relationship between cell density and effect. (author)
Eringen, A Cemal
2013-01-01
Continuum Physics: Volume 1 - Mathematics is a collection of papers that discusses certain selected mathematical methods used in the study of continuum physics. Papers in this collection deal with developments in mathematics in continuum physics and its applications such as, group theory functional analysis, theory of invariants, and stochastic processes. Part I explains tensor analysis, including the geometry of subspaces and the geometry of Finsler. Part II discusses group theory, which also covers lattices, morphisms, and crystallographic groups. Part III reviews the theory of invariants th
Stein, Sherman K
2010-01-01
Anyone can appreciate the beauty, depth, and vitality of mathematics with the help of this highly readable text, specially developed from a college course designed to appeal to students in a variety of fields. Readers with little mathematical background are exposed to a broad range of subjects chosen from number theory, topology, set theory, geometry, algebra, and analysis. Starting with a survey of questions on weight, the text discusses the primes, the fundamental theorem of arithmetic, rationals and irrationals, tiling, tiling and electricity, probability, infinite sets, and many other topi
a Predator-Prey Model Based on the Fully Parallel Cellular Automata
He, Mingfeng; Ruan, Hongbo; Yu, Changliang
We presented a predator-prey lattice model containing moveable wolves and sheep, which are characterized by Penna double bit strings. Sexual reproduction and child-care strategies are considered. To implement this model in an efficient way, we build a fully parallel Cellular Automata based on a new definition of the neighborhood. We show the roles played by the initial densities of the populations, the mutation rate and the linear size of the lattice in the evolution of this model.
Demazure, M.
1988-01-01
The 1988 progress report of the Mathematics center (Polytechnic School, France), is presented. The Center is composed of different research teams: analysis, Riemann geometry, group theory, formal calculus and algorithm geometry, dynamical systems, topology and singularity. For each team, the members, the research topics, the national and international cooperations, are given. The papers concerning the investigations carried out in 1988, are listed [fr
Ingrid Paine
2016-04-01
Full Text Available Mathematics is often used to model biological systems. In mammary gland development, mathematical modeling has been limited to acinar and branching morphogenesis and breast cancer, without reference to normal duct formation. We present a model of ductal elongation that exploits the geometrically-constrained shape of the terminal end bud (TEB, the growing tip of the duct, and incorporates morphometrics, region-specific proliferation and apoptosis rates. Iterative model refinement and behavior analysis, compared with biological data, indicated that the traditional metric of nipple to the ductal front distance, or percent fat pad filled to evaluate ductal elongation rate can be misleading, as it disregards branching events that can reduce its magnitude. Further, model driven investigations of the fates of specific TEB cell types confirmed migration of cap cells into the body cell layer, but showed their subsequent preferential elimination by apoptosis, thus minimizing their contribution to the luminal lineage and the mature duct.
Day, Judy D.; Metes, Diana M.; Vodovotz, Yoram
2015-01-01
A mathematical model of the early inflammatory response in transplantation is formulated with ordinary differential equations. We first consider the inflammatory events associated only with the initial surgical procedure and the subsequent ischemia/reperfusion (I/R) events that cause tissue damage to the host as well as the donor graft. These events release damage-associated molecular pattern molecules (DAMPs), thereby initiating an acute inflammatory response. In simulations of this model, resolution of inflammation depends on the severity of the tissue damage caused by these events and the patient’s (co)-morbidities. We augment a portion of a previously published mathematical model of acute inflammation with the inflammatory effects of T cells in the absence of antigenic allograft mismatch (but with DAMP release proportional to the degree of graft damage prior to transplant). Finally, we include the antigenic mismatch of the graft, which leads to the stimulation of potent memory T cell responses, leading to further DAMP release from the graft and concomitant increase in allograft damage. Regulatory mechanisms are also included at the final stage. Our simulations suggest that surgical injury and I/R-induced graft damage can be well-tolerated by the recipient when each is present alone, but that their combination (along with antigenic mismatch) may lead to acute rejection, as seen clinically in a subset of patients. An emergent phenomenon from our simulations is that low-level DAMP release can tolerize the recipient to a mismatched allograft, whereas different restimulation regimens resulted in an exaggerated rejection response, in agreement with published studies. We suggest that mechanistic mathematical models might serve as an adjunct for patient- or sub-group-specific predictions, simulated clinical studies, and rational design of immunosuppression. PMID:26441988
Jain, Harsh; Jackson, Trachette
2018-05-01
Tumor growth and progression are critically dependent on the establishment of a vascular support system. This is often accomplished via the expression of pro-angiogenic growth factors, including members of the vascular endothelial growth factor (VEGF) family of ligands. VEGF ligands are overexpressed in a wide variety of solid tumors and therefore have inspired optimism that inhibition of the different axes of the VEGF pathway-alone or in combination-would represent powerful anti-angiogenic therapies for most cancer types. When considering treatments that target VEGF and its receptors, it is difficult to tease out the differential anti-angiogenic and anti-tumor effects of all combinations experimentally because tumor cells and vascular endothelial cells are engaged in a dynamic cross-talk that impacts key aspects of tumorigenesis, independent of angiogenesis. Here we develop a mathematical model that connects intracellular signaling responsible for both endothelial and tumor cell proliferation and death to population-level cancer growth and angiogenesis. We use this model to investigate the effect of bidirectional communication between endothelial cells and tumor cells on treatments targeting VEGF and its receptors both in vitro and in vivo. Our results underscore the fact that in vitro therapeutic outcomes do not always translate to the in vivo situation. For example, our model predicts that certain therapeutic combinations result in antagonism in vivo that is not observed in vitro. Mathematical modeling in this direction can shed light on the mechanisms behind experimental observations that manipulating VEGF and its receptors is successful in some cases but disappointing in others.
Cellular Automata as a learning process in Architecture and Urban design
Jensen, Mads Brath; Foged, Isak Worre
2014-01-01
. An architectural methodological response to this situation is presented through the development of a conceptual computational design system that allows these dynamics to unfold and to be observed for architectural design decision taking. Reflecting on the development and implementation of a cellular automata based...... design approach on a master level urban design studio this paper will discuss the strategies for dealing with complexity at an urban scale as well as the pedagogical considerations behind applying computational tools and methods to a urban design education....
Matthäus, Franziska; Pahle, Jürgen
2017-01-01
This contributed volume comprises research articles and reviews on topics connected to the mathematical modeling of cellular systems. These contributions cover signaling pathways, stochastic effects, cell motility and mechanics, pattern formation processes, as well as multi-scale approaches. All authors attended the workshop on "Modeling Cellular Systems" which took place in Heidelberg in October 2014. The target audience primarily comprises researchers and experts in the field, but the book may also be beneficial for graduate students.
Nakajima, Kohei; Haruna, Taichi
2011-09-01
In this paper, we propose a new class of cellular automata based on the modification of its state space. It is introduced to model a computation which is exposed to an environment. We formalized the computation as extension and projection processes of its state space and resulting misidentifications of the state. This is motivated to embed the role of an environment into the system itself, which naturally induces self-organized internal perturbations rather than the usual external perturbations. Implementing this structure into the elementary cellular automata, we characterized its effect by means of input entropy and power spectral analysis. As a result, the cellular automata with this structure showed robust class IV behavior and a 1/f power spectrum in a wide range of rule space comparative to the notion of the edge of chaos. Copyright © 2011 Elsevier Ireland Ltd. All rights reserved.
Janssen, W.E.
1984-01-01
In recent years, an in vitro system for the culturing of hematopoietic stem cells and precursor cells over extended time periods has been developed. It has been clearly demonstrated that these cultures are supporting ongoing hematopoiesis, which makes them an ideal model system for investigating questions relating to both normal and abnormal hematopoiesis. The most easily measured aspect of this culture system is its ongoing production of hematopoietic cells which are recoverable at weekly culture feedings. The current study develops a mathematical model of the production of cells in these cultures and then applies that model in the form of a computer simulation to several experimental protocols, particularly those involving the exposure of the culture system to ionizing radiation. Extensive experimental testing is described, which verifies the validity of the mathematical description presented, and further supports the hypothesis of a radiation insensitive hematopoietic microenvironment
Ebrahimi, Ahmad; Kia, Reza; Komijan, Alireza Rashidi
2016-01-01
In this article, a novel integrated mixed-integer nonlinear programming model is presented for designing a cellular manufacturing system (CMS) considering machine layout and part scheduling problems simultaneously as interrelated decisions. The integrated CMS model is formulated to incorporate several design features including part due date, material handling time, operation sequence, processing time, an intra-cell layout of unequal-area facilities, and part scheduling. The objective function is to minimize makespan, tardiness penalties, and material handling costs of inter-cell and intra-cell movements. Two numerical examples are solved by the Lingo software to illustrate the results obtained by the incorporated features. In order to assess the effects and importance of integration of machine layout and part scheduling in designing a CMS, two approaches, sequentially and concurrent are investigated and the improvement resulted from a concurrent approach is revealed. Also, due to the NP-hardness of the integrated model, an efficient genetic algorithm is designed. As a consequence, computational results of this study indicate that the best solutions found by GA are better than the solutions found by B&B in much less time for both sequential and concurrent approaches. Moreover, the comparisons between the objective function values (OFVs) obtained by sequential and concurrent approaches demonstrate that the OFV improvement is averagely around 17 % by GA and 14 % by B&B.
Statistical mechanics of cellular automata
Wolfram, S.
1983-01-01
Cellular automata are used as simple mathematical models to investigate self-organization in statistical mechanics. A detailed analysis is given of ''elementary'' cellular automata consisting of a sequence of sites with values 0 or 1 on a line, with each site evolving deterministically in discrete time steps according to p definite rules involving the values of its nearest neighbors. With simple initial configurations, the cellular automata either tend to homogeneous states, or generate self-similar patterns with fractal dimensions approx. =1.59 or approx. =1.69. With ''random'' initial configurations, the irreversible character of the cellular automaton evolution leads to several self-organization phenomena. Statistical properties of the structures generated are found to lie in two universality classes, independent of the details of the initial state or the cellular automaton rules. More complicated cellular automata are briefly considered, and connections with dynamical systems theory and the formal theory of computation are discussed
F.C. Gruau; J.T. Tromp (John)
1999-01-01
textabstractWe consider the problem of establishing gravity in cellular automata. In particular, when cellular automata states can be partitioned into empty, particle, and wall types, with the latter enclosing rectangular areas, we desire rules that will make the particles fall down and pile up on
Mathematical modelling of metabolism
Gombert, Andreas Karoly; Nielsen, Jens
2000-01-01
Mathematical models of the cellular metabolism have a special interest within biotechnology. Many different kinds of commercially important products are derived from the cell factory, and metabolic engineering can be applied to improve existing production processes, as well as to make new processes...... availability of genomic information and powerful analytical techniques, mathematical models also serve as a tool for understanding the cellular metabolism and physiology....... available. Both stoichiometric and kinetic models have been used to investigate the metabolism, which has resulted in defining the optimal fermentation conditions, as well as in directing the genetic changes to be introduced in order to obtain a good producer strain or cell line. With the increasing...
Mathematical Modelling Plant Signalling Networks
Muraro, D.; Byrne, H.M.; King, J.R.; Bennett, M.J.
2013-01-01
methods for modelling gene and signalling networks and their application in plants. We then describe specific models of hormonal perception and cross-talk in plants. This mathematical analysis of sub-cellular molecular mechanisms paves the way for more
Cellular automata analysis and applications
Hadeler, Karl-Peter
2017-01-01
This book focuses on a coherent representation of the main approaches to analyze the dynamics of cellular automata. Cellular automata are an inevitable tool in mathematical modeling. In contrast to classical modeling approaches as partial differential equations, cellular automata are straightforward to simulate but hard to analyze. In this book we present a review of approaches and theories that allow the reader to understand the behavior of cellular automata beyond simulations. The first part consists of an introduction of cellular automata on Cayley graphs, and their characterization via the fundamental Cutis-Hedlund-Lyndon theorems in the context of different topological concepts (Cantor, Besicovitch and Weyl topology). The second part focuses on classification results: What classification follows from topological concepts (Hurley classification), Lyapunov stability (Gilman classification), and the theory of formal languages and grammars (Kůrka classification). These classifications suggest to cluster cel...
Communicative automata based programming. Society Framework
Andrei Micu
2015-10-01
Full Text Available One of the aims of this paper is to present a new programming paradigm based on the new paradigms intensively used in IT industry. Implementation of these techniques can improve the quality of code through modularization, not only in terms of entities used by a program, but also in terms of states in which they pass. Another aspect followed in this paper takes into account that in the development of software applications, the transition from the design to the source code is a very expensive step in terms of effort and time spent. Diagrams can hide very important details for simplicity of understanding, which can lead to incorrect or incomplete implementations. To improve this process communicative automaton based programming comes with an intermediate step. We will see how it goes after creating modeling diagrams to communicative automata and then to writing code for each of them. We show how the transition from one step to another is much easier and intuitive.
Automata-Based CSL Model Checking
Zhang, Lijun; Jansen, David N.; Nielson, Flemming
2011-01-01
For continuous-time Markov chains, the model-checking problem with respect to continuous-time stochastic logic (CSL) has been introduced and shown to be decidable by Aziz, Sanwal, Singhal and Brayton in 1996. The presented decision procedure, however, has exponential complexity. In this paper, we...... probability can then be approximated in polynomial time (using uniformization). This makes the present work the centerpiece of a broadly applicable full CSL model checker. Recently, the decision algorithm by Aziz et al. was shown to be incorrect in general. In fact, it works only for stratified CTMCs...
Luther, Kenneth H.
2012-01-01
Mathematical modeling of groundwater flow is a topic at the intersection of mathematics and geohydrology and is rarely encountered in undergraduate mathematics. However, this subject is full of interesting and meaningful examples of truly "applied" mathematics accessible to undergraduates, from the pre-calculus to advanced mathematics levels. This…
Hildebrand, C.E.; Walters, R.A.
1977-01-01
Progress is reported on the following research projects: chromatin structure; the use of circular synthetic polydeoxynucleotides as substrates for the study of DNA repair enzymes; human cellular kinetic response following exposure to DNA-interactive compounds; histone phosphorylation and chromatin structure in cell proliferation; photoaddition products induced in chromatin by uv light; pollutants and genetic information transfer; altered RNA metabolism as a function of cadmium accumulation and intracellular distribution in cultured cells; and thymidylate chromophore destruction by water free radicals
MATHEMATICS CONNECTION aims at providing a forum topromote the development of Mathematics Education in Ghana. Articles that seekto enhance the teaching and/or learning of mathematics at all levels of theeducational system are welcome.
Algorithm for cellular reprogramming.
Ronquist, Scott; Patterson, Geoff; Muir, Lindsey A; Lindsly, Stephen; Chen, Haiming; Brown, Markus; Wicha, Max S; Bloch, Anthony; Brockett, Roger; Rajapakse, Indika
2017-11-07
The day we understand the time evolution of subcellular events at a level of detail comparable to physical systems governed by Newton's laws of motion seems far away. Even so, quantitative approaches to cellular dynamics add to our understanding of cell biology. With data-guided frameworks we can develop better predictions about, and methods for, control over specific biological processes and system-wide cell behavior. Here we describe an approach for optimizing the use of transcription factors (TFs) in cellular reprogramming, based on a device commonly used in optimal control. We construct an approximate model for the natural evolution of a cell-cycle-synchronized population of human fibroblasts, based on data obtained by sampling the expression of 22,083 genes at several time points during the cell cycle. To arrive at a model of moderate complexity, we cluster gene expression based on division of the genome into topologically associating domains (TADs) and then model the dynamics of TAD expression levels. Based on this dynamical model and additional data, such as known TF binding sites and activity, we develop a methodology for identifying the top TF candidates for a specific cellular reprogramming task. Our data-guided methodology identifies a number of TFs previously validated for reprogramming and/or natural differentiation and predicts some potentially useful combinations of TFs. Our findings highlight the immense potential of dynamical models, mathematics, and data-guided methodologies for improving strategies for control over biological processes. Copyright © 2017 the Author(s). Published by PNAS.
Global properties of cellular automata
Jen, E.
1986-01-01
Cellular automata are discrete mathematical systems that generate diverse, often complicated, behavior using simple deterministic rules. Analysis of the local structure of these rules makes possible a description of the global properties of the associated automata. A class of cellular automata that generate infinitely many aperoidic temporal sequences is defined,a s is the set of rules for which inverses exist. Necessary and sufficient conditions are derived characterizing the classes of ''nearest-neighbor'' rules for which arbitrary finite initial conditions (i) evolve to a homogeneous state; (ii) generate at least one constant temporal sequence
Mathematical Footprints Discovering Mathematics Everywhere
Pappas, Theoni
1999-01-01
MATHEMATICAL FOOTPRINTS takes a creative look at the role mathematics has played since prehistoric times, and will play in the future, and uncovers mathematics where you least expect to find it from its many uses in medicine, the sciences, and its appearance in art to its patterns in nature and its central role in the development of computers. Pappas presents mathematical ideas in a readable non-threatening manner. MATHEMATICAL FOOTPRINTS is another gem by the creator of THE MATHEMATICS CALENDAR and author of THE JOY OF MATHEMATICS. "Pappas's books have been gold mines of mathematical ent
Anon.
1982-01-01
Testing the applicability of mathematical models with carefully designed experiments is a powerful tool in the investigations of the effects of ionizing radiation on cells. The modeling and cellular studies complement each other, for modeling provides guidance for designing critical experiments which must provide definitive results, while the experiments themselves provide new input to the model. Based on previous experimental results the model for the accumulation of damage in Chlamydomonas reinhardi has been extended to include various multiple two-event combinations. Split dose survival experiments have shown that models tested to date predict most but not all the observed behavior. Stationary-phase mammalian cells, required for tests of other aspects of the model, have been shown to be at different points in the cell cycle depending on how they were forced to stop proliferating. These cultures also demonstrate different capacities for repair of sublethal radiation damage
Leamy, Michael J.; Springer, Adam C.
In this research we report parallel implementation of a Cellular Automata-based simulation tool for computing elastodynamic response on complex, two-dimensional domains. Elastodynamic simulation using Cellular Automata (CA) has recently been presented as an alternative, inherently object-oriented technique for accurately and efficiently computing linear and nonlinear wave propagation in arbitrarily-shaped geometries. The local, autonomous nature of the method should lead to straight-forward and efficient parallelization. We address this notion on symmetric multiprocessor (SMP) hardware using a Java-based object-oriented CA code implementing triangular state machines (i.e., automata) and the MPI bindings written in Java (MPJ Express). We use MPJ Express to reconfigure our existing CA code to distribute a domain's automata to cores present on a dual quad-core shared-memory system (eight total processors). We note that this message passing parallelization strategy is directly applicable to computer clustered computing, which will be the focus of follow-on research. Results on the shared memory platform indicate nearly-ideal, linear speed-up. We conclude that the CA-based elastodynamic simulator is easily configured to run in parallel, and yields excellent speed-up on SMP hardware.
Andreescu, Titu; Tetiva, Marian
2017-01-01
Building bridges between classical results and contemporary nonstandard problems, Mathematical Bridges embraces important topics in analysis and algebra from a problem-solving perspective. Blending old and new techniques, tactics and strategies used in solving challenging mathematical problems, readers will discover numerous genuine mathematical gems throughout that will heighten their appreciation of the inherent beauty of mathematics. Most of the problems are original to the authors and are intertwined in a well-motivated exposition driven by representative examples. The book is structured to assist the reader in formulating and proving conjectures, as well as devising solutions to important mathematical problems by making connections between various concepts and ideas from different areas of mathematics. Instructors and educators teaching problem-solving courses or organizing mathematics clubs, as well as motivated mathematics students from high school juniors to college seniors, will find Mathematical Bri...
Humm, J.L.; Chin, L.M.
1989-01-01
Radiation dose is a useful predictive parameter for describing radiation toxicity in conventional radiotherapy. Traditionally, in vitro radiation biology dose-effect relations are expressed in the form of cell survival curves, a semilog plot of cell survival versus dose. However, the characteristic linear or linear quadratic survival curve shape, for high- and low-LET radiations respectively, is only strictly valid when the radiation dose is uniform across the entire target population. With an external beam of 60 Co gamma rays or x-rays, a uniform field may be readily achievable. When radionuclides are incorporated into a cell milieu, several new problems emerge which can result in a departure from uniformity in energy deposition throughout a cell population. This nonuniformity can have very important consequences for the shape of the survival curve. Cases in which perturbations of source uniformity may arise include: 1. Elemental sources may equilibrate in the cell medium with partition coefficients between the extracellular, cytosol, and nuclear compartments. The effect of preferential cell internalization or binding to cell membrane of some radionuclides can increase or decrease the slope of the survival curve. 2. Radionuclides bound to antibodies, hormones, metabolite precursors, etc., may result in a source localization pattern characteristic of the carrier agent, i.e., the sources may bind to cell surface receptors or antigens, be internalized, bind to secreted antigen concentrated around a fraction of the cell population, or become directly incorporated into the cell DNA. We propose to relate the distribution of energy deposition in cell nuclei to biological correlates of cellular inactivation. The probability of each cell's survival is weighted by its individual radiation burden, and the summation of these probabilities for the cell population can be used to predict the number or fraction of cell survivors
... this page: //medlineplus.gov/ency/article/001534.htm Mathematics disorder To use the sharing features on this page, please enable JavaScript. Mathematics disorder is a condition in which a child's ...
Trinajstić, Nenad; Gutman, Ivan
2002-01-01
A brief description is given of the historical development of mathematics and chemistry. A path leading to the meeting of these two sciences is described. An attempt is made to define mathematical chemistry, and journals containing the term mathematical chemistry in their titles are noted. In conclusion, the statement is made that although chemistry is an experimental science aimed at preparing new compounds and materials, mathematics is very useful in chemistry, among other things, to produc...
Kilpatrick, Jeremy
2014-01-01
This paper addresses the contested way that ethnomathematics has sometimes been received by mathematicians and others and what that disagreement might suggest about issues in mathematics education; namely, (a) the relation of ethnomathematics to academic mathematics; (b) recent efforts to reform secondary school mathematics so that it prepares…
Blomhøj, Morten
2004-01-01
Developing competences for setting up, analysing and criticising mathematical models are normally seen as relevant only from and above upper secondary level. The general belief among teachers is that modelling activities presuppose conceptual understanding of the mathematics involved. Mathematical...... roots for the construction of important mathematical concepts. In addition competences for setting up, analysing and criticising modelling processes and the possible use of models is a formative aim in this own right for mathematics teaching in general education. The paper presents a theoretical...... modelling, however, can be seen as a practice of teaching that place the relation between real life and mathematics into the centre of teaching and learning mathematics, and this is relevant at all levels. Modelling activities may motivate the learning process and help the learner to establish cognitive...
Sørensen, John Aasted
2011-01-01
The objectives of Discrete Mathematics (IDISM2) are: The introduction of the mathematics needed for analysis, design and verification of discrete systems, including the application within programming languages for computer systems. Having passed the IDISM2 course, the student will be able...... to accomplish the following: -Understand and apply formal representations in discrete mathematics. -Understand and apply formal representations in problems within discrete mathematics. -Understand methods for solving problems in discrete mathematics. -Apply methods for solving problems in discrete mathematics......; construct a finite state machine for a given application. Apply these concepts to new problems. The teaching in Discrete Mathematics is a combination of sessions with lectures and students solving problems, either manually or by using Matlab. Furthermore a selection of projects must be solved and handed...
Mathematical Modeling and Pure Mathematics
Usiskin, Zalman
2015-01-01
Common situations, like planning air travel, can become grist for mathematical modeling and can promote the mathematical ideas of variables, formulas, algebraic expressions, functions, and statistics. The purpose of this article is to illustrate how the mathematical modeling that is present in everyday situations can be naturally embedded in…
Stöltzner, Michael
Answering to the double-faced influence of string theory on mathematical practice and rigour, the mathematical physicists Arthur Jaffe and Frank Quinn have contemplated the idea that there exists a `theoretical' mathematics (alongside `theoretical' physics) whose basic structures and results still require independent corroboration by mathematical proof. In this paper, I shall take the Jaffe-Quinn debate mainly as a problem of mathematical ontology and analyse it against the backdrop of two philosophical views that are appreciative towards informal mathematical development and conjectural results: Lakatos's methodology of proofs and refutations and John von Neumann's opportunistic reading of Hilbert's axiomatic method. The comparison of both approaches shows that mitigating Lakatos's falsificationism makes his insights about mathematical quasi-ontology more relevant to 20th century mathematics in which new structures are introduced by axiomatisation and not necessarily motivated by informal ancestors. The final section discusses the consequences of string theorists' claim to finality for the theory's mathematical make-up. I argue that ontological reductionism as advocated by particle physicists and the quest for mathematically deeper axioms do not necessarily lead to identical results.
Cellular Automata Rules and Linear Numbers
Nayak, Birendra Kumar; Sahoo, Sudhakar; Biswal, Sagarika
2012-01-01
In this paper, linear Cellular Automta (CA) rules are recursively generated using a binary tree rooted at "0". Some mathematical results on linear as well as non-linear CA rules are derived. Integers associated with linear CA rules are defined as linear numbers and the properties of these linear numbers are studied.
Designing cellular manufacturing system under risk conditions ...
This paper develops a mathematical modeling to design a cellular manufacturing system. In addition some of the total or portion of the demand of the part types can be subcontracted.. In order to designing the optimal CMS, we needs to detrmined a plan to produce and subcontract parts at a minimum cost and to mitigate the ...
Aigner, Martin; Spain, Philip G
2010-01-01
Mathematics is all around us. Often we do not realize it, though. Mathematics Everywhere is a collection of presentations on the role of mathematics in everyday life, through science, technology, and culture. The common theme is the unique position of mathematics as the art of pure thought and at the same time as a universally applicable science. The authors are renowned mathematicians; their presentations cover a wide range of topics. From compact discs to the stock exchange, from computer tomography to traffic routing, from electronic money to climate change, they make the "math inside" unde
Jothi, A Lenin
2009-01-01
Financial services, particularly banking and insurance services is the prominent sector for the development of a nation. After the liberalisation of financial sector in India, the scope of getting career opportunities has been widened. It is heartening to note that various universities in India have introduced professional courses on banking and insurance. A new field of applied mathematics has come into prominence under the name of Financial Mathematics. Financial mathematics has attained much importance in the recent years because of the role played by mathematical concepts in decision - m
Pappas, Theoni
1997-01-01
In this highly readable volume of vignettes of mathematical scandals and gossip, Theoni Pappas assembles 29 fascinating stories of intrigue and the bizarre ? in short, the human background of the history of mathematics. Might a haberdasher have changed Einstein's life? Why was the first woman mathematician murdered? How come there's no Nobel Prize in mathematics?Mathematics is principally about numbers, equations, and solutions, all of them precise and timeless. But, behind this arcane matter lies the sometimes sordid world of real people, whose rivalries and deceptions
Stroud, K A
2013-01-01
A groundbreaking and comprehensive reference that's been a bestseller since it first debuted in 1970, the new seventh edition of Engineering Mathematics has been thoroughly revised and expanded. Providing a broad mathematical survey, this innovative volume covers a full range of topics from the very basic to the advanced. Whether you're an engineer looking for a useful on-the-job reference or want to improve your mathematical skills, or you are a student who needs an in-depth self-study guide, Engineering Mathematics is sure to come in handy time and time again.
Universal map for cellular automata
García-Morales, V.
2012-01-01
A universal map is derived for all deterministic 1D cellular automata (CAs) containing no freely adjustable parameters and valid for any alphabet size and any neighborhood range (including non-symmetrical neighborhoods). The map can be extended to an arbitrary number of dimensions and topologies and to arbitrary order in time. Specific CA maps for the famous Conway's Game of Life and Wolfram's 256 elementary CAs are given. An induction method for CAs, based in the universal map, allows mathematical expressions for the orbits of a wide variety of elementary CAs to be systematically derived. -- Highlights: ► A universal map is derived for all deterministic 1D cellular automata (CA). ► The map is generalized to 2D for Von Neumann, Moore and hexagonal neighborhoods. ► A map for all Wolfram's 256 elementary CAs is derived. ► A map for Conway's “Game of Life” is obtained.
Game of Life Cellular Automata
Adamatzky, Andrew
2010-01-01
In the late 1960s, British mathematician John Conway invented a virtual mathematical machine that operates on a two-dimensional array of square cell. Each cell takes two states, live and dead. The cells' states are updated simultaneously and in discrete time. A dead cell comes to life if it has exactly three live neighbours. A live cell remains alive if two or three of its neighbours are alive, otherwise the cell dies. Conway's Game of Life became the most programmed solitary game and the most known cellular automaton. The book brings together results of forty years of study into computational
Kleene, Stephen Cole
1967-01-01
Undergraduate students with no prior instruction in mathematical logic will benefit from this multi-part text. Part I offers an elementary but thorough overview of mathematical logic of 1st order. Part II introduces some of the newer ideas and the more profound results of logical research in the 20th century. 1967 edition.
Huckstep, Peter
2002-01-01
Contends teachers must resist the temptation to suggest that, while children can create stories and melodies, they cannot create mathematics. Quotes mathematician G. H. Hardy: "A mathematician, like a painter or poet, is a 'maker' of patterns." Considers mathematics should be able to stand up for itself. (BT)
Batchelder, William H
2010-09-01
Mathematical psychology is a sub-field of psychology that started in the 1950s and has continued to grow as an important contributor to formal psychological theory, especially in the cognitive areas of psychology such as learning, memory, classification, choice response time, decision making, attention, and problem solving. In addition, there are several scientific sub-areas that were originated by mathematical psychologists such as the foundations of measurement, stochastic memory models, and psychologically motivated reformulations of expected utility theory. Mathematical psychology does not include all uses of mathematics and statistics in psychology, and indeed there is a long history of such uses especially in the areas of perception and psychometrics. What is most unique about mathematical psychology is its approach to theory construction. While accepting the behaviorist dictum that the data in psychology must be observable and replicable, mathematical models are specified in terms of unobservable formal constructs that can predict detailed aspects of data across multiple experimental and natural settings. By now almost all the substantive areas of cognitive and experimental psychology have formal mathematical models and theories, and many of these are due to researchers that identify with mathematical psychology. Copyright © 2010 John Wiley & Sons, Ltd. For further resources related to this article, please visit the WIREs website. Copyright © 2010 John Wiley & Sons, Ltd.
Kodaira, Kunihiko
1996-01-01
This is the translation from the Japanese textbook for the grade 11 course, "General Mathematics". It is part of the easier of the three elective courses in mathematics offered at this level and is taken by about 40% of students. The book covers basic notions of probability and statistics, vectors, exponential, logarithmic, and trigonometric functions, and an introduction to differentiation and integration.
Sørensen, John Aasted
2011-01-01
; construct a finite state machine for a given application. Apply these concepts to new problems. The teaching in Discrete Mathematics is a combination of sessions with lectures and students solving problems, either manually or by using Matlab. Furthermore a selection of projects must be solved and handed...... to accomplish the following: -Understand and apply formal representations in discrete mathematics. -Understand and apply formal representations in problems within discrete mathematics. -Understand methods for solving problems in discrete mathematics. -Apply methods for solving problems in discrete mathematics...... to new problems. Relations and functions: Define a product set; define and apply equivalence relations; construct and apply functions. Apply these concepts to new problems. Natural numbers and induction: Define the natural numbers; apply the principle of induction to verify a selection of properties...
Murray, James D
1993-01-01
The book is a textbook (with many exercises) giving an in-depth account of the practical use of mathematical modelling in the biomedical sciences. The mathematical level required is generally not high and the emphasis is on what is required to solve the real biological problem. The subject matter is drawn, e.g. from population biology, reaction kinetics, biological oscillators and switches, Belousov-Zhabotinskii reaction, reaction-diffusion theory, biological wave phenomena, central pattern generators, neural models, spread of epidemics, mechanochemical theory of biological pattern formation and importance in evolution. Most of the models are based on real biological problems and the predictions and explanations offered as a direct result of mathematical analysis of the models are important aspects of the book. The aim is to provide a thorough training in practical mathematical biology and to show how exciting and novel mathematical challenges arise from a genuine interdisciplinary involvement with the biosci...
Parshall, Karen Hunger
2002-01-01
Although today's mathematical research community takes its international character very much for granted, this "global nature" is relatively recent, having evolved over a period of roughly 150 years-from the beginning of the nineteenth century to the middle of the twentieth century. During this time, the practice of mathematics changed from being centered on a collection of disparate national communities to being characterized by an international group of scholars for whom the goal of mathematical research and cooperation transcended national boundaries. Yet, the development of an international community was far from smooth and involved obstacles such as war, political upheaval, and national rivalries. Until now, this evolution has been largely overlooked by historians and mathematicians alike. This book addresses the issue by bringing together essays by twenty experts in the history of mathematics who have investigated the genesis of today's international mathematical community. This includes not only develo...
Sead Rešić
2015-09-01
Full Text Available It is very difficult to motivate students when it comes to a school subject like Mathematics. Teachers spend a lot of time trying to find something that will arouse interest in students. It is particularly difficult to find materials that are motivating enough for students that they eagerly wait for the next lesson. One of the solutions may be found in Vedic Mathematics. Traditional methods of teaching Mathematics create fear of this otherwise interesting subject in the majority of students. Fear increases failure. Often the traditional, conventional mathematical methods consist of very long lessons which are difficult to understand. Vedic Mathematics is an ancient system that is very flexible and encourages the development of intuition and innovation. It is a mental calculating tool that does not require a calculator because the calculator is embedded in each of us. Starting from the above problems of fear and failure in Mathematics, the goal of this paper is to do research with the control and the experimental group and to compare the test results. Two tests should be done for each of the groups. The control group would do the tests in the conventional way. The experimental group would do the first test in a conventional manner and then be subjected to different treatment, that is to say, be taught on the basis of Vedic Mathematics. After that, the second group would do the second test according to the principles of Vedic Mathematics. Expectations are that after short lectures on Vedic mathematics results of the experimental group would improve and that students will show greater interest in Mathematics.
Bird, John
2014-01-01
A practical introduction to the core mathematics required for engineering study and practiceNow in its seventh edition, Engineering Mathematics is an established textbook that has helped thousands of students to succeed in their exams.John Bird's approach is based on worked examples and interactive problems. This makes it ideal for students from a wide range of academic backgrounds as the student can work through the material at their own pace. Mathematical theories are explained in a straightforward manner, being supported by practical engineering examples and applications in order to ensure
Geroch, Robert
1985-01-01
Mathematical Physics is an introduction to such basic mathematical structures as groups, vector spaces, topological spaces, measure spaces, and Hilbert space. Geroch uses category theory to emphasize both the interrelationships among different structures and the unity of mathematics. Perhaps the most valuable feature of the book is the illuminating intuitive discussion of the ""whys"" of proofs and of axioms and definitions. This book, based on Geroch's University of Chicago course, will be especially helpful to those working in theoretical physics, including such areas as relativity, particle
Logan, J David
2013-01-01
Praise for the Third Edition"Future mathematicians, scientists, and engineers should find the book to be an excellent introductory text for coursework or self-study as well as worth its shelf space for reference." -MAA Reviews Applied Mathematics, Fourth Edition is a thoroughly updated and revised edition on the applications of modeling and analyzing natural, social, and technological processes. The book covers a wide range of key topics in mathematical methods and modeling and highlights the connections between mathematics and the applied and nat
Handley, Bill
2012-01-01
This new, revised edition of the bestselling Speed Mathematics features new chapters on memorising numbers and general information, calculating statistics and compound interest, square roots, logarithms and easy trig calculations. Written so anyone can understand, this book teaches simple strategies that will enable readers to make lightning-quick calculations. People who excel at mathematics use better strategies than the rest of us; they are not necessarily more intelligent. With Speed Mathematics you'll discover methods to make maths easy and fun. This book is perfect for stud
Virdi, Surinder; Virdi, Narinder Kaur
2014-01-01
Construction Mathematics is an introductory level mathematics text, written specifically for students of construction and related disciplines. Learn by tackling exercises based on real-life construction maths. Examples include: costing calculations, labour costs, cost of materials and setting out of building components. Suitable for beginners and easy to follow throughout. Learn the essential basic theory along with the practical necessities. The second edition of this popular textbook is fully updated to match new curricula, and expanded to include even more learning exercises. End of chapter exercises cover a range of theoretical as well as practical problems commonly found in construction practice, and three detailed assignments based on practical tasks give students the opportunity to apply all the knowledge they have gained. Construction Mathematics addresses all the mathematical requirements of Level 2 construction NVQs from City & Guilds/CITB and Edexcel courses, including the BTEC First Diploma in...
2016-01-01
This book provides a thorough introduction to the challenge of applying mathematics in real-world scenarios. Modelling tasks rarely involve well-defined categories, and they often require multidisciplinary input from mathematics, physics, computer sciences, or engineering. In keeping with this spirit of modelling, the book includes a wealth of cross-references between the chapters and frequently points to the real-world context. The book combines classical approaches to modelling with novel areas such as soft computing methods, inverse problems, and model uncertainty. Attention is also paid to the interaction between models, data and the use of mathematical software. The reader will find a broad selection of theoretical tools for practicing industrial mathematics, including the analysis of continuum models, probabilistic and discrete phenomena, and asymptotic and sensitivity analysis.
Hougardy, Stefan
2016-01-01
Algorithms play an increasingly important role in nearly all fields of mathematics. This book allows readers to develop basic mathematical abilities, in particular those concerning the design and analysis of algorithms as well as their implementation. It presents not only fundamental algorithms like the sieve of Eratosthenes, the Euclidean algorithm, sorting algorithms, algorithms on graphs, and Gaussian elimination, but also discusses elementary data structures, basic graph theory, and numerical questions. In addition, it provides an introduction to programming and demonstrates in detail how to implement algorithms in C++. This textbook is suitable for students who are new to the subject and covers a basic mathematical lecture course, complementing traditional courses on analysis and linear algebra. Both authors have given this "Algorithmic Mathematics" course at the University of Bonn several times in recent years.
Sneyd, James
2009-01-01
There has been a long history of interaction between mathematics and physiology. This book looks in detail at a wide selection of mathematical models in physiology, showing how physiological problems can be formulated and studied mathematically, and how such models give rise to interesting and challenging mathematical questions. With its coverage of many recent models it gives an overview of the field, while many older models are also discussed, to put the modern work in context. In this second edition the coverage of basic principles has been expanded to include such topics as stochastic differential equations, Markov models and Gibbs free energy, and the selection of models has also been expanded to include some of the basic models of fluid transport, respiration/perfusion, blood diseases, molecular motors, smooth muscle, neuroendrocine cells, the baroreceptor loop, turboglomerular oscillations, blood clotting and the retina. Owing to this extensive coverage, the second edition is published in two volumes. ...
Eck, Christof; Knabner, Peter
2017-01-01
Mathematical models are the decisive tool to explain and predict phenomena in the natural and engineering sciences. With this book readers will learn to derive mathematical models which help to understand real world phenomena. At the same time a wealth of important examples for the abstract concepts treated in the curriculum of mathematics degrees are given. An essential feature of this book is that mathematical structures are used as an ordering principle and not the fields of application. Methods from linear algebra, analysis and the theory of ordinary and partial differential equations are thoroughly introduced and applied in the modeling process. Examples of applications in the fields electrical networks, chemical reaction dynamics, population dynamics, fluid dynamics, elasticity theory and crystal growth are treated comprehensively.
Pestman, Wiebe R
2009-01-01
This textbook provides a broad and solid introduction to mathematical statistics, including the classical subjects hypothesis testing, normal regression analysis, and normal analysis of variance. In addition, non-parametric statistics and vectorial statistics are considered, as well as applications of stochastic analysis in modern statistics, e.g., Kolmogorov-Smirnov testing, smoothing techniques, robustness and density estimation. For students with some elementary mathematical background. With many exercises. Prerequisites from measure theory and linear algebra are presented.
Berman, Elizabeth
1979-01-01
Mathematics Revealed focuses on the principles, processes, operations, and exercises in mathematics.The book first offers information on whole numbers, fractions, and decimals and percents. Discussions focus on measuring length, percent, decimals, numbers as products, addition and subtraction of fractions, mixed numbers and ratios, division of fractions, addition, subtraction, multiplication, and division. The text then examines positive and negative numbers and powers and computation. Topics include division and averages, multiplication, ratios, and measurements, scientific notation and estim
Sørensen, John Aasted
2010-01-01
The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Spring 2010 Ectent: 5 ects Class size: 18......The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Spring 2010 Ectent: 5 ects Class size: 18...
Sørensen, John Aasted
2010-01-01
The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Autumn 2010 Ectent: 5 ects Class size: 15......The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Autumn 2010 Ectent: 5 ects Class size: 15...
Glimm, J.
2009-10-14
Progress for the past decade or so has been extraordinary. The solution of Fermat's Last Theorem [11] and of the Poincare Conjecture [1] have resolved two of the most outstanding challenges to mathematics. For both cases, deep and advanced theories and whole subfields of mathematics came into play and were developed further as part of the solutions. And still the future is wide open. Six of the original seven problems from the Clay Foundation challenge remain open, the 23 DARPA challenge problems are open. Entire new branches of mathematics have been developed, including financial mathematics and the connection between geometry and string theory, proposed to solve the problems of quantized gravity. New solutions of the Einstein equations, inspired by shock wave theory, suggest a cosmology model which fits accelerating expansion of the universe possibly eliminating assumptions of 'dark matter'. Intellectual challenges and opportunities for mathematics are greater than ever. The role of mathematics in society continues to grow; with this growth comes new opportunities and some growing pains; each will be analyzed here. We see a broadening of the intellectual and professional opportunities and responsibilities for mathematicians. These trends are also occuring across all of science. The response can be at the level of the professional societies, which can work to deepen their interactions, not only within the mathematical sciences, but also with other scientific societies. At a deeper level, the choices to be made will come from individual mathematicians. Here, of course, the individual choices will be varied, and we argue for respect and support for this diversity of responses. In such a manner, we hope to preserve the best of the present while welcoming the best of the new.
Capacity on wireless quantum cellular communication system
Zhou, Xiang-Zhen; Yu, Xu-Tao; Zhang, Zai-Chen
2018-03-01
Quantum technology is making excellent prospects in future communication networks. Entanglement generation and purification are two major components in quantum networks. Combining these two techniques with classical cellular mobile communication, we proposed a novel wireless quantum cellular(WQC) communication system which is possible to realize commercial mobile quantum communication. In this paper, the architecture and network topology of WQC communication system are discussed, the mathematical model of WQC system is extracted and the serving capacity, indicating the ability to serve customers, is defined and calculated under certain circumstances.
Aggelis, G.
1995-10-01
Full Text Available Microbial oil production from fatty materials of animal or plant origin has been an object of research and industrial interest for many years. During the process of microbial growth/accumulation of fat reserves, the dominating phenomena that define the composition of endocellular fat are, first, the specific process of incorporation of substrate fatty acids into the microbial cell and, second, the endocellular changes of fatty acids defined by the enzymic capabilities of the microorganism. The fatty acids will either be degraded for growth needs or act as substrate of endocellular biotransformation processes, leading to concentration changes and production of "new" fatty acids which did not previously exist in the substrate.
The purpose of the present work is to study the endocellular lipids of Mucor circinelloidesCBS 172-27 grown on sunflower oil. The mathematical model, described in part I, was applied in order to investigate the following:
a. Microorganism specificity in the incorporation of substrate fatty acids.
b. Microorganism specificity in the degradation of fatty acids present in the reserve fat.
c. Possibilities of endocellular biotransformations during the microbial growth.
In conclusion, this work is aimed at developing a quantitative expression of parameters defining the lipid composition of fat reserves. The proposed mathematical model can be used not only for selection of microbial strains having specific enzymic potential but also for substrate selection.
La producción de aceites microbianos a partir de materiales grasos de origen animal o vegetal ha sido objeto de investigación e interés industrial durante muchos años. En el proceso de crecimiento microbiano/acumulación de reservas grasas, los fenómenos dominantes que definen la composición de grasa endocelular son, primero, el proceso específico de incorporación de ácidos grasos como sustratos en la célula microbiana
Jost, Jürgen
2015-01-01
The main intention of this book is to describe and develop the conceptual, structural and abstract thinking of mathematics. Specific mathematical structures are used to illustrate the conceptual approach; providing a deeper insight into mutual relationships and abstract common features. These ideas are carefully motivated, explained and illustrated by examples so that many of the more technical proofs can be omitted. The book can therefore be used: · simply as an overview of the panorama of mathematical structures and the relations between them, to be supplemented by more detailed texts whenever you want to acquire a working knowledge of some structure · by itself as a first introduction to abstract mathematics · together with existing textbooks, to put their results into a more general perspective · to gain a new and hopefully deeper perspective after having studied such textbooks Mathematical Concepts has a broader scope and is less detaile...
Rubin, Andrew
2014-01-01
This book presents concise descriptions and analysis of the classical and modern models used in mathematical biophysics. The authors ask the question "what new information can be provided by the models that cannot be obtained directly from experimental data?" Actively developing fields such as regulatory mechanisms in cells and subcellular systems and electron transport and energy transport in membranes are addressed together with more classical topics such as metabolic processes, nerve conduction and heart activity, chemical kinetics, population dynamics, and photosynthesis. The main approach is to describe biological processes using different mathematical approaches necessary to reveal characteristic features and properties of simulated systems. With the emergence of powerful mathematics software packages such as MAPLE, Mathematica, Mathcad, and MatLab, these methodologies are now accessible to a wide audience. Provides succinct but authoritative coverage of a broad array of biophysical topics and models Wr...
Hiriart-Urruty, Jean-Baptiste
This book contains a collection of exercises (called “tapas”) at undergraduate level, mainly from the fields of real analysis, calculus, matrices, convexity, and optimization. Most of the problems presented here are non-standard and some require broad knowledge of different mathematical subjects in order to be solved. The author provides some hints and (partial) answers and also puts these carefully chosen exercises into context, presents information on their origins, and comments on possible extensions. With stars marking the levels of difficulty, these tapas show or prove something interesting, challenge the reader to solve and learn, and may have surprising results. This first volume of Mathematical Tapas will appeal to mathematicians, motivated undergraduate students from science-based areas, and those generally interested in mathematics.
Vivaldi, Franco
2014-01-01
This book teaches the art of writing mathematics, an essential -and difficult- skill for any mathematics student. The book begins with an informal introduction on basic writing principles and a review of the essential dictionary for mathematics. Writing techniques are developed gradually, from the small to the large: words, phrases, sentences, paragraphs, to end with short compositions. These may represent the introduction of a concept, the abstract of a presentation or the proof of a theorem. Along the way the student will learn how to establish a coherent notation, mix words and symbols effectively, write neat formulae, and structure a definition. Some elements of logic and all common methods of proofs are featured, including various versions of induction and existence proofs. The book concludes with advice on specific aspects of thesis writing (choosing of a title, composing an abstract, compiling a bibliography) illustrated by large number of real-life examples. Many exercises are included; over 150...
Cahill, Kevin
2013-01-01
Unique in its clarity, examples and range, Physical Mathematics explains as simply as possible the mathematics that graduate students and professional physicists need in their courses and research. The author illustrates the mathematics with numerous physical examples drawn from contemporary research. In addition to basic subjects such as linear algebra, Fourier analysis, complex variables, differential equations and Bessel functions, this textbook covers topics such as the singular-value decomposition, Lie algebras, the tensors and forms of general relativity, the central limit theorem and Kolmogorov test of statistics, the Monte Carlo methods of experimental and theoretical physics, the renormalization group of condensed-matter physics and the functional derivatives and Feynman path integrals of quantum field theory.
Bartocci, Claudio; Guerraggio, Angelo; Lucchetti, Roberto; Williams, Kim
2011-01-01
Steps forward in mathematics often reverberate in other scientific disciplines, and give rise to innovative conceptual developments or find surprising technological applications. This volume brings to the forefront some of the proponents of the mathematics of the twentieth century, who have put at our disposal new and powerful instruments for investigating the reality around us. The portraits present people who have impressive charisma and wide-ranging cultural interests, who are passionate about defending the importance of their own research, are sensitive to beauty, and attentive to the soci
Quotable Quotes in Mathematics
Lo, Bruce W. N.
1983-01-01
As a way to dispel negative feelings toward mathematics, a variety of quotations are given. They are categorized by: what mathematics is, mathematicians, mathematics and other disciplines, different areas of mathematics, mathematics and humor, applications of mathematics, and pure versus applied mathematics. (MNS)
Wainwright, J.
1990-01-01
The workshop on mathematical cosmology was devoted to four topics of current interest. This report contains a brief discussion of the historical background of each topic and a concise summary of the content of each talk. The topics were; the observational cosmology program, the cosmological perturbation program, isotropic singularities, and the evolution of Bianchi cosmologies. (author)
Weaver, Nik
2001-01-01
With a unique approach and presenting an array of new and intriguing topics, Mathematical Quantization offers a survey of operator algebras and related structures from the point of view that these objects are quantizations of classical mathematical structures. This approach makes possible, with minimal mathematical detail, a unified treatment of a variety of topics.Detailed here for the first time, the fundamental idea of mathematical quantization is that sets are replaced by Hilbert spaces. Building on this idea, and most importantly on the fact that scalar-valued functions on a set correspond to operators on a Hilbert space, one can determine quantum analogs of a variety of classical structures. In particular, because topologies and measure classes on a set can be treated in terms of scalar-valued functions, we can transfer these constructions to the quantum realm, giving rise to C*- and von Neumann algebras.In the first half of the book, the author quickly builds the operator algebra setting. He uses this ...
Fujita, Shinsaku
2015-01-01
Chirality and stereogenicity are closely related concepts and their differentiation and description is still a challenge in chemoinformatics. A new stereoisogram approach, developed by the author, is introduced in this book, providing a theoretical framework for mathematical aspects of modern stereochemistry. The discussion covers point-groups and permutation symmetry and exemplifies the concepts using organic molecules and inorganic complexes.
The language of mathematics telling mathematical tales
Barton, Bill
2008-01-01
Everyday mathematical ideas are expressed differently in different languages. This book probes those differences and explores their implications for mathematics education, arguing for alternatives to how we teach and learn mathematics.
Wireless Cellular Mobile Communications
Zalud, V.
2002-01-01
In this article is briefly reviewed the history of wireless cellular mobile communications, examined the progress in current second generation (2G) cellular standards and discussed their migration to the third generation (3G). The European 2G cellular standard GSM and its evolution phases GPRS and EDGE are described somewhat in detail. The third generation standard UMTS taking up on GSM/GPRS core network and equipped with a new advanced access network on the basis of code division multiple ac...
Cellular-automata method for phase unwrapping
Ghiglia, D.C.; Mastin, G.A.; Romero, L.A.
1987-01-01
Research into two-dimensional phase unwrapping has uncovered interesting and troublesome inconsistencies that cause path-dependent results. Cellular automata, which are simple, discrete mathematical systems, offered promise of computation in nondirectional, parallel manner. A cellular automaton was discovered that can unwrap consistent phase data in n dimensions in a path-independent manner and can automatically accommodate noise-induced (pointlike) inconsistencies and arbitrary boundary conditions (region partitioning). For data with regional (nonpointlike) inconsistencies, no phase-unwrapping algorithm will converge, including the cellular-automata approach. However, the automata method permits more simple visualization of the regional inconsistencies. Examples of its behavior on one- and two-dimensional data are presented
Biomechanics of cellular solids.
Gibson, Lorna J
2005-03-01
Materials with a cellular structure are widespread in nature and include wood, cork, plant parenchyma and trabecular bone. Natural cellular materials are often mechanically efficient: the honeycomb-like microstructure of wood, for instance, gives it an exceptionally high performance index for resisting bending and buckling. Here we review the mechanics of a wide range of natural cellular materials and examine their role in lightweight natural sandwich structures (e.g. iris leaves) and natural tubular structures (e.g. plant stems or animal quills). We also describe two examples of engineered biomaterials with a cellular structure, designed to replace or regenerate tissue in the body.
Sierpinska, Anna
1994-01-01
The concept of understanding in mathematics with regard to mathematics education is considered in this volume, the main problem for mathematics teachers being how to facilitate their students'' understanding of the mathematics being taught.
Driessche, Pauline; Wu, Jianhong
2008-01-01
Based on lecture notes of two summer schools with a mixed audience from mathematical sciences, epidemiology and public health, this volume offers a comprehensive introduction to basic ideas and techniques in modeling infectious diseases, for the comparison of strategies to plan for an anticipated epidemic or pandemic, and to deal with a disease outbreak in real time. It covers detailed case studies for diseases including pandemic influenza, West Nile virus, and childhood diseases. Models for other diseases including Severe Acute Respiratory Syndrome, fox rabies, and sexually transmitted infections are included as applications. Its chapters are coherent and complementary independent units. In order to accustom students to look at the current literature and to experience different perspectives, no attempt has been made to achieve united writing style or unified notation. Notes on some mathematical background (calculus, matrix algebra, differential equations, and probability) have been prepared and may be downlo...
Nedelec, J.C.
1988-01-01
The 1988 progress report of the Applied Mathematics center (Polytechnic School, France), is presented. The research fields of the Center are the scientific calculus, the probabilities and statistics and the video image synthesis. The research topics developed are: the analysis of numerical methods, the mathematical analysis of the physics and mechanics fundamental models, the numerical solution of complex models related to the industrial problems, the stochastic calculus and the brownian movement, the stochastic partial differential equations, the identification of the adaptive filtering parameters, the discrete element systems, statistics, the stochastic control and the development, the image synthesis techniques for education and research programs. The published papers, the congress communications and the thesis are listed [fr
Dilemma in Teaching Mathematics
Md Kamaruddin, Nafisah Kamariah; Md Amin, Zulkarnain
2012-01-01
The challenge in mathematics education is finding the best way to teach mathematics. When students learn the reasoning and proving in mathematics, they will be proficient in mathematics. Students must know mathematics before they can apply it. Symbolism and logic is the key to both the learning of mathematics and its effective application to…
Linearizable cellular automata
Nobe, Atsushi; Yura, Fumitaka
2007-01-01
The initial value problem for a class of reversible elementary cellular automata with periodic boundaries is reduced to an initial-boundary value problem for a class of linear systems on a finite commutative ring Z 2 . Moreover, a family of such linearizable cellular automata is given
Teaching Mathematical Modeling in Mathematics Education
Saxena, Ritu; Shrivastava, Keerty; Bhardwaj, Ramakant
2016-01-01
Mathematics is not only a subject but it is also a language consisting of many different symbols and relations. Taught as a compulsory subject up the 10th class, students are then able to choose whether or not to study mathematics as a main subject. The present paper discusses mathematical modeling in mathematics education. The article provides…
Doing Mathematics with Purpose: Mathematical Text Types
Dostal, Hannah M.; Robinson, Richard
2018-01-01
Mathematical literacy includes learning to read and write different types of mathematical texts as part of purposeful mathematical meaning making. Thus in this article, we describe how learning to read and write mathematical texts (proof text, algorithmic text, algebraic/symbolic text, and visual text) supports the development of students'…
Teachers' Mathematics as Mathematics-at-Work
Bednarz, Nadine; Proulx, Jérôme
2017-01-01
Through recognising mathematics teachers as professionals who use mathematics in their workplace, this article traces a parallel between the mathematics enacted by teachers in their practice and the mathematics used in workplaces found in studies of professionals (e.g. nurses, engineers, bankers). This parallel is developed through the five…
DURIP: Mitigating Attacks on Mobile Devices and Critical Cellular Infrastructure
2016-03-03
services. From mobile banking and location- based services to the real-time streaming of music and video, cellular networks now provide advanced voice...time streaming of music and video, cellular networks now provide advanced voice and data services to more than 4.5 billion subscribers around the world...will receive scholarships or fellowships for further studies in science , mathematics, engineering or technology fields: Student Metrics This section
PASSENGER TRAFFIC MOVEMENT MODELLING BY THE CELLULAR-AUTOMAT APPROACH
T. Mikhaylovskaya
2009-01-01
Full Text Available The mathematical model of passenger traffic movement developed on the basis of the cellular-automat approach is considered. The program realization of the cellular-automat model of pedastrians streams movement in pedestrian subways at presence of obstacles, at subway structure narrowing is presented. The optimum distances between the obstacles and the angle of subway structure narrowing providing pedastrians stream safe movement and traffic congestion occurance are determined.
Peculiarities of hardware implementation of generalized cellular tetra automaton
Аноприенко, Александр Яковлевич; Федоров, Евгений Евгениевич; Иваница, Сергей Васильевич; Альрабаба, Хамза
2015-01-01
Cellular automata are widely used in many fields of knowledge for the study of variety of complex real processes: computer engineering and computer science, cryptography, mathematics, physics, chemistry, ecology, biology, medicine, epidemiology, geology, architecture, sociology, theory of neural networks. Thus, cellular automata (CA) and tetra automata are gaining relevance taking into account the hardware and software solutions.Also it is marked a trend towards an increase in the number of p...
Dragalin, A G
1988-01-01
This monograph is intended to present the most important methods of proof theory in intuitionistic logic, assuming the reader to have mastered an introductory course in mathematical logic. The book starts with purely syntactical methods based on Gentzen's cut-elimination theorem, followed by intuitionistic arithmetic where Kleene's realizability method plays a central role. The author then studies algebraic models and completeness theorems for them. After giving a survey on the principles of intuitionistic analysis, the last part of the book presents the cut-elimination theorem in intuitionistic simple theory of types with an extensionality rule.
Heterogeneous cellular networks
Hu, Rose Qingyang
2013-01-01
A timely publication providing coverage of radio resource management, mobility management and standardization in heterogeneous cellular networks The topic of heterogeneous cellular networks has gained momentum in industry and the research community, attracting the attention of standardization bodies such as 3GPP LTE and IEEE 802.16j, whose objectives are looking into increasing the capacity and coverage of the cellular networks. This book focuses on recent progresses, covering the related topics including scenarios of heterogeneous network deployment, interference management i
Cellular decomposition in vikalloys
Belyatskaya, I.S.; Vintajkin, E.Z.; Georgieva, I.Ya.; Golikov, V.A.; Udovenko, V.A.
1981-01-01
Austenite decomposition in Fe-Co-V and Fe-Co-V-Ni alloys at 475-600 deg C is investigated. The cellular decomposition in ternary alloys results in the formation of bcc (ordered) and fcc structures, and in quaternary alloys - bcc (ordered) and 12R structures. The cellular 12R structure results from the emergence of stacking faults in the fcc lattice with irregular spacing in four layers. The cellular decomposition results in a high-dispersion structure and magnetic properties approaching the level of well-known vikalloys [ru
Romanofsky, Robert R.
2010-01-01
The cellular reflectarray antenna is intended to replace conventional parabolic reflectors that must be physically aligned with a particular satellite in geostationary orbit. These arrays are designed for specified geographical locations, defined by latitude and longitude, each called a "cell." A particular cell occupies nominally 1,500 square miles (3,885 sq. km), but this varies according to latitude and longitude. The cellular reflectarray antenna designed for a particular cell is simply positioned to align with magnetic North, and the antenna surface is level (parallel to the ground). A given cellular reflectarray antenna will not operate in any other cell.
Mogensen, Arne; Georgiev, Vladimir; Ulovec, Andreas
To encourage many more young people to appreciate the real nature and spirit of mathematics and possibly to be enrolled in mathematics study it is important to involve them in doing mathematics (not just learning about mathematics). This goal could be achieved if mathematics teachers are prepared...... to identify and work with mathematically gifted students (without loosing the rest). The book offers chapters on gifted students, mathematical competences and other issues....
Magnetohydrodynamics cellular automata
Hatori, Tadatsugu.
1990-02-01
There has been a renewal of interest in cellular automata, partly because they give an architecture for a special purpose computer with parallel processing optimized to solve a particular problem. The lattice gas cellular automata are briefly surveyed, which are recently developed to solve partial differential equations such as hydrodynamics or magnetohydrodynamics. A new model is given in the present paper to implement the magnetic Lorentz force in a more deterministic and local procedure than the previous one. (author)
Epigenetics and Cellular Metabolism
Wenyi Xu; Fengzhong Wang; Zhongsheng Yu; Fengjiao Xin
2016-01-01
Living eukaryotic systems evolve delicate cellular mechanisms for responding to various environmental signals. Among them, epigenetic machinery (DNA methylation, histone modifications, microRNAs, etc.) is the hub in transducing external stimuli into transcriptional response. Emerging evidence reveals the concept that epigenetic signatures are essential for the proper maintenance of cellular metabolism. On the other hand, the metabolite, a main environmental input, can also influence the proce...
Magnetohydrodynamic cellular automata
Hatori, Tadatsugu [National Inst. for Fusion Science, Nagoya (Japan)
1990-03-01
There has been a renewal of interest in cellular automata, partly because they give an architecture for a special purpose computer with parallel processing optimized to solve a particular problem. The lattice gas cellular automata are briefly surveyed, which are recently developed to solve partial differential equations such as hydrodynamics or magnetohydrodynamics. A new model is given in the present paper to implement the magnetic Lorentz force in a more deterministic and local procedure than the previous one. (author).
Magnetohydrodynamic cellular automata
Hatori, Tadatsugu
1990-01-01
There has been a renewal of interest in cellular automata, partly because they give an architecture for a special purpose computer with parallel processing optimized to solve a particular problem. The lattice gas cellular automata are briefly surveyed, which are recently developed to solve partial differential equations such as hydrodynamics or magnetohydrodynamics. A new model is given in the present paper to implement the magnetic Lorentz force in a more deterministic and local procedure than the previous one. (author)
Michel Modo
2005-07-01
Full Text Available Cellular MR imaging is a young field that aims to visualize targeted cells in living organisms. In order to provide a different signal intensity of the targeted cell, they are either labeled with MR contrast agents in vivo or prelabeled in vitro. Either (ultrasmall superparamagnetic iron oxide [(USPIO] particles or (polymeric paramagnetic chelates can be used for this purpose. For in vivo cellular labeling, Gd3+- and Mn2+- chelates have mainly been used for targeted hepatobiliary imaging, and (USPIO-based cellular imaging has been focused on imaging of macrophage activity. Several of these magneto-pharmaceuticals have been FDA-approved or are in late-phase clinical trials. As for prelabeling of cells in vitro, a challenge has been to induce a sufficient uptake of contrast agents into nonphagocytic cells, without affecting normal cellular function. It appears that this issue has now largely been resolved, leading to an active research on monitoring the cellular biodistribution in vivo following transplantation or transfusion of these cells, including cell migration and trafficking. New applications of cellular MR imaging will be directed, for instance, towards our understanding of hematopoietic (immune cell trafficking and of novel guided (stem cell-based therapies aimed to be translated to the clinic in the future.
Mathematics, the Computer, and the Impact on Mathematics Education.
Tooke, D. James
2001-01-01
Discusses the connection between mathematics and the computer; mathematics curriculum; mathematics instruction, including teachers learning to use computers; and the impact of the computer on learning mathematics. (LRW)
Path searching in switching networks using cellular algorithm
Koczy, L T; Langer, J; Legendi, T
1981-01-01
After a survey of the important statements in the paper A Mathematical Model of Path Searching in General Type Switching Networks (see IBID., vol.25, no.1, p.31-43, 1981) the authors consider the possible implementation for cellular automata of the algorithm introduced there. The cellular field used consists of 5 neighbour 8 state cells. Running times required by a traditional serial processor and by the cellular field, respectively, are compared. By parallel processing this running time can be reduced. 5 references.
Authenticity of Mathematical Modeling
Tran, Dung; Dougherty, Barbara J.
2014-01-01
Some students leave high school never quite sure of the relevancy of the mathematics they have learned. They fail to see links between school mathematics and the mathematics of everyday life that requires thoughtful decision making and often complex problem solving. Is it possible to bridge the gap between school mathematics and the mathematics in…
Automata-Based Verification of Temporal Properties on Running Programs
Giannakopoulou, Dimitra; Havelund, Klaus; Lan, Sonie (Technical Monitor)
2001-01-01
This paper presents an approach to checking a running program against its Linear Temporal Logic (LTL) specifications. LTL is a widely used logic for expressing properties of programs viewed as sets of executions. Our approach consists of translating LTL formulae to finite-state automata, which are used as observers of the program behavior. The translation algorithm we propose modifies standard LTL to Buchi automata conversion techniques to generate automata that check finite program traces. The algorithm has been implemented in a tool, which has been integrated with the generic JPaX framework for runtime analysis of Java programs.
An Automata Based Intrusion Detection Method for Internet of Things
Yulong Fu
2017-01-01
Full Text Available Internet of Things (IoT transforms network communication to Machine-to-Machine (M2M basis and provides open access and new services to citizens and companies. It extends the border of Internet and will be developed as one part of the future 5G networks. However, as the resources of IoT’s front devices are constrained, many security mechanisms are hard to be implemented to protect the IoT networks. Intrusion detection system (IDS is an efficient technique that can be used to detect the attackers when cryptography is broken, and it can be used to enforce the security of IoT networks. In this article, we analyzed the intrusion detection requirements of IoT networks and then proposed a uniform intrusion detection method for the vast heterogeneous IoT networks based on an automata model. The proposed method can detect and report the possible IoT attacks with three types: jam-attack, false-attack, and reply-attack automatically. We also design an experiment to verify the proposed IDS method and examine the attack of RADIUS application.
Some applications and prospects of cellular automata in traffic problems
Goldengorin, Boris; Makarenko, Alexander; Smelyanec, Natalia; Yacoubi, SE; Chopard, B; Bandini, S
2006-01-01
In this paper we deal with mathematical modeling of participants' movement based on cellular automata (CA). We describe some improvements of CA models of pedestrian motion taking into account the real geometrical constraints induced by a specific restricted space. Also some presumable optimization
Simulating Complex Systems by Cellular Automata
Kroc, Jiri; Hoekstra, Alfons G
2010-01-01
Deeply rooted in fundamental research in Mathematics and Computer Science, Cellular Automata (CA) are recognized as an intuitive modeling paradigm for Complex Systems. Already very basic CA, with extremely simple micro dynamics such as the Game of Life, show an almost endless display of complex emergent behavior. Conversely, CA can also be designed to produce a desired emergent behavior, using either theoretical methodologies or evolutionary techniques. Meanwhile, beyond the original realm of applications - Physics, Computer Science, and Mathematics – CA have also become work horses in very different disciplines such as epidemiology, immunology, sociology, and finance. In this context of fast and impressive progress, spurred further by the enormous attraction these topics have on students, this book emerges as a welcome overview of the field for its practitioners, as well as a good starting point for detailed study on the graduate and post-graduate level. The book contains three parts, two major parts on th...
Teaching mathematics using excel
Bonello, Mary Rose; Camilleri, Silvana
2004-01-01
'Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students' learning.' (Principles and Standards for School Mathematics-NCTM April 2000)
Figures of thought mathematics and mathematical texts
Reed, David
2003-01-01
Examines the ways in which mathematical works can be read as texts, examines their textual strategiesand demonstrates that such readings provide a rich source of philosophical debate regarding mathematics.
Designing beauty the art of cellular automata
Martínez, Genaro
2016-01-01
This fascinating, colourful book offers in-depth insights and first-hand working experiences in the production of art works, using simple computational models with rich morphological behaviour, at the edge of mathematics, computer science, physics and biology. It organically combines ground breaking scientific discoveries in the theory of computation and complex systems with artistic representations of the research results. In this appealing book mathematicians, computer scientists, physicists, and engineers brought together marvelous and esoteric patterns generated by cellular automata, which are arrays of simple machines with complex behavior. Configurations produced by cellular automata uncover mechanics of dynamic patterns formation, their propagation and interaction in natural systems: heart pacemaker, bacterial membrane proteins, chemical rectors, water permeation in soil, compressed gas, cell division, population dynamics, reaction-diffusion media and self-organisation. The book inspires artists to tak...
A cellular automata model of bone formation.
Van Scoy, Gabrielle K; George, Estee L; Opoku Asantewaa, Flora; Kerns, Lucy; Saunders, Marnie M; Prieto-Langarica, Alicia
2017-04-01
Bone remodeling is an elegantly orchestrated process by which osteocytes, osteoblasts and osteoclasts function as a syncytium to maintain or modify bone. On the microscopic level, bone consists of cells that create, destroy and monitor the bone matrix. These cells interact in a coordinated manner to maintain a tightly regulated homeostasis. It is this regulation that is responsible for the observed increase in bone gain in the dominant arm of a tennis player and the observed increase in bone loss associated with spaceflight and osteoporosis. The manner in which these cells interact to bring about a change in bone quality and quantity has yet to be fully elucidated. But efforts to understand the multicellular complexity can ultimately lead to eradication of metabolic bone diseases such as osteoporosis and improved implant longevity. Experimentally validated mathematical models that simulate functional activity and offer eventual predictive capabilities offer tremendous potential in understanding multicellular bone remodeling. Here we undertake the initial challenge to develop a mathematical model of bone formation validated with in vitro data obtained from osteoblastic bone cells induced to mineralize and quantified at 26 days of culture. A cellular automata model was constructed to simulate the in vitro characterization. Permutation tests were performed to compare the distribution of the mineralization in the cultures and the distribution of the mineralization in the mathematical models. The results of the permutation test show the distribution of mineralization from the characterization and mathematical model come from the same probability distribution, therefore validating the cellular automata model. Copyright © 2017 Elsevier Inc. All rights reserved.
Cellularized Cellular Solids via Freeze-Casting.
Christoph, Sarah; Kwiatoszynski, Julien; Coradin, Thibaud; Fernandes, Francisco M
2016-02-01
The elaboration of metabolically active cell-containing materials is a decisive step toward the successful application of cell based technologies. The present work unveils a new process allowing to simultaneously encapsulate living cells and shaping cell-containing materials into solid-state macroporous foams with precisely controlled morphology. Our strategy is based on freeze casting, an ice templating materials processing technique that has recently emerged for the structuration of colloids into macroporous materials. Our results indicate that it is possible to combine the precise structuration of the materials with cellular metabolic activity for the model organism Saccharomyces cerevisiae. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Mathematical Modelling Approach in Mathematics Education
Arseven, Ayla
2015-01-01
The topic of models and modeling has come to be important for science and mathematics education in recent years. The topic of "Modeling" topic is especially important for examinations such as PISA which is conducted at an international level and measures a student's success in mathematics. Mathematical modeling can be defined as using…
Discrete Mathematics and the Secondary Mathematics Curriculum.
Dossey, John
Discrete mathematics, the mathematics of decision making for finite settings, is a topic of great interest in mathematics education at all levels. Attention is being focused on resolving the diversity of opinion concerning the exact nature of the subject, what content the curriculum should contain, who should study that material, and how that…
Introducing philosophy of mathematics
Friend, Michele
2014-01-01
What is mathematics about? Does the subject-matter of mathematics exist independently of the mind or are they mental constructions? How do we know mathematics? Is mathematical knowledge logical knowledge? And how is mathematics applied to the material world? In this introduction to the philosophy of mathematics, Michele Friend examines these and other ontological and epistemological problems raised by the content and practice of mathematics. Aimed at a readership with limited proficiency in mathematics but with some experience of formal logic it seeks to strike a balance between conceptual acc
Epigenetics and Cellular Metabolism
Wenyi Xu
2016-01-01
Full Text Available Living eukaryotic systems evolve delicate cellular mechanisms for responding to various environmental signals. Among them, epigenetic machinery (DNA methylation, histone modifications, microRNAs, etc. is the hub in transducing external stimuli into transcriptional response. Emerging evidence reveals the concept that epigenetic signatures are essential for the proper maintenance of cellular metabolism. On the other hand, the metabolite, a main environmental input, can also influence the processing of epigenetic memory. Here, we summarize the recent research progress in the epigenetic regulation of cellular metabolism and discuss how the dysfunction of epigenetic machineries influences the development of metabolic disorders such as diabetes and obesity; then, we focus on discussing the notion that manipulating metabolites, the fuel of cell metabolism, can function as a strategy for interfering epigenetic machinery and its related disease progression as well.
Wireless Cellular Mobile Communications
V. Zalud
2002-12-01
Full Text Available In this article is briefly reviewed the history of wireless cellularmobile communications, examined the progress in current secondgeneration (2G cellular standards and discussed their migration to thethird generation (3G. The European 2G cellular standard GSM and itsevolution phases GPRS and EDGE are described somewhat in detail. Thethird generation standard UMTS taking up on GSM/GPRS core network andequipped with a new advanced access network on the basis of codedivision multiple access (CDMA is investigated too. A sketch of theperspective of mobile communication beyond 3G concludes this article.
Mathematical methods in biology and neurobiology
Jost, Jürgen
2014-01-01
Mathematical models can be used to meet many of the challenges and opportunities offered by modern biology. The description of biological phenomena requires a range of mathematical theories. This is the case particularly for the emerging field of systems biology. Mathematical Methods in Biology and Neurobiology introduces and develops these mathematical structures and methods in a systematic manner. It studies: • discrete structures and graph theory • stochastic processes • dynamical systems and partial differential equations • optimization and the calculus of variations. The biological applications range from molecular to evolutionary and ecological levels, for example: • cellular reaction kinetics and gene regulation • biological pattern formation and chemotaxis • the biophysics and dynamics of neurons • the coding of information in neuronal systems • phylogenetic tree reconstruction • branching processes and population genetics • optimal resource allocation • sexual recombi...
Mathematics related anxiety: Mathematics bogeyman or not?
Videnović Marina
2011-01-01
Full Text Available Data of the PISA 2003 survey indicate high levels of mathematics anxiety of students in Serbia. More than half of our students worry whether they will have difficulties in mathematics class or whether they will earn poor marks. Aims of this study therefore are: examining relationship between math anxiety and achievement at mathematics literacy scale; establishing possible predictors of math anxiety and identification of students' groups in relations to their relationship towards mathematics as a subject. Mathematics anxiety is statistically negatively correlated with school achievement and achievement at mathematics literacy scale. Socio-demographic factors, motivational and cognitive aspects related to learning mathematics, perception of school and classroom climate explain 40% variance of mathematics anxiety. Based on students' relationship towards mathematics they cam be divided into three groups; while dimensions that apart them are uninterested-interested in mathematics and presence-absence of anxiety. The group displaying anxiety scores lowest among the three. Applying qualitative analysis students' and teachers' attitudes on specific issues related to teaching and learning mathematics was examined.
Radiolabelled cellular blood elements
Sinzinger, H.
1990-01-01
This book reports on radiolabelled cellular blood elements, covering new advances made during the past several years, in particular the use of Tc-99 as a tracer for blood elements. Coverage extends to several radiolabelled monoclonal antibodies that are specific for blood components and may label blood elements in vivo
Building synthetic cellular organization
Polka, Jessica K.; Silver, Pamela A.
2013-01-01
The elaborate spatial organization of cells enhances, restricts, and regulates protein–protein interactions. However, the biological significance of this organization has been difficult to study without ways of directly perturbing it. We highlight synthetic biology tools for engineering novel cellular organization, describing how they have been, and can be, used to advance cell biology.
Claman, Henry N.
1973-01-01
Discusses the nature of the immune response and traces many of the discoveries that have led to the present state of knowledge in immunology. The new cellular immunology is directing its efforts toward improving health by proper manipulation of the immune mechanisms of the body. (JR)
Electromagnetic cellular interactions.
Cifra, Michal; Fields, Jeremy Z; Farhadi, Ashkan
2011-05-01
Chemical and electrical interaction within and between cells is well established. Just the opposite is true about cellular interactions via other physical fields. The most probable candidate for an other form of cellular interaction is the electromagnetic field. We review theories and experiments on how cells can generate and detect electromagnetic fields generally, and if the cell-generated electromagnetic field can mediate cellular interactions. We do not limit here ourselves to specialized electro-excitable cells. Rather we describe physical processes that are of a more general nature and probably present in almost every type of living cell. The spectral range included is broad; from kHz to the visible part of the electromagnetic spectrum. We show that there is a rather large number of theories on how cells can generate and detect electromagnetic fields and discuss experimental evidence on electromagnetic cellular interactions in the modern scientific literature. Although small, it is continuously accumulating. Copyright © 2010 Elsevier Ltd. All rights reserved.
Genetic Dominance & Cellular Processes
Seager, Robert D.
2014-01-01
In learning genetics, many students misunderstand and misinterpret what "dominance" means. Understanding is easier if students realize that dominance is not a mechanism, but rather a consequence of underlying cellular processes. For example, metabolic pathways are often little affected by changes in enzyme concentration. This means that…
Predictive model to describe water migration in cellular solid foods during storage
Voogt, J.A.; Hirte, A.; Meinders, M.B.J.
2011-01-01
BACKGROUND: Water migration in cellular solid foods during storage causes loss of crispness. To improve crispness retention, physical understanding of this process is needed. Mathematical models are suitable tools to gain this physical knowledge. RESULTS: Water migration in cellular solid foods
Predictive model to describe water migration in cellular solid foods during storage
Voogt, J.A.; Hirte, A.; Meinders, M.B.J.
2011-01-01
Background: Water migration in cellular solid foods during storage causes loss of crispness. To improve crispness retention, physical understanding of this process is needed. Mathematical models are suitable tools to gain this physical knowledge. Results: Water migration in cellular solid foods
Umphrey, Jan
2011-01-01
The National Council of Teachers of Mathematics (NCTM) is a voice and advocate for mathematics educators, working to ensure that all students receive equitable mathematics learning of the highest quality. To help teachers and school leaders understand the Common Core State Standards for Mathematics (CCSSM) and to point out how the CCSSM can be…
Hansen, Vagn Lundsgaard
2005-01-01
A brief tour through the history of mathematics from the very beginnings to modern times, with an emphasis on the main contributions and important periods of mathematics in various civilizations.......A brief tour through the history of mathematics from the very beginnings to modern times, with an emphasis on the main contributions and important periods of mathematics in various civilizations....
Hansen, Vagn Lundsgaard
A brief tour through the history of mathematics from the very beginnings to modern times, with an emphasis on the main contributions and important periods of mathematics in various civilizations.......A brief tour through the history of mathematics from the very beginnings to modern times, with an emphasis on the main contributions and important periods of mathematics in various civilizations....
Mumcu, Hayal Yavuz
2016-01-01
The purpose of this theoretical study is to explore the relationships between the concepts of using mathematics in the daily life, mathematical applications, mathematical modelling, and mathematical literacy. As these concepts are generally taken as independent concepts in the related literature, they are confused with each other and it becomes…
Optimizing Cellular Networks Enabled with Renewal Energy via Strategic Learning.
Sohn, Insoo; Liu, Huaping; Ansari, Nirwan
2015-01-01
An important issue in the cellular industry is the rising energy cost and carbon footprint due to the rapid expansion of the cellular infrastructure. Greening cellular networks has thus attracted attention. Among the promising green cellular network techniques, the renewable energy-powered cellular network has drawn increasing attention as a critical element towards reducing carbon emissions due to massive energy consumption in the base stations deployed in cellular networks. Game theory is a branch of mathematics that is used to evaluate and optimize systems with multiple players with conflicting objectives and has been successfully used to solve various problems in cellular networks. In this paper, we model the green energy utilization and power consumption optimization problem of a green cellular network as a pilot power selection strategic game and propose a novel distributed algorithm based on a strategic learning method. The simulation results indicate that the proposed algorithm achieves correlated equilibrium of the pilot power selection game, resulting in optimum green energy utilization and power consumption reduction.
Mathematical Modelling Plant Signalling Networks
Muraro, D.
2013-01-01
During the last two decades, molecular genetic studies and the completion of the sequencing of the Arabidopsis thaliana genome have increased knowledge of hormonal regulation in plants. These signal transduction pathways act in concert through gene regulatory and signalling networks whose main components have begun to be elucidated. Our understanding of the resulting cellular processes is hindered by the complex, and sometimes counter-intuitive, dynamics of the networks, which may be interconnected through feedback controls and cross-regulation. Mathematical modelling provides a valuable tool to investigate such dynamics and to perform in silico experiments that may not be easily carried out in a laboratory. In this article, we firstly review general methods for modelling gene and signalling networks and their application in plants. We then describe specific models of hormonal perception and cross-talk in plants. This mathematical analysis of sub-cellular molecular mechanisms paves the way for more comprehensive modelling studies of hormonal transport and signalling in a multi-scale setting. © EDP Sciences, 2013.
Molecular and Cellular Signaling
Beckerman, Martin
2005-01-01
A small number of signaling pathways, no more than a dozen or so, form a control layer that is responsible for all signaling in and between cells of the human body. The signaling proteins belonging to the control layer determine what kinds of cells are made during development and how they function during adult life. Malfunctions in the proteins belonging to the control layer are responsible for a host of human diseases ranging from neurological disorders to cancers. Most drugs target components in the control layer, and difficulties in drug design are intimately related to the architecture of the control layer. Molecular and Cellular Signaling provides an introduction to molecular and cellular signaling in biological systems with an emphasis on the underlying physical principles. The text is aimed at upper-level undergraduates, graduate students and individuals in medicine and pharmacology interested in broadening their understanding of how cells regulate and coordinate their core activities and how diseases ...
Quasthoff, U.
1985-07-01
Cellular automata by definition consist of a finite or infinite number of cells, say of unit length, with each cell having the same transition function. These cells are usually considered as the smallest elements and so the space filled with these cells becomes discrete. Nevertheless, large pictures created by such cellular automata look very fractal. So we try to replace each cell by a couple of smaller cells, which have the same transition functions as the large ones. There are automata where this replacement does not destroy the macroscopic structure. In these cases this nesting process can be iterated. The paper contains large classes of automata with the above properties. In the case of one dimensional automata with two states and next neighbour interaction and a nesting function of the same type a complete classification is given. (author)
Predictability in cellular automata.
Agapie, Alexandru; Andreica, Anca; Chira, Camelia; Giuclea, Marius
2014-01-01
Modelled as finite homogeneous Markov chains, probabilistic cellular automata with local transition probabilities in (0, 1) always posses a stationary distribution. This result alone is not very helpful when it comes to predicting the final configuration; one needs also a formula connecting the probabilities in the stationary distribution to some intrinsic feature of the lattice configuration. Previous results on the asynchronous cellular automata have showed that such feature really exists. It is the number of zero-one borders within the automaton's binary configuration. An exponential formula in the number of zero-one borders has been proved for the 1-D, 2-D and 3-D asynchronous automata with neighborhood three, five and seven, respectively. We perform computer experiments on a synchronous cellular automaton to check whether the empirical distribution obeys also that theoretical formula. The numerical results indicate a perfect fit for neighbourhood three and five, which opens the way for a rigorous proof of the formula in this new, synchronous case.
Probabilistic cellular automata.
Agapie, Alexandru; Andreica, Anca; Giuclea, Marius
2014-09-01
Cellular automata are binary lattices used for modeling complex dynamical systems. The automaton evolves iteratively from one configuration to another, using some local transition rule based on the number of ones in the neighborhood of each cell. With respect to the number of cells allowed to change per iteration, we speak of either synchronous or asynchronous automata. If randomness is involved to some degree in the transition rule, we speak of probabilistic automata, otherwise they are called deterministic. With either type of cellular automaton we are dealing with, the main theoretical challenge stays the same: starting from an arbitrary initial configuration, predict (with highest accuracy) the end configuration. If the automaton is deterministic, the outcome simplifies to one of two configurations, all zeros or all ones. If the automaton is probabilistic, the whole process is modeled by a finite homogeneous Markov chain, and the outcome is the corresponding stationary distribution. Based on our previous results for the asynchronous case-connecting the probability of a configuration in the stationary distribution to its number of zero-one borders-the article offers both numerical and theoretical insight into the long-term behavior of synchronous cellular automata.
Wavefront cellular learning automata.
Moradabadi, Behnaz; Meybodi, Mohammad Reza
2018-02-01
This paper proposes a new cellular learning automaton, called a wavefront cellular learning automaton (WCLA). The proposed WCLA has a set of learning automata mapped to a connected structure and uses this structure to propagate the state changes of the learning automata over the structure using waves. In the WCLA, after one learning automaton chooses its action, if this chosen action is different from the previous action, it can send a wave to its neighbors and activate them. Each neighbor receiving the wave is activated and must choose a new action. This structure for the WCLA is necessary in many dynamic areas such as social networks, computer networks, grid computing, and web mining. In this paper, we introduce the WCLA framework as an optimization tool with diffusion capability, study its behavior over time using ordinary differential equation solutions, and present its accuracy using expediency analysis. To show the superiority of the proposed WCLA, we compare the proposed method with some other types of cellular learning automata using two benchmark problems.
Wavefront cellular learning automata
Moradabadi, Behnaz; Meybodi, Mohammad Reza
2018-02-01
This paper proposes a new cellular learning automaton, called a wavefront cellular learning automaton (WCLA). The proposed WCLA has a set of learning automata mapped to a connected structure and uses this structure to propagate the state changes of the learning automata over the structure using waves. In the WCLA, after one learning automaton chooses its action, if this chosen action is different from the previous action, it can send a wave to its neighbors and activate them. Each neighbor receiving the wave is activated and must choose a new action. This structure for the WCLA is necessary in many dynamic areas such as social networks, computer networks, grid computing, and web mining. In this paper, we introduce the WCLA framework as an optimization tool with diffusion capability, study its behavior over time using ordinary differential equation solutions, and present its accuracy using expediency analysis. To show the superiority of the proposed WCLA, we compare the proposed method with some other types of cellular learning automata using two benchmark problems.
Mathematics without boundaries surveys in pure mathematics
Pardalos, Panos
2014-01-01
The contributions in this volume have been written by eminent scientists from the international mathematical community and present significant advances in several theories, methods and problems of Mathematical Analysis, Discrete Mathematics, Geometry and their Applications. The chapters focus on both old and recent developments in Functional Analysis, Harmonic Analysis, Complex Analysis, Operator Theory, Combinatorics, Functional Equations, Differential Equations as well as a variety of Applications. The book also contains some review works, which could prove particularly useful for a broader audience of readers in Mathematical Sciences, and especially to graduate students looking for the latest information.
Environment Aware Cellular Networks
Ghazzai, Hakim
2015-02-01
The unprecedented rise of mobile user demand over the years have led to an enormous growth of the energy consumption of wireless networks as well as the greenhouse gas emissions which are estimated currently to be around 70 million tons per year. This significant growth of energy consumption impels network companies to pay huge bills which represent around half of their operating expenditures. Therefore, many service providers, including mobile operators, are looking for new and modern green solutions to help reduce their expenses as well as the level of their CO2 emissions. Base stations are the most power greedy element in cellular networks: they drain around 80% of the total network energy consumption even during low traffic periods. Thus, there is a growing need to develop more energy-efficient techniques to enhance the green performance of future 4G/5G cellular networks. Due to the problem of traffic load fluctuations in cellular networks during different periods of the day and between different areas (shopping or business districts and residential areas), the base station sleeping strategy has been one of the main popular research topics in green communications. In this presentation, we present several practical green techniques that provide significant gains for mobile operators. Indeed, combined with the base station sleeping strategy, these techniques achieve not only a minimization of the fossil fuel consumption but also an enhancement of mobile operator profits. We start with an optimized cell planning method that considers varying spatial and temporal user densities. We then use the optimal transport theory in order to define the cell boundaries such that the network total transmit power is reduced. Afterwards, we exploit the features of the modern electrical grid, the smart grid, as a new tool of power management for cellular networks and we optimize the energy procurement from multiple energy retailers characterized by different prices and pollutant
Cellular signaling identifiability analysis: a case study.
Roper, Ryan T; Pia Saccomani, Maria; Vicini, Paolo
2010-05-21
Two primary purposes for mathematical modeling in cell biology are (1) simulation for making predictions of experimental outcomes and (2) parameter estimation for drawing inferences from experimental data about unobserved aspects of biological systems. While the former purpose has become common in the biological sciences, the latter is less common, particularly when studying cellular and subcellular phenomena such as signaling-the focus of the current study. Data are difficult to obtain at this level. Therefore, even models of only modest complexity can contain parameters for which the available data are insufficient for estimation. In the present study, we use a set of published cellular signaling models to address issues related to global parameter identifiability. That is, we address the following question: assuming known time courses for some model variables, which parameters is it theoretically impossible to estimate, even with continuous, noise-free data? Following an introduction to this problem and its relevance, we perform a full identifiability analysis on a set of cellular signaling models using DAISY (Differential Algebra for the Identifiability of SYstems). We use our analysis to bring to light important issues related to parameter identifiability in ordinary differential equation (ODE) models. We contend that this is, as of yet, an under-appreciated issue in biological modeling and, more particularly, cell biology. Copyright (c) 2010 Elsevier Ltd. All rights reserved.
Pulsed feedback defers cellular differentiation.
Joe H Levine
2012-01-01
Full Text Available Environmental signals induce diverse cellular differentiation programs. In certain systems, cells defer differentiation for extended time periods after the signal appears, proliferating through multiple rounds of cell division before committing to a new fate. How can cells set a deferral time much longer than the cell cycle? Here we study Bacillus subtilis cells that respond to sudden nutrient limitation with multiple rounds of growth and division before differentiating into spores. A well-characterized genetic circuit controls the concentration and phosphorylation of the master regulator Spo0A, which rises to a critical concentration to initiate sporulation. However, it remains unclear how this circuit enables cells to defer sporulation for multiple cell cycles. Using quantitative time-lapse fluorescence microscopy of Spo0A dynamics in individual cells, we observed pulses of Spo0A phosphorylation at a characteristic cell cycle phase. Pulse amplitudes grew systematically and cell-autonomously over multiple cell cycles leading up to sporulation. This pulse growth required a key positive feedback loop involving the sporulation kinases, without which the deferral of sporulation became ultrasensitive to kinase expression. Thus, deferral is controlled by a pulsed positive feedback loop in which kinase expression is activated by pulses of Spo0A phosphorylation. This pulsed positive feedback architecture provides a more robust mechanism for setting deferral times than constitutive kinase expression. Finally, using mathematical modeling, we show how pulsing and time delays together enable "polyphasic" positive feedback, in which different parts of a feedback loop are active at different times. Polyphasic feedback can enable more accurate tuning of long deferral times. Together, these results suggest that Bacillus subtilis uses a pulsed positive feedback loop to implement a "timer" that operates over timescales much longer than a cell cycle.
Cosserat modeling of cellular solids
Onck, P.R.
Cellular solids inherit their macroscopic mechanical properties directly from the cellular microstructure. However, the characteristic material length scale is often not small compared to macroscopic dimensions, which limits the applicability of classical continuum-type constitutive models. Cosserat
Evaluation of Structural Cellular Glass
Adams, M. A.; Zwissler, J. G.
1984-01-01
Preliminary design information presented. First report discusses state of structural-cellular-glass programs as of June 1979. Second report gives further details of program to develop improved cellular glasses and to characterize properties of glasses and commercially available materials.
Schleicher, Dierk
2011-01-01
This "Invitation to Mathematics" consists of 14 contributions, many from the world's leading mathematicians, which introduce the readers to exciting aspects of current mathematical research. The contributions are as varied as the personalities of active mathematicians, but together they show mathematics as a rich and lively field of research. The contributions are written for interested students at the age of transition between high school and university who know high school mathematics and perhaps competition mathematics and who want to find out what current research mathematics is
Cellular communication through light.
Daniel Fels
Full Text Available Information transfer is a fundamental of life. A few studies have reported that cells use photons (from an endogenous source as information carriers. This study finds that cells can have an influence on other cells even when separated with a glass barrier, thereby disabling molecule diffusion through the cell-containing medium. As there is still very little known about the potential of photons for intercellular communication this study is designed to test for non-molecule-based triggering of two fundamental properties of life: cell division and energy uptake. The study was performed with a cellular organism, the ciliate Paramecium caudatum. Mutual exposure of cell populations occurred under conditions of darkness and separation with cuvettes (vials allowing photon but not molecule transfer. The cell populations were separated either with glass allowing photon transmission from 340 nm to longer waves, or quartz being transmittable from 150 nm, i.e. from UV-light to longer waves. Even through glass, the cells affected cell division and energy uptake in neighboring cell populations. Depending on the cuvette material and the number of cells involved, these effects were positive or negative. Also, while paired populations with lower growth rates grew uncorrelated, growth of the better growing populations was correlated. As there were significant differences when separating the populations with glass or quartz, it is suggested that the cell populations use two (or more frequencies for cellular information transfer, which influences at least energy uptake, cell division rate and growth correlation. Altogether the study strongly supports a cellular communication system, which is different from a molecule-receptor-based system and hints that photon-triggering is a fine tuning principle in cell chemistry.
Engineering Cellular Metabolism
Nielsen, Jens; Keasling, Jay
2016-01-01
Metabolic engineering is the science of rewiring the metabolism of cells to enhance production of native metabolites or to endow cells with the ability to produce new products. The potential applications of such efforts are wide ranging, including the generation of fuels, chemicals, foods, feeds...... of metabolic engineering and will discuss how new technologies can enable metabolic engineering to be scaled up to the industrial level, either by cutting off the lines of control for endogenous metabolism or by infiltrating the system with disruptive, heterologous pathways that overcome cellular regulation....
Cellular mechanics and motility
Hénon, Sylvie; Sykes, Cécile
2015-10-01
The term motility defines the movement of a living organism. One widely known example is the motility of sperm cells, or the one of flagellar bacteria. The propulsive element of such organisms is a cilium(or flagellum) that beats. Although cells in our tissues do not have a flagellum in general, they are still able to move, as we will discover in this chapter. In fact, in both cases of movement, with or without a flagellum, cell motility is due to a dynamic re-arrangement of polymers inside the cell. Let us first have a closer look at the propulsion mechanism in the case of a flagellum or a cilium, which is the best known, but also the simplest, and which will help us to define the hydrodynamic general conditions of cell movement. A flagellum is sustained by cellular polymers arranged in semi-flexible bundles and flagellar beating generates cell displacement. These polymers or filaments are part of the cellular skeleton, or "cytoskeleton", which is, in this case, external to the cellular main body of the organism. In fact, bacteria move in a hydrodynamic regime in which viscosity dominates over inertia. The system is thus in a hydrodynamic regime of low Reynolds number (Box 5.1), which is nearly exclusively the case in all cell movements. Bacteria and their propulsion mode by flagella beating are our unicellular ancestors 3.5 billion years ago. Since then, we have evolved to form pluricellular organisms. However, to keep the ability of displacement, to heal our wounds for example, our cells lost their flagellum, since it was not optimal in a dense cell environment: cells are too close to each other to leave enough space for the flagella to accomplish propulsion. The cytoskeleton thus developed inside the cell body to ensure cell shape changes and movement, and also mechanical strength within a tissue. The cytoskeleton of our cells, like the polymers or filaments that sustain the flagellum, is also composed of semi-flexible filaments arranged in bundles, and also in
Cellular automaton modeling of biological pattern formation characterization, examples, and analysis
Deutsch, Andreas
2017-01-01
This text explores the use of cellular automata in modeling pattern formation in biological systems. It describes several mathematical modeling approaches utilizing cellular automata that can be used to study the dynamics of interacting cell systems both in simulation and in practice. New in this edition are chapters covering cell migration, tissue development, and cancer dynamics, as well as updated references and new research topic suggestions that reflect the rapid development of the field. The book begins with an introduction to pattern-forming principles in biology and the various mathematical modeling techniques that can be used to analyze them. Cellular automaton models are then discussed in detail for different types of cellular processes and interactions, including random movement, cell migration, adhesive cell interaction, alignment and cellular swarming, growth processes, pigment cell pattern formation, tissue development, tumor growth and invasion, and Turing-type patterns and excitable media. In ...
Aberdein, Andrew
2014-01-01
This book presents a comprehensive investigation into the relationship between argumentation theory and the philosophy of mathematical practice. It offers large array of examples ranging from the history of mathematics to formal proof verification.
Mathematical knowledge in teaching
Rowland, Tim
2011-01-01
This book examines issues of considerable significance in addressing global aspirations to raise standards of teaching and learning in mathematics by developing approaches to characterizing, assessing and developing mathematical knowledge for teaching.
Developing My Mathematics Identity
Gonzalez, Lidia
2016-01-01
Assuming the role of storyteller, the author uses her experiences as a graduate student and beginning teacher to reflect critically on issues related to mathematics, mathematics education, gender, and diversity.
Journal of applied mathematics
2001-01-01
"[The] Journal of Applied Mathematics is a refereed journal devoted to the publication of original research papers and review articles in all areas of applied, computational, and industrial mathematics...
Semiotic Scaffolding in Mathematics
Johansen, Mikkel Willum; Misfeldt, Morten
2015-01-01
This paper investigates the notion of semiotic scaffolding in relation to mathematics by considering its influence on mathematical activities, and on the evolution of mathematics as a research field. We will do this by analyzing the role different representational forms play in mathematical...... cognition, and more broadly on mathematical activities. In the main part of the paper, we will present and analyze three different cases. For the first case, we investigate the semiotic scaffolding involved in pencil and paper multiplication. For the second case, we investigate how the development of new...... in both mathematical cognition and in the development of mathematics itself, but mathematical cognition cannot itself be reduced to the use of semiotic scaffolding....
Mathematics for the nonmathematician
Kline, Morris
1967-01-01
Erudite and entertaining overview follows development of mathematics from ancient Greeks to present. Topics include logic and mathematics, the fundamental concept, differential calculus, probability theory, much more. Exercises and problems.
Mathematical Modeling Using MATLAB
Phillips, Donovan
1998-01-01
.... Mathematical Modeling Using MA MATLAB acts as a companion resource to A First Course in Mathematical Modeling with the goal of guiding the reader to a fuller understanding of the modeling process...
Modern mathematics made simple
Murphy, Patrick
1982-01-01
Modern Mathematics: Made Simple presents topics in modern mathematics, from elementary mathematical logic and switching circuits to multibase arithmetic and finite systems. Sets and relations, vectors and matrices, tesselations, and linear programming are also discussed.Comprised of 12 chapters, this book begins with an introduction to sets and basic operations on sets, as well as solving problems with Venn diagrams. The discussion then turns to elementary mathematical logic, with emphasis on inductive and deductive reasoning; conjunctions and disjunctions; compound statements and conditional
Modern Versus Traditional Mathematics
Roberts, A. M.
1974-01-01
The effect of different secondary school mathematics syllabi on first-year performance in college-level mathematics was studied in an attempt to evaluate the syllabus change. Students with a modern mathematics background performed sigficantly better on most first-year units. A topic-by-topic analysis of results is included. (DT)
Darlington, Ellie
2014-01-01
This article describes part of a study which investigated the role of questions in students' approaches to learning mathematics at the secondary-tertiary interface, focussing on the enculturation of students at the University of Oxford. Use of the Mathematical Assessment Task Hierarchy taxonomy revealed A-level Mathematics and Further Mathematics…
Mathematics and quantum mechanics
Santander, M.
2000-01-01
Several episodes in the relation between Mathematics and Quantum Mechanics are discussed; and the emphasis is put in the existence of multiple and sometimes unexpected connections between ideas originating in Mathematics and in Quantum Physics. The question of the unresasonable effectiveness of Mathematics in Physics is also presented in the same light. (Author) 3 refs
Mathematics Teaching as Praxis
Grootenboer, Peter; Edwards-Groves, Christine
2014-01-01
In this paper we argue that mathematics teaching can be conceptualised as a form of praxis. Viewing mathematics teaching as praxis foregrounds the moral nature of teaching and the educational practices that are developed in response to the educational needs in particular sites. The case for praxis in mathematics education is then made by drawing…
Martin, Tami S.; Speer, William R.
2009-01-01
This article describes features, consistent messages, and new components of "Mathematics Teaching Today: Improving Practice, Improving Student Learning" (NCTM 2007), an updated edition of "Professional Standards for Teaching Mathematics" (NCTM 1991). The new book describes aspects of high-quality mathematics teaching; offers a model for observing,…
Empowering Mathematical Practices
Coomes, Jacqueline; Lee, Hyung Sook
2017-01-01
Mathematics teachers want to empower students as mathematical thinkers and doers (NCTM 2000). Specific ways of thinking and doing mathematics were described in the Process Standards (NCTM 2000); they were further characterized as habits of mind (Mark, Goldenberg, and Sword 2010); and more recently, they were detailed in the Common Core's Standards…
Learning Environments in Mathematics
Turner, Vanshelle E.
2017-01-01
Learning mathematics is problematic for most primary school age children because mathematics is rote and the memorization of steps rather than an approach to seeing relationships that builds inquiry and understanding. Therefore, the traditional "algorithmic" way of teaching mathematics has not fully prepared students to be critical…
Mathematics a minimal introduction
Buium, Alexandru
2013-01-01
Pre-Mathematical Logic Languages Metalanguage Syntax Semantics Tautologies Witnesses Theories Proofs Argot Strategies Examples Mathematics ZFC Sets Maps Relations Operations Integers Induction Rationals Combinatorics Sequences Reals Topology Imaginaries Residues p-adics Groups Orders Vectors Matrices Determinants Polynomials Congruences Lines Conics Cubics Limits Series Trigonometry Integrality Reciprocity Calculus Metamodels Categories Functors Objectives Mathematical Logic Models Incompleteness Bibliography Index
Mendick, Heather
2006-01-01
The study of mathematics, with other ''gendered'' subjects such as science and engineering, usually attracts more male than female pupils. This book explores this phenomenon, addressing the important question of why more boys than girls choose to study mathematics. It illuminates what studying mathematics means for both students and teachers.
Mathematics Connection: Editorial Policies
Focus and Scope. MATHEMATICS CONNECTION aims at providing a forum to promote the development of Mathematics Education in Ghana. Articles that seek to enhance the teaching and/or learning of mathematics at all levels of the educational system are welcome ...
Mathematics Connection: Contact
Principal Contact. Dr. Kofi Mereku Executive Editor Department of Mathematics Education, UCE Mathematical Association of Ghana, C/o Department of Mathematics Education University College of Education of Winneba P. O. Box 25, Winneba, Ghana Phone: +233244961318. Email: dkmereku@uew.edu.gh ...
Mathematical Discovery: Hadamard Resurected
Liljedahl, Peter
2004-01-01
In 1943 Jacques Hadamard gave a series of lectures on mathematical invention at the Ecole Libre des Hautes Etudes in New York City. These talks were subsequently published as The Psychology of Mathematical Invention in the Mathematical Field (Hadamard, 1945). In this article I present a study that mirrors the work of Hadamard. Results both…
Utah State Office of Education, 2011
2011-01-01
Utah has adopted more rigorous mathematics standards known as the Utah Mathematics Core Standards. They are the foundation of the mathematics curriculum for the State of Utah. The standards include the skills and understanding students need to succeed in college and careers. They include rigorous content and application of knowledge and reflect…
Mathematical Sciences in Australia
Thomas, Jan; Muchatuta, Michelle; Wood, Leigh
2009-01-01
This article investigates enrolment trends in mathematical sciences in Australian universities. Data has been difficult to extract and the coding for mathematical disciplines has made investigation challenging. We show that the number of mathematics major undergraduates in Australia is steadily declining though the number studying…
Walshaw, Margaret
2014-01-01
This paper explores contemporary thinking about learning mathematics, and within that, social justice within mathematics education. The discussion first looks at mechanisms offered by conventional explanations on the emancipatory project and then moves towards more recent insights developed within mathematics education. Synergies are drawn between…
Variation and Mathematics Pedagogy
Leung, Allen
2012-01-01
This discussion paper put forwards variation as a theme to structure mathematical experience and mathematics pedagogy. Patterns of variation from Marton's Theory of Variation are understood and developed as types of variation interaction that enhance mathematical understanding. An idea of a discernment unit comprising mutually supporting variation…
Amidon, Joel C.
2011-01-01
What happens when the problem of inequitable access to mathematics is addressed by agape (pronounced agapa) or attending to the relationships students develop with mathematics? To respond to this question, this paper offers a description of the journey towards teaching mathematics as agape. First, I organized examples of equity pedagogy around the…
Author Affiliations. K B Athreya1 2 M G Nadkarni3. Department of Mathematics Iowa State University, Ames, Iowa; I M I, Department of Mathematics, Indian Institute of Science, Bangalore, 560012, India. Department of Mathematics, University of Mumbai Kalina, Mumbai, 400098, India.
The Algorithm of Continuous Optimization Based on the Modified Cellular Automaton
Oleg Evsutin
2016-08-01
Full Text Available This article is devoted to the application of the cellular automata mathematical apparatus to the problem of continuous optimization. The cellular automaton with an objective function is introduced as a new modification of the classic cellular automaton. The algorithm of continuous optimization, which is based on dynamics of the cellular automaton having the property of geometric symmetry, is obtained. The results of the simulation experiments with the obtained algorithm on standard test functions are provided, and a comparison between the analogs is shown.
Xu, Xiang; Lin, Feng
2017-01-01
This book introduces new techniques for cellular image feature extraction, pattern recognition and classification. The authors use the antinuclear antibodies (ANAs) in patient serum as the subjects and the Indirect Immunofluorescence (IIF) technique as the imaging protocol to illustrate the applications of the described methods. Throughout the book, the authors provide evaluations for the proposed methods on two publicly available human epithelial (HEp-2) cell datasets: ICPR2012 dataset from the ICPR'12 HEp-2 cell classification contest and ICIP2013 training dataset from the ICIP'13 Competition on cells classification by fluorescent image analysis. First, the reading of imaging results is significantly influenced by one’s qualification and reading systems, causing high intra- and inter-laboratory variance. The authors present a low-order LP21 fiber mode for optical single cell manipulation and imaging staining patterns of HEp-2 cells. A focused four-lobed mode distribution is stable and effective in optical...
Crossley, J N; Brickhill, CJ; Stillwell, JC
2010-01-01
Although mathematical logic can be a formidably abstruse topic, even for mathematicians, this concise book presents the subject in a lively and approachable fashion. It deals with the very important ideas in modern mathematical logic without the detailed mathematical work required of those with a professional interest in logic.The book begins with a historical survey of the development of mathematical logic from two parallel streams: formal deduction, which originated with Aristotle, Euclid, and others; and mathematical analysis, which dates back to Archimedes in the same era. The streams beg
Introductory discrete mathematics
Balakrishnan, V K
2010-01-01
This concise text offers an introduction to discrete mathematics for undergraduate students in computer science and mathematics. Mathematics educators consider it vital that their students be exposed to a course in discrete methods that introduces them to combinatorial mathematics and to algebraic and logical structures focusing on the interplay between computer science and mathematics. The present volume emphasizes combinatorics, graph theory with applications to some stand network optimization problems, and algorithms to solve these problems.Chapters 0-3 cover fundamental operations involv
Mathematics for physical chemistry
Mortimer, Robert G
2013-01-01
Mathematics for Physical Chemistry is the ideal supplementary text for practicing chemists and students who want to sharpen their mathematics skills while enrolled in general through physical chemistry courses. This book specifically emphasizes the use of mathematics in the context of physical chemistry, as opposed to being simply a mathematics text. This 4e includes new exercises in each chapter that provide practice in a technique immediately after discussion or example and encourage self-study. The early chapters are constructed around a sequence of mathematical topics, wit
Fundamental concepts of mathematics
Goodstein, R L
Fundamental Concepts of Mathematics, 2nd Edition provides an account of some basic concepts in modern mathematics. The book is primarily intended for mathematics teachers and lay people who wants to improve their skills in mathematics. Among the concepts and problems presented in the book include the determination of which integral polynomials have integral solutions; sentence logic and informal set theory; and why four colors is enough to color a map. Unlike in the first edition, the second edition provides detailed solutions to exercises contained in the text. Mathematics teachers and people
Mathematics for the imagination
Higgins, Peter
2002-01-01
Mathematics for the Imagination provides an accessible and entertaining investigation into mathematical problems in the world around us. From world navigation, family trees, and calendars to patterns, tessellations, and number tricks, this informative and fun new book helps you to understand the maths behind real-life questions and rediscover your arithmetical mind.This is a follow-up to the popular Mathematics for the Curious, Peter Higgins's first investigation into real-life mathematical problems.A highly involving book which encourages the reader to enter into the spirit of mathematical ex
Gabbay, Dov M; Woods, John
2009-01-01
One of the most striking features of mathematics is the fact that we are much more certain about the mathematical knowledge we have than about what mathematical knowledge is knowledge of. Are numbers, sets, functions and groups physical entities of some kind? Are they objectively existing objects in some non-physical, mathematical realm? Are they ideas that are present only in the mind? Or do mathematical truths not involve referents of any kind? It is these kinds of questions that have encouraged philosophers and mathematicians alike to focus their attention on issues in the philosophy of mat
Jourdain, Philip E B
2007-01-01
Anyone with an interest in mathematics will welcome the republication of this little volume by a remarkable mathematician who was also a logician, a philosopher, and an occasional writer of fiction and poetry. Originally published in 1913, and later included in the acclaimed anthology The World of Mathematics, Jourdain's survey shows how and why the methods of mathematics were developed, traces the development of mathematical science from the earliest to modern times, and chronicles the application of mathematics to natural science.Starting with the ancient Egyptians and Greeks, the author p
The development of mathematics
Bell, Eric Temple
1945-01-01
""This important book . . . presents a broad account of the part played by mathematics in the evolution of civilization, describing clearly the main principles, methods, and theories of mathematics that have survived from about 4000 BC to 1940.""― BooklistIn this time-honored study, one of the 20th century's foremost scholars and interpreters of the history and meaning of mathematics masterfully outlines the development of its leading ideas, and clearly explains the mathematics involved in each. According to the author, a professor of mathematics at the California Institute of Technology from
Dantzig, Tobias
2006-01-01
More than a history of mathematics, this lively book traces mathematical ideas and processes to their sources, stressing the methods used by the masters of the ancient world. Author Tobias Dantzig portrays the human story behind mathematics, showing how flashes of insight in the minds of certain gifted individuals helped mathematics take enormous forward strides. Dantzig demonstrates how the Greeks organized their precursors' melange of geometric maxims into an elegantly abstract deductive system. He also explains the ways in which some of the famous mathematical brainteasers of antiquity led
Martin, B R
2015-01-01
Mathematics for Physicists is a relatively short volume covering all the essential mathematics needed for a typical first degree in physics, from a starting point that is compatible with modern school mathematics syllabuses. Early chapters deliberately overlap with senior school mathematics, to a degree that will depend on the background of the individual reader, who may quickly skip over those topics with which he or she is already familiar. The rest of the book covers the mathematics that is usually compulsory for all students in their first two years of a typical university physics degree, plus a little more. There are worked examples throughout the text, and chapter-end problem sets. Mathematics for Physicists features: * Interfaces with modern school mathematics syllabuses * All topics usually taught in the first two years of a physics degree * Worked examples throughout * Problems in every chapter, with answers to selected questions at the end of the book and full solutions on a website This text will ...
Meaning in mathematics education
Valero, Paola; Hoyles, Celia; Skovsmose, Ole
2005-01-01
What does it mean to know mathematics? How does meaning in mathematics education connect to common sense or to the meaning of mathematics itself? How are meanings constructed and communicated and what are the dilemmas related to these processes? There are many answers to these questions, some of which might appear to be contradictory. Thus understanding the complexity of meaning in mathematics education is a matter of huge importance. There are twin directions in which discussions have developed - theoretical and practical - and this book seeks to move the debate forward along both dimensions while seeking to relate them where appropriate. A discussion of meaning can start from a theoretical examination of mathematics and how mathematicians over time have made sense of their work. However, from a more practical perspective, anybody involved in teaching mathematics is faced with the need to orchestrate the myriad of meanings derived from multiple sources that students develop of mathematical knowledge.
Stochastic properties of disturbed Elementary Cellular Automata
Posiewnik, M.
2005-01-01
Cellular automata are class of simple mathematical systems that generate diverse, often complicated behaviour. Evolution of such a system is given by set of local and deterministic rules. However, in spite of simplicity of 'interactions' it's global behaviour can't be, in general, simply predicted or even can not be predicted in time shorter that time of it's strict evolution. We get as, a systems well known 1-dimensional, Wolfram class automata, and connect it into the reservoir consists of some random source (noise). In our experiment we are interested in: a) numeric verification of ergodicity for such a coupled system. b) finding it's probability distribution and evolution. c) finding some analogous for 'real' quantities and behaviour. d) using the dynamical systems and Markov chains theory to describe the system, and to make any predictions of it's behaviour. (author)
Particles and Patterns in Cellular Automata
Jen, E.; Das, R.; Beasley, C.E.
1999-01-01
This is the final report of a three-year, Laboratory Directed Research and Development (LDRD) project at Los Alamos National Laboratory (LANL). Our objective has been to develop tools for studying particle interactions in a class of dynamical systems characterized by discreteness, determinism, local interaction, and an inherently parallel form of evolution. These systems can be described by cellular automata (CA) and the behavior we studied has improved our understanding of the nature of patterns generated by CAs, their ability to perform global computations, and their relationship to continuous dynamical systems. We have also developed a rule-table mathematics that enables one to custom-design CA rule tables to generate patterns of specified types, or to perform specified computational tasks
The History of Mathematics and Mathematical Education
Grattan-Guinness, I.
1977-01-01
Answers to questions which were asked after the author's various lectures in Australia are gathered here. Topics touched upon include "new" mathematics, unknown constants and free variables, propositional functions, linear algebra, arithmetic and geometry, and student assessment. (MN)
Discrete dynamic modeling of cellular signaling networks.
Albert, Réka; Wang, Rui-Sheng
2009-01-01
Understanding signal transduction in cellular systems is a central issue in systems biology. Numerous experiments from different laboratories generate an abundance of individual components and causal interactions mediating environmental and developmental signals. However, for many signal transduction systems there is insufficient information on the overall structure and the molecular mechanisms involved in the signaling network. Moreover, lack of kinetic and temporal information makes it difficult to construct quantitative models of signal transduction pathways. Discrete dynamic modeling, combined with network analysis, provides an effective way to integrate fragmentary knowledge of regulatory interactions into a predictive mathematical model which is able to describe the time evolution of the system without the requirement for kinetic parameters. This chapter introduces the fundamental concepts of discrete dynamic modeling, particularly focusing on Boolean dynamic models. We describe this method step-by-step in the context of cellular signaling networks. Several variants of Boolean dynamic models including threshold Boolean networks and piecewise linear systems are also covered, followed by two examples of successful application of discrete dynamic modeling in cell biology.
47 CFR 22.909 - Cellular markets.
2010-10-01
... 47 Telecommunication 2 2010-10-01 2010-10-01 false Cellular markets. 22.909 Section 22.909... Cellular Radiotelephone Service § 22.909 Cellular markets. Cellular markets are standard geographic areas used by the FCC for administrative convenience in the licensing of cellular systems. Cellular markets...
Mathematical Sciences Institute Workshop
Scott, Philip
1990-01-01
A so-called "effective" algorithm may require arbitrarily large finite amounts of time and space resources, and hence may not be practical in the real world. A "feasible" algorithm is one which only requires a limited amount of space and/or time for execution; the general idea is that a feasible algorithm is one which may be practical on today's or at least tomorrow's computers. There is no definitive analogue of Church's thesis giving a mathematical definition of feasibility; however, the most widely studied mathematical model of feasible computability is polynomial-time computability. Feasible Mathematics includes both the study of feasible computation from a mathematical and logical point of view and the reworking of traditional mathematics from the point of view of feasible computation. The diversity of Feasible Mathematics is illustrated by the. contents of this volume which includes papers on weak fragments of arithmetic, on higher type functionals, on bounded linear logic, on sub recursive definitions ...
Nash, Jr, John Forbes
2016-01-01
The goal in putting together this unique compilation was to present the current status of the solutions to some of the most essential open problems in pure and applied mathematics. Emphasis is also given to problems in interdisciplinary research for which mathematics plays a key role. This volume comprises highly selected contributions by some of the most eminent mathematicians in the international mathematical community on longstanding problems in very active domains of mathematical research. A joint preface by the two volume editors is followed by a personal farewell to John F. Nash, Jr. written by Michael Th. Rassias. An introduction by Mikhail Gromov highlights some of Nash’s legendary mathematical achievements. The treatment in this book includes open problems in the following fields: algebraic geometry, number theory, analysis, discrete mathematics, PDEs, differential geometry, topology, K-theory, game theory, fluid mechanics, dynamical systems and ergodic theory, cryptography, theoretical computer sc...
Advances in mathematical economics
Maruyama, Toru
2015-01-01
The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research. A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories.
Advances in mathematical economics
Maruyama, Toru
2014-01-01
A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories. The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research.
Advances in mathematical economics
Yamazaki, Akira
2006-01-01
A lot of economic problems can formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories. The series is designed to bring together those mathematicians who were seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking for effective mathematical tools for their researchers.
Ideation in mathematical writing
Misfeldt, Morten
2007-01-01
This paper considers idea generation during the mathematical writing process. Two contrasting explanations of the creative potential in connection to writing is presented; writing as a process of setting and obtaining rhetorical goals and writing as a process of discovery. These views...... are then related to two empirically found categories of functions that writing serves researchers in the field of mathematics, concluding that both views contributes to understanding the creative potential in relation to mathematical writing....
Advances in mathematical economics
Yamazaki, Akira
2006-01-01
A lot of economic problems can formulated as constrained optimizations and equilibration of their solutions.Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories. The series is designed to bring together those mathematicians who were seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking for effective mathematical tools for their researchers.
Interactive Mathematics Textbooks
Sinclair, Robert
1999-01-01
We claim that important considerations have been overlooked in designinginteractive mathematics educational software in the past.In particular,most previous work has concentrated on how to make use ofpre-existing software in mathematics education, rather than firstasking the more...... fundamentalquestion of which requirements mathematics education puts on software, and thendesigning software to fulfil these requirements.We present a working prototype system which takes a script defining an interactivemathematicaldocument and then provides a reader with an interactive realization of thatdocument....
Learning Mathematics through Programming
Misfeldt, Morten; Ejsing-Duun, Stine
2015-01-01
In this paper we explore the potentials for learning mathematics through programming by a combination of theoretically derived potentials and cases of practical pedagogical work. We propose a model with three interdependent learning potentials as programming which can: (1) help reframe the students...... to mathematics is paramount. Analyzing two cases, we suggest a number of ways in which didactical attention to epistemic mediation can support learning mathematics....
Educating mathematics teacher educators
Højgaard, Tomas; Jankvist, Uffe Thomas
2014-01-01
The paper argues for a three-dimensional course design structure for future mathematics teacher educators. More precisely we describe the design and implementation of a course basing itself on: the two mathematical competencies of modelling and problem tackling, this being the first dimension......; the two mathematical topics of differential equations and stochastics, this being the second dimension; and finally a third dimension the purpose of which is to deepen the two others by means of a didactical perspective....
Advances in mathematical economics
Maruyama, Toru
2017-01-01
The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research. A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories.
Advances in mathematical economics
Maruyama, Toru
2016-01-01
The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research. A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories.
International Mathematical Internet Olympiad
Alexander Domoshnitsky
2012-10-01
Full Text Available Modern Internet technologies open new possibilities in wide spectrum of traditional methods used in mathematical education. One of the areas, where these technologies can be efficiently used, is an organization of mathematical competitions. Contestants can stay at their schools or universities and try to solve as many mathematical problems as possible and then submit their solutions through Internet. Simple Internet technologies supply audio and video connection between participants and organizers.
House, Peggy A.
1994-01-01
Describes some mathematical investigations of the necktie which includes applications of geometry, statistics, data analysis, sampling, probability, symmetry, proportion, problem solving, and business. (MKR)
Mathematical fallacies and paradoxes
Bunch, Bryan
1982-01-01
Stimulating, thought-provoking analysis of the most interesting intellectual inconsistencies in mathematics, physics, and language, including being led astray by algebra (De Morgan's paradox). 1982 edition.
Plumpton, C
1968-01-01
Sixth Form Pure Mathematics, Volume 1, Second Edition, is the first of a series of volumes on Pure Mathematics and Theoretical Mechanics for Sixth Form students whose aim is entrance into British and Commonwealth Universities or Technical Colleges. A knowledge of Pure Mathematics up to G.C.E. O-level is assumed and the subject is developed by a concentric treatment in which each new topic is used to illustrate ideas already treated. The major topics of Algebra, Calculus, Coordinate Geometry, and Trigonometry are developed together. This volume covers most of the Pure Mathematics required for t
Berkeley's Philosophy of Mathematics
Jesseph, Douglas M
1993-01-01
In this first modern, critical assessment of the place of mathematics in Berkeley's philosophy and Berkeley's place in the history of mathematics, Douglas M. Jesseph provides a bold reinterpretation of Berkeley's work. Jesseph challenges the prevailing view that Berkeley's mathematical writings are peripheral to his philosophy and argues that mathematics is in fact central to his thought, developing out of his critique of abstraction. Jesseph's argument situates Berkeley's ideas within the larger historical and intellectual context of the Scientific Revolution. Jesseph begins with Berkeley's r
Teaching secondary mathematics
Rock, David
2013-01-01
Solidly grounded in up-to-date research, theory and technology,?Teaching Secondary Mathematics?is a practical, student-friendly, and popular text for secondary mathematics methods courses. It provides clear and useful approaches for mathematics teachers, and shows how concepts typically found in a secondary mathematics curriculum can be taught in a positive and encouraging way. The thoroughly revised fourth edition combines this pragmatic approach with truly innovative and integrated technology content throughout. Synthesized content between the book and comprehensive companion websi
Resnikoff, Howard L
2015-01-01
Space flight, computers, lasers, and information technology ― these are but a few examples of the spectacular growth, development, and far-reaching applications of mathematics. But what of the field's past? Upon which intellectual milestones were the foundations of modern mathematics constructed? How has our comprehension of the physical universe, language, and the nature of thought itself been influenced and informed by the developments of mathematics through the ages?This lucid presentation examines how mathematics shaped and was shaped by the course of human events. In a format suited to co
2011-01-01
Is mathematics a highly sophisticated intellectual game in which the adepts display their skill by tackling invented problems, or are mathematicians engaged in acts of discovery as they explore an independent realm of mathematical reality? Why does this seemingly abstract discipline provide the key to unlocking the deep secrets of the physical universe? How one answers these questions will significantly influence metaphysical thinking about reality. This book is intended to fill a gap between popular 'wonders of mathematics' books and the technical writings of the philosophers of mathematics.
Winsløw, Carl
2015-01-01
Mathematics is studied in universities by a large number of students. At the same time it is a field of research for a (smaller) number of university teachers. What relations, if any, exist between university research and teaching of mathematics? Can research “support” teaching? What research...... and what teaching? In this presentation we propose a theoretical framework to study these questions more precisely, based on the anthropological theory of didactics. As a main application, the links between the practices of mathematical research and university mathematics teaching are examined...
Plofker, Kim
2009-01-01
Based on extensive research in Sanskrit sources, Mathematics in India chronicles the development of mathematical techniques and texts in South Asia from antiquity to the early modern period. Kim Plofker reexamines the few facts about Indian mathematics that have become common knowledge--such as the Indian origin of Arabic numerals--and she sets them in a larger textual and cultural framework. The book details aspects of the subject that have been largely passed over in the past, including the relationships between Indian mathematics and astronomy, and their cross-fertilizations with Islamic sc
Kuipers, L
1969-01-01
International Series of Monographs in Pure and Applied Mathematics, Volume 99: Handbook of Mathematics provides the fundamental mathematical knowledge needed for scientific and technological research. The book starts with the history of mathematics and the number systems. The text then progresses to discussions of linear algebra and analytical geometry including polar theories of conic sections and quadratic surfaces. The book then explains differential and integral calculus, covering topics, such as algebra of limits, the concept of continuity, the theorem of continuous functions (with examp
Philosophy and mathematics: interactions.
Rashed, Roshdi
From Plato to the beginnings of the last century, mathematics provided philosophers with methods of exposition, procedures of demonstration, and instruments of analysis. The unprecedented development of mathematics on the one hand, and the mathematicians' appropriation of Logic from the philosophers on the other hand, have given rise to two problems with which the philosophers have to contend: (1) Is there still a place for the philosophy of mathematics? and (2) To what extent is a philosophy of mathematics still possible? This article offers some reflections on these questions, which have preoccupied a good many philosophers and continue to do so.
Winkler, Peter
2007-01-01
Peter Winkler is at it again. Following the enthusiastic reaction to Mathematical Puzzles: A Connoisseur's Collection, Peter has compiled a new collection of elegant mathematical puzzles to challenge and entertain the reader. The original puzzle connoisseur shares these puzzles, old and new, so that you can add them to your own anthology. This book is for lovers of mathematics, lovers of puzzles, lovers of a challenge. Most of all, it is for those who think that the world of mathematics is orderly, logical, and intuitive-and are ready to learn otherwise! A pdf with errata is updated by the aut
Exploring Differential Effects of Mathematics Courses on Mathematics Achievement
Ma, Xin; McIntyre, Laureen J.
2005-01-01
Using data from the Longitudinal Study of Mathematics Participation (N = 1,518 students from 34 schools), we investigated the effects of pure and applied mathematics courses on mathematics achievement, controlling for prior mathematics achievement. Results of multilevel modelling showed that the effects of pure mathematics were significant after…
Hands-On Mathematics: Two Cases from Ancient Chinese Mathematics
Wang, Youjun
2009-01-01
In modern mathematical teaching, it has become increasingly emphasized that mathematical knowledge should be taught by problem-solving, hands-on activities, and interactive learning experiences. Comparing the ideas of modern mathematical education with the development of ancient Chinese mathematics, we find that the history of mathematics in…
A Capstone Mathematics Course for Prospective Secondary Mathematics Teachers
Artzt, Alice F.; Sultan, Alan; Curcio, Frances R.; Gurl, Theresa
2012-01-01
This article describes an innovative capstone mathematics course that links college mathematics with school mathematics and pedagogy. It describes how college juniors in a secondary mathematics teacher preparation program engage in leadership experiences that enable them to learn mathematics for teaching while developing student-centered…
On Mathematical Understanding: Perspectives of Experienced Chinese Mathematics Teachers
Cai, Jinfa; Ding, Meixia
2017-01-01
Researchers have long debated the meaning of mathematical understanding and ways to achieve mathematical understanding. This study investigated experienced Chinese mathematics teachers' views about mathematical understanding. It was found that these mathematics teachers embrace the view that understanding is a web of connections, which is a result…
Using Mathematics Literature with Prospective Secondary Mathematics Teachers
Jett, Christopher C.
2014-01-01
Literature in mathematics has been found to foster positive improvements in mathematics learning. This manuscript reports on a mathematics teacher educator's use of literature via literature circles with 11 prospective secondary mathematics teachers in a mathematics content course. Using survey and reflection data, the author found that…
Finite Mathematics and Discrete Mathematics: Is There a Difference?
Johnson, Marvin L.
Discrete mathematics and finite mathematics differ in a number of ways. First, finite mathematics has a longer history and is therefore more stable in terms of course content. Finite mathematics courses emphasize certain particular mathematical tools which are useful in solving the problems of business and the social sciences. Discrete mathematics…
MSAT and cellular hybrid networking
Baranowsky, Patrick W., II
Westinghouse Electric Corporation is developing both the Communications Ground Segment and the Series 1000 Mobile Phone for American Mobile Satellite Corporation's (AMSC's) Mobile Satellite (MSAT) system. The success of the voice services portion of this system depends, to some extent, upon the interoperability of the cellular network and the satellite communication circuit switched communication channels. This paper will describe the set of user-selectable cellular interoperable modes (cellular first/satellite second, etc.) provided by the Mobile Phone and described how they are implemented with the ground segment. Topics including roaming registration and cellular-to-satellite 'seamless' call handoff will be discussed, along with the relevant Interim Standard IS-41 Revision B Cellular Radiotelecommunications Intersystem Operations and IOS-553 Mobile Station - Land Station Compatibility Specification.
MIMO Communication for Cellular Networks
Huang, Howard; Venkatesan, Sivarama
2012-01-01
As the theoretical foundations of multiple-antenna techniques evolve and as these multiple-input multiple-output (MIMO) techniques become essential for providing high data rates in wireless systems, there is a growing need to understand the performance limits of MIMO in practical networks. To address this need, MIMO Communication for Cellular Networks presents a systematic description of MIMO technology classes and a framework for MIMO system design that takes into account the essential physical-layer features of practical cellular networks. In contrast to works that focus on the theoretical performance of abstract MIMO channels, MIMO Communication for Cellular Networks emphasizes the practical performance of realistic MIMO systems. A unified set of system simulation results highlights relative performance gains of different MIMO techniques and provides insights into how best to use multiple antennas in cellular networks under various conditions. MIMO Communication for Cellular Networks describes single-user,...
Programmable cellular arrays. Faults testing and correcting in cellular arrays
Cercel, L.
1978-03-01
A review of some recent researches about programmable cellular arrays in computing and digital processing of information systems is presented, and includes both combinational and sequential arrays, with full arbitrary behaviour, or which can realize better implementations of specialized blocks as: arithmetic units, counters, comparators, control systems, memory blocks, etc. Also, the paper presents applications of cellular arrays in microprogramming, in implementing of a specialized computer for matrix operations, in modeling of universal computing systems. The last section deals with problems of fault testing and correcting in cellular arrays. (author)
Proof and knowledge in mathematics
Detlefsen, Michael
2005-01-01
These questions arise from any attempt to discover an epistemology for mathematics. This collection of essays considers various questions concerning the nature of justification in mathematics and possible sources of that justification. Among these are the question of whether mathematical justification is a priori or a posteriori in character, whether logical and mathematical differ, and if formalization plays a significant role in mathematical justification,
Unlu, Melihan; Ertekin, Erhan; Dilmac, Bulent
2017-01-01
The purpose of the research is to investigate the relationships betweenself-efficacy beliefs toward mathematics, mathematics anxiety and self-efficacybeliefs toward mathematics teaching, mathematics teaching anxiety variables andtesting the relationships between these variables with structural equationmodel. The sample of the research, which was conducted in accordance withrelational survey model, consists of 380 university students, who studied atthe department of Elementary Mathematics Educ...
Two Phase Flow Simulation Using Cellular Automata
Marcel, C.P.
2002-01-01
The classical mathematical treatment of two-phase flows is based on the average of the conservation equations for each phase.In this work, a complementary approach to the modeling of these systems based on statistical population balances of aut omata sets is presented.Automata are entities defined by mathematical states that change following iterative rules representing interactions with the neighborhood.A model of automata for two-phase flow simulation is presented.This model consists of fie lds of virtual spheres that change their volumes and move around a certain environment.The model is more general than the classical cellular automata in two respects: the grid of cellular automata is dismissed in favor of a trajectory generator, and the rules of interaction involve parameters representing the actual physical interactions between phases.Automata simulation was used to study unsolved two-phase flow problems involving high heat flux rates. One system described in this work consists of a vertical channel with saturated water at normal pressure heated from the lower surface.The heater causes water to boil and starts the bubble production.We used cellular automata to describe two-phase flows and the interaction with the heater.General rule s for such cellular automata representing bubbles moving in stagnant liquid were used, with special attention to correct modeling of different mechanisms of heat transfer.The results of the model were compared to previous experiments and correlations finding good agreement.One of the most important findings is the confirmation of Kutateladze's idea about a close relation between the start of critical heat flux and a change in the flow's topology.This was analyzed using a control volume located in the upper surface of the heater.A strong decrease in the interfacial surface just before the CHF start was encountered.The automata describe quite well some characteristic parameters such as the shape of the local void fraction in the
Sinclair, Robert
1998-01-01
Course notes of a PhD course held in 1998. The central idea is to introduce students to computational mathematics using object oriented programming in C++.......Course notes of a PhD course held in 1998. The central idea is to introduce students to computational mathematics using object oriented programming in C++....
Hansen, Vagn Lundsgaard; Gray, Jeremy
Volume 1 in Theme on "History of Mathematics", in "Encyclopedia of Life Support Systems (EOLSS), developed under the auspices of the UNESCO.......Volume 1 in Theme on "History of Mathematics", in "Encyclopedia of Life Support Systems (EOLSS), developed under the auspices of the UNESCO....
Abu Darda
2016-01-01
Full Text Available The objective of mathematics education is not only preparingmathematicians but making well-informed citizens. This is a broad generalterms for objective of the teaching of mathematics. And, this might beimplemented as “accurate thorough knowledge” or “original logicalthinking”. So, teaching mathematics is not the conversation andtransmission of mathematical knowledge, but on the aim of preparing wellinformedcitizens trained in independent, critical thinking.By the mathematics, sciences become simple, clearer, and easier to bedeveloped. The mathematics is often applied for solving any problem ofother field of sciences, either in the physics such as astronomy, chemistry,technique; or social sciences such as economy, demography, and assurance.Those all need an analysis reading ability.Mathematical skill, therefore, relates strongly with the analysisreading ability in the human intellectual structure. This study is about therelationship between them. And, result of the study shows us as below:Both Mathematical skill and analysis reading ability possess the “high type”of thinking operation. Both also involve the same content of the abstractintelligent, i.e. symbolic and semantic contents. Last but not least, both alsouse the same product of thinking, i.e. units, classes, relations, and systems.Both can be transformed and have an implication.
Mathematics for computer graphics
Vince, John
2006-01-01
Helps you understand the mathematical ideas used in computer animation, virtual reality, CAD, and other areas of computer graphics. This work also helps you to rediscover the mathematical techniques required to solve problems and design computer programs for computer graphic applications
Høyrup, Jens
2017-01-01
The paper discusses the question “What is mathematics?” from a point of view inspired by anthropology. In this perspective, the character of mathematical thinking and argument is strongly affected - almost essentially determined, indeed - by the dynamics of the specific social, mostly professional...
Mathematical Graphic Organizers
Zollman, Alan
2009-01-01
As part of a math-science partnership, a university mathematics educator and ten elementary school teachers developed a novel approach to mathematical problem solving derived from research on reading and writing pedagogy. Specifically, research indicates that students who use graphic organizers to arrange their ideas improve their comprehension…
Mathematical thinking and origami
Wares, Arsalan
2016-01-01
The purpose of this paper is to describe the mathematics that emanates from the construction of an origami box. We first construct a simple origami box from a rectangular sheet and then discuss some of the mathematical questions that arise in the context of geometry and calculus.
Modularizing Remedial Mathematics
Wong, Aaron
2013-01-01
As remedial mathematics education has become an increasingly important topic of conversation in higher education. Mathematics departments have been put under increased pressure to change their programs to increase the student success rate. A number of models have been introduced over the last decade that represent a wide range of new ideas and…
Elementary Mathematics Leaders
Fennell, Francis; Kobett, Beth McCord; Wray, Jonathan A.
2013-01-01
Elementary school mathematics leaders often come to the realization that their position, however titled and determined, although dedicated to addressing needs in math teaching and learning, also entails and directly involves leadership. Elementary school math specialists/instructional leaders (referenced here as elementary mathematics leaders, or…
Archives: Mathematics Connection
Items 1 - 9 of 9 ... Archives: Mathematics Connection. Journal Home > Archives: Mathematics Connection. Log in or Register to get access to full text downloads. Username, Password, Remember me, or Register · Journal Home · ABOUT THIS JOURNAL · Advanced Search · Current Issue · Archives. 1 - 9 of 9 Items. 2011 ...
Mathematics Teaching and Inclusion
This volume contains the proceedings of the 3rd Nordic Research Conference on Special Needs Education in Mathematics, which took place in Rebild organised by Aalborg University in November 23-25, 2005. The theme of the conference was Mathematics Education and Inclusion. The conference theme...
田琳
2016-01-01
In both China and the West, mathematics is closely connected with literature. The maths thought implied in Chinese and western literature is worth our study, and the maths thought in the field of literature is also appear in aesthetics and philoso-phy, so literature, mathematics, aesthetics and philosophy become a network of interconnected.
Dyslexia, Dyspraxia and Mathematics.
Yeo, Dorian
This book explores how primary school children with dyslexia or dyspraxia and difficulty in math can learn math and provides practical support and detailed teaching suggestions. It considers cognitive features that underlie difficulty with mathematics generally or with specific aspects of mathematics. It outlines the ways in which children usually…
Mathematics. [SITE 2002 Section].
Connell, Michael L., Ed.; Lowery, Norene Vail, Ed.; Harnisch, Delwyn L., Ed.
This document contains the following papers on mathematics from the SITE (Society for Information Technology & Teacher Education) 2002 conference: (1) "Teachers' Learning of Mathematics in the Presence of Technology: Participatory Cognitive Apprenticeship" (Mara Alagic); (2) "A Fractal Is a Pattern in Your Neighborhood" (Craig N. Bach); (3)…
Seeley, Cathy
2004-01-01
This article addresses some important issues in mathematics instruction at the middle and secondary levels, including the structuring of a district's mathematics program; the choice of textbooks and use of calculators in the classroom; the need for more rigorous lesson planning practices; and the dangers of teaching to standardized tests rather…
Mathematical Education for Geographers
Wilson, Alan
1978-01-01
Outlines mathematical topics of use to college geography students identifies teaching methods for mathematical techniques in geography at the University of Leeds; and discusses problem of providing students with a framework for synthesizing all content of geography education. For journal availability, see SO 506 593. (Author/AV)
CLASSICS On Teaching Mathematics
give a better and more correct idea of modern mathematics than whole volumes of the. Bourbaki ... The de-geometrisation of mathematical education and the divorce from physics sever these ties. ... is their traditional national trait. I do not ...
Sharp, Karen Tobey
This paper cites information received from a number of sources, e.g., mathematics teachers in two-year colleges, publishers, and convention speakers, about the nature of discrete mathematics and about what topics a course in this subject should contain. Note is taken of the book edited by Ralston and Young which discusses the future of college…
Discrete Mathematics Re "Tooled."
Grassl, Richard M.; Mingus, Tabitha T. Y.
1999-01-01
Indicates the importance of teaching discrete mathematics. Describes how the use of technology can enhance the teaching and learning of discrete mathematics. Explorations using Excel, Derive, and the TI-92 proved how preservice and inservice teachers experienced a new dimension in problem solving and discovery. (ASK)
Corle, Clyde G.
This guide is to assist teachers with motivational ideas for teaching elementary school mathematics. The items included are a wide variety of games (paper and pencil, verbal, and physical), jingles, contests, teaching devices, and thought provoking exercises. Suggestions for selection of mathematical games are offered. The devices are used to…
Mathematics through Experience
Hristozova, Nedyalka
2016-01-01
The author shares some examples from her Bulgarian project, "Mathematics Through Experience", which approaches mathematics from a practical, real-life perspective in order to develop creative thinking: just like science! What was most important to her was to motivate her students to study maths and science by giving them a taste of how…
Under Threes' Mathematical Learning
Franzén, Karin
2015-01-01
The article focuses on mathematics for toddlers in preschool, with the aim of challenging a strong learning discourse that mainly focuses on cognitive learning. By devoting more attention to other perspectives on learning, the hope is to better promote children's early mathematical development. Sweden is one of few countries to have a curriculum…
Rethinking the mathematics curriculum
Hoyles, Celia; Woodhouse, Geoffrey
1998-01-01
At a time when political interest in mathematics education is at its highest, this book demonstrates that the issues are far from straightforward. A wide range of international contributors address such questions as: What is mathematics, and what is it for? What skills does mathematics education need to provide as technology advances? What are the implications for teacher education? What can we learn from past attempts to change the mathematics curriculum? Rethinking the Mathematics Curriculum offers stimulating discussions, showing much is to be learnt from the differences in culture, national expectations, and political restraints revealed in the book. This accessible book will be of particular interest to policy makers, curriculum developers, educators, researchers and employers as well as the general reader.
Developing mathematical modelling competence
Blomhøj, Morten; Jensen, Tomas Højgaard
2003-01-01
In this paper we introduce the concept of mathematical modelling competence, by which we mean being able to carry through a whole mathematical modelling process in a certain context. Analysing the structure of this process, six sub-competences are identified. Mathematical modelling competence...... cannot be reduced to these six sub-competences, but they are necessary elements in the development of mathematical modelling competence. Experience from the development of a modelling course is used to illustrate how the different nature of the sub-competences can be used as a tool for finding...... the balance between different kinds of activities in a particular educational setting. Obstacles of social, cognitive and affective nature for the students' development of mathematical modelling competence are reported and discussed in relation to the sub-competences....
Advanced engineering mathematics
Jeffrey, Alan
2001-01-01
Advanced Engineering Mathematics provides comprehensive and contemporary coverage of key mathematical ideas, techniques, and their widespread applications, for students majoring in engineering, computer science, mathematics and physics. Using a wide range of examples throughout the book, Jeffrey illustrates how to construct simple mathematical models, how to apply mathematical reasoning to select a particular solution from a range of possible alternatives, and how to determine which solution has physical significance. Jeffrey includes material that is not found in works of a similar nature, such as the use of the matrix exponential when solving systems of ordinary differential equations. The text provides many detailed, worked examples following the introduction of each new idea, and large problem sets provide both routine practice, and, in many cases, greater challenge and insight for students. Most chapters end with a set of computer projects that require the use of any CAS (such as Maple or Mathematica) th...
Mathematics of aperiodic order
Lenz, Daniel; Savinien, Jean
2015-01-01
What is order that is not based on simple repetition, that is, periodicity? How must atoms be arranged in a material so that it diffracts like a quasicrystal? How can we describe aperiodically ordered systems mathematically? Originally triggered by the – later Nobel prize-winning – discovery of quasicrystals, the investigation of aperiodic order has since become a well-established and rapidly evolving field of mathematical research with close ties to a surprising variety of branches of mathematics and physics. This book offers an overview of the state of the art in the field of aperiodic order, presented in carefully selected authoritative surveys. It is intended for non-experts with a general background in mathematics, theoretical physics or computer science, and offers a highly accessible source of first-hand information for all those interested in this rich and exciting field. Topics covered include the mathematical theory of diffraction, the dynamical systems of tilings or Delone sets, their cohomolog...
MATHEMATICAL MODEL MANIPULATOR ROBOTS
O. N. Krakhmalev
2015-12-01
Full Text Available A mathematical model to describe the dynamics of manipulator robots. Mathematical model are the implementation of the method based on the Lagrange equation and using the transformation matrices of elastic coordinates. Mathematical model make it possible to determine the elastic deviations of manipulator robots from programmed motion trajectories caused by elastic deformations in hinges, which are taken into account in directions of change of the corresponding generalized coordinates. Mathematical model is approximated and makes it possible to determine small elastic quasi-static deviations and elastic vibrations. The results of modeling the dynamics by model are compared to the example of a two-link manipulator system. The considered model can be used when performing investigations of the mathematical accuracy of the manipulator robots.
Haigh, John
2016-01-01
How does mathematics impact everyday events? The purpose of this book is to show a range of examples where mathematics can be seen at work in everyday life. From money (APR, mortgage repayments, personal finance), simple first and second order ODEs, sport and games (tennis, rugby, athletics, darts, tournament design, soccer, snooker), business (stock control, linear programming, check digits, promotion policies, investment), the social sciences (voting methods, Simpson’s Paradox, drug testing, measurements of inequality) to TV game shows and even gambling (lotteries, roulette, poker, horse racing), the mathematics behind commonplace events is explored. Fully worked examples illustrate the ideas discussed and each chapter ends with a collection of exercises. Everyday Mathematics supports other first year modules by giving students extra practice in working with calculus, linear algebra, geometry, trigonometry and probability. Secondary/high school level mathematics is all that is required for students to und...
Canadian Mathematical Congress
1977-01-01
For two weeks in August, 1975 more than 140 mathematicians and other scientists gathered at the Universite de Sherbrooke. The occasion was the 15th Biennial Seminar of the Canadian Mathematical Congress, entitled Mathematics and the Life Sciences. Participants in this inter disciplinary gathering included researchers and graduate students in mathematics, seven different areas of biological science, physics, chemistry and medical science. Geographically, those present came from the United States and the United Kingdom as well as from academic departments and government agencies scattered across Canada. In choosing this particular interdisciplinary topic the programme committee had two chief objectives. These were to promote Canadian research in mathematical problems of the life sciences, and to encourage co-operation and exchanges between mathematical scientists" biologists and medical re searchers. To accomplish these objective the committee assembled a stim ulating programme of lectures and talks. Six ...
Wu, A Y; Rosenfeld, A
1983-10-01
A cellular pyramid is an exponentially tapering stack of arrays of processors (cells), where each cell is connected to its neighbors (siblings) on its own level, to a parent on the level above, and to its children on the level below. It is shown that in some situations, if information flows top-down only, from fathers to sons, then a cellular pyramid may be no faster than a one-level cellular array; but it may be possible to use simpler cells in the pyramid case. 23 references.
Bates, Alan B.; Latham, Nancy; Kim, Jin-ah
2011-01-01
This study examined preservice teachers' mathematics self-efficacy and mathematics teaching efficacy and compared them to their mathematical performance. Participants included 89 early childhood preservice teachers at a Midwestern university. Instruments included the Mathematics Self-Efficacy Scale (MSES), Mathematics Teaching Efficacy Beliefs…
Hebert, Michael A.; Powell, Sarah R.
2016-01-01
Increasingly, students are expected to write about mathematics. Mathematics writing may be informal (e.g., journals, exit slips) or formal (e.g., writing prompts on high-stakes mathematics assessments). In order to develop an effective mathematics-writing intervention, research needs to be conducted on how students organize mathematics writing and…
Overcoming Conditioned Helplessness in Mathematics.
Wieschenberg, Agnes Arvai
1994-01-01
A discussion of mathematics anxiety and learned helplessness in mathematics focuses on student failure and avoidance in college mathematics learning. It explores possible causes and suggests classroom activities to foster students' interest and success. (MSE)
Cellular senescence and organismal aging.
Jeyapalan, Jessie C; Sedivy, John M
2008-01-01
Cellular senescence, first observed and defined using in vitro cell culture studies, is an irreversible cell cycle arrest which can be triggered by a variety of factors. Emerging evidence suggests that cellular senescence acts as an in vivo tumor suppression mechanism by limiting aberrant proliferation. It has also been postulated that cellular senescence can occur independently of cancer and contribute to the physiological processes of normal organismal aging. Recent data have demonstrated the in vivo accumulation of senescent cells with advancing age. Some characteristics of senescent cells, such as the ability to modify their extracellular environment, could play a role in aging and age-related pathology. In this review, we examine current evidence that links cellular senescence and organismal aging.
Origami interleaved tube cellular materials
Cheung, Kenneth C; Tachi, Tomohiro; Calisch, Sam; Miura, Koryo
2014-01-01
A novel origami cellular material based on a deployable cellular origami structure is described. The structure is bi-directionally flat-foldable in two orthogonal (x and y) directions and is relatively stiff in the third orthogonal (z) direction. While such mechanical orthotropicity is well known in cellular materials with extruded two dimensional geometry, the interleaved tube geometry presented here consists of two orthogonal axes of interleaved tubes with high interfacial surface area and relative volume that changes with fold-state. In addition, the foldability still allows for fabrication by a flat lamination process, similar to methods used for conventional expanded two dimensional cellular materials. This article presents the geometric characteristics of the structure together with corresponding kinematic and mechanical modeling, explaining the orthotropic elastic behavior of the structure with classical dimensional scaling analysis. (paper)
Origami interleaved tube cellular materials
Cheung, Kenneth C.; Tachi, Tomohiro; Calisch, Sam; Miura, Koryo
2014-09-01
A novel origami cellular material based on a deployable cellular origami structure is described. The structure is bi-directionally flat-foldable in two orthogonal (x and y) directions and is relatively stiff in the third orthogonal (z) direction. While such mechanical orthotropicity is well known in cellular materials with extruded two dimensional geometry, the interleaved tube geometry presented here consists of two orthogonal axes of interleaved tubes with high interfacial surface area and relative volume that changes with fold-state. In addition, the foldability still allows for fabrication by a flat lamination process, similar to methods used for conventional expanded two dimensional cellular materials. This article presents the geometric characteristics of the structure together with corresponding kinematic and mechanical modeling, explaining the orthotropic elastic behavior of the structure with classical dimensional scaling analysis.
Cellular Angiofibroma of the Nasopharynx.
Erdur, Zülküf Burak; Yener, Haydar Murat; Yilmaz, Mehmet; Karaaltin, Ayşegül Batioğlu; Inan, Hakki Caner; Alaskarov, Elvin; Gozen, Emine Deniz
2017-11-01
Angiofibroma is a common tumor of the nasopharynx region but cellular type is extremely rare in head and neck. A 13-year-old boy presented with frequent epistaxis and nasal obstruction persisting for 6 months. According to the clinical symptoms and imaging studies juvenile angiofibroma was suspected. Following angiographic embolization total excision of the lesion by midfacial degloving approach was performed. Histological examination revealed that the tumor consisted of staghorn blood vessels and irregular fibrous stroma. Stellate fibroblasts with small pyknotic to large vesicular nuclei were seen in a highly cellular stroma. These findings identified cellular angiofibroma mimicking juvenile angiofibroma. This article is about a very rare patient of cellular angiofibroma of nasopharynx.
Philosophical dimensions in mathematics education
Francois, Karen
2007-01-01
This book brings together diverse recent developments exploring the philosophy of mathematics in education. The unique combination of ethnomathematics, philosophy, history, education, statistics and mathematics offers a variety of different perspectives from which existing boundaries in mathematics education can be extended. The ten chapters in this book offer a balance between philosophy of and philosophy in mathematics education. Attention is paid to the implementation of a philosophy of mathematics within the mathematics curriculum.
Unified Stochastic Geometry Model for MIMO Cellular Networks with Retransmissions
Afify, Laila H.
2016-10-11
This paper presents a unified mathematical paradigm, based on stochastic geometry, for downlink cellular networks with multiple-input-multiple-output (MIMO) base stations (BSs). The developed paradigm accounts for signal retransmission upon decoding errors, in which the temporal correlation among the signal-to-interference-plus-noise-ratio (SINR) of the original and retransmitted signals is captured. In addition to modeling the effect of retransmission on the network performance, the developed mathematical model presents twofold analysis unification for MIMO cellular networks literature. First, it integrates the tangible decoding error probability and the abstracted (i.e., modulation scheme and receiver type agnostic) outage probability analysis, which are largely disjoint in the literature. Second, it unifies the analysis for different MIMO configurations. The unified MIMO analysis is achieved by abstracting unnecessary information conveyed within the interfering signals by Gaussian signaling approximation along with an equivalent SISO representation for the per-data stream SINR in MIMO cellular networks. We show that the proposed unification simplifies the analysis without sacrificing the model accuracy. To this end, we discuss the diversity-multiplexing tradeoff imposed by different MIMO schemes and shed light on the diversity loss due to the temporal correlation among the SINRs of the original and retransmitted signals. Finally, several design insights are highlighted.
Unified Stochastic Geometry Model for MIMO Cellular Networks with Retransmissions
Afify, Laila H.; Elsawy, Hesham; Al-Naffouri, Tareq Y.; Alouini, Mohamed-Slim
2016-01-01
This paper presents a unified mathematical paradigm, based on stochastic geometry, for downlink cellular networks with multiple-input-multiple-output (MIMO) base stations (BSs). The developed paradigm accounts for signal retransmission upon decoding errors, in which the temporal correlation among the signal-to-interference-plus-noise-ratio (SINR) of the original and retransmitted signals is captured. In addition to modeling the effect of retransmission on the network performance, the developed mathematical model presents twofold analysis unification for MIMO cellular networks literature. First, it integrates the tangible decoding error probability and the abstracted (i.e., modulation scheme and receiver type agnostic) outage probability analysis, which are largely disjoint in the literature. Second, it unifies the analysis for different MIMO configurations. The unified MIMO analysis is achieved by abstracting unnecessary information conveyed within the interfering signals by Gaussian signaling approximation along with an equivalent SISO representation for the per-data stream SINR in MIMO cellular networks. We show that the proposed unification simplifies the analysis without sacrificing the model accuracy. To this end, we discuss the diversity-multiplexing tradeoff imposed by different MIMO schemes and shed light on the diversity loss due to the temporal correlation among the SINRs of the original and retransmitted signals. Finally, several design insights are highlighted.
Fermentation process diagnosis using a mathematical model
Yerushalmi, L; Volesky, B; Votruba, J
1988-09-01
Intriguing physiology of a solvent-producing strain of Clostridium acetobutylicum led to the synthesis of a mathematical model of the acetone-butanol fermentation process. The model presented is capable of describing the process dynamics and the culture behavior during a standard and a substandard acetone-butanol fermentation. In addition to the process kinetic parameters, the model includes the culture physiological parameters, such as the cellular membrane permeability and the number of membrane sites for active transport of sugar. Computer process simulation studies for different culture conditions used the model, and quantitatively pointed out the importance of selected culture parameters that characterize the cell membrane behaviour and play an important role in the control of solvent synthesis by the cell. The theoretical predictions by the new model were confirmed by experimental determination of the cellular membrane permeability.
Mathematics as verbal behavior.
Marr, M Jackson
2015-04-01
"Behavior which is effective only through the mediation of other persons has so many distinguishing dynamic and topographical properties that a special treatment is justified and indeed demanded" (Skinner, 1957, p. 2). Skinner's demand for a special treatment of verbal behavior can be extended within that field to domains such as music, poetry, drama, and the topic of this paper: mathematics. For centuries, mathematics has been of special concern to philosophers who have continually argued to the present day about what some deem its "special nature." Two interrelated principal questions have been: (1) Are the subjects of mathematical interest pre-existing in some transcendental realm and thus are "discovered" as one might discover a new planet; and (2) Why is mathematics so effective in the practices of science and engineering even though originally such mathematics was "pure" with applications neither contemplated or even desired? I argue that considering the actual practice of mathematics in its history and in the context of acquired verbal behavior one can address at least some of its apparent mysteries. To this end, I discuss some of the structural and functional features of mathematics including verbal operants, rule-and contingency-modulated behavior, relational frames, the shaping of abstraction, and the development of intuition. How is it possible to understand Nature by properly talking about it? Essentially, it is because nature taught us how to talk. Copyright © 2015 Elsevier B.V. All rights reserved.
Constructing mathematical knowledge
Ernest, Paul
2012-01-01
This book provides a panorama of complimentary and forward looking perspectives on the learning of mathematics and epistemology from some of the leading contributors to the field. It explores constructivist and social theories of learning, and discusses the role of the computer in the light of these theories. It brings analyses from psychoanalysis, Hermeneutics and other perspectives to bear on the issues of mathematics and learning. It enquires into the nature of enquiry itself, and an important emergent theme is the role of language. Finally it relates the history of mathematics to its te
Mentoring in mathematics education
Hyde, Rosalyn
2013-01-01
Designed to support both teachers and university-based tutors in mentoring pre-service and newly qualified mathematics teachers at both primary and secondary levels, Mentoring Mathematics Teachers offers straightforward practical advice that is based on practice, underpinned by research, and geared specifically towards this challenging subject area.Developed by members of The Association of Mathematics Education Teachers, the authors draw upon the most up-to-date research and theory to provide evidence-based practical guidance. Themes covered include:
Khan, I.A.
1991-06-01
In India and in so many other countries, the science students are generally separated into two main streams: one opting mathematical sciences, the other studying biological sciences. As a result, medicos and biologists have no adequate knowledge of mathematical sciences. It causes a great drawback to them in order to be perfect and updated in their profession, due to the tremendous application of mathematics in bio-sciences, now-a-days. The main aim of this article is to emphasize on the need of the time to produce the mathematico-biologists in abundance for the better service of mankind. (author)
Alexander, Serena; Poggo, Tammy
2014-01-01
Features the complete set of answers to the exercises in Mathematics Year 5, to save you time marking work and enable you to identify areas requiring further attention. The book includes diagrams and workings where necessary, to ensure pupils understand how to present their answers. Also available from Galore Park www.galorepark.co.uk :. - Mathematics Year 5. - Mathematics Year 6. - 11+ Maths Practice Exercises. - 11+ Maths Revision Guide. - 10-Minute Maths Tests Workbook Age 8-10. - 10-Minute Maths Tests Workbook Age 9-11. - Mental Arithmetic Workbook Age 8-10. - Mental Arithmetic Workbook Ag
Boisvert, R F; Donahue, M J; Lozier, D W; McMichael, R; Rust, B W
2001-01-01
In this paper we describe the role that mathematics plays in measurement science at NIST. We first survey the history behind NIST's current work in this area, starting with the NBS Math Tables project of the 1930s. We then provide examples of more recent efforts in the application of mathematics to measurement science, including the solution of ill-posed inverse problems, characterization of the accuracy of software for micromagnetic modeling, and in the development and dissemination of mathematical reference data. Finally, we comment on emerging issues in measurement science to which mathematicians will devote their energies in coming years.
Higher engineering mathematics
John Bird
2014-01-01
A practical introduction to the core mathematics principles required at higher engineering levelJohn Bird's approach to mathematics, based on numerous worked examples and interactive problems, is ideal for vocational students that require an advanced textbook.Theory is kept to a minimum, with the emphasis firmly placed on problem-solving skills, making this a thoroughly practical introduction to the advanced mathematics engineering that students need to master. The extensive and thorough topic coverage makes this an ideal text for upper level vocational courses. Now in
Applied impulsive mathematical models
Stamova, Ivanka
2016-01-01
Using the theory of impulsive differential equations, this book focuses on mathematical models which reflect current research in biology, population dynamics, neural networks and economics. The authors provide the basic background from the fundamental theory and give a systematic exposition of recent results related to the qualitative analysis of impulsive mathematical models. Consisting of six chapters, the book presents many applicable techniques, making them available in a single source easily accessible to researchers interested in mathematical models and their applications. Serving as a valuable reference, this text is addressed to a wide audience of professionals, including mathematicians, applied researchers and practitioners.
Equations of mathematical physics
Tikhonov, A N
2011-01-01
Mathematical physics plays an important role in the study of many physical processes - hydrodynamics, elasticity, and electrodynamics, to name just a few. Because of the enormous range and variety of problems dealt with by mathematical physics, this thorough advanced-undergraduate or graduate-level text considers only those problems leading to partial differential equations. The authors - two well-known Russian mathematicians - have focused on typical physical processes and the principal types of equations deailing with them. Special attention is paid throughout to mathematical formulation, ri
Banagl, Markus
2011-01-01
The present volume grew out of the Heidelberg Knot Theory Semester, organized by the editors in winter 2008/09 at Heidelberg University. The contributed papers bring the reader up to date on the currently most actively pursued areas of mathematical knot theory and its applications in mathematical physics and cell biology. Both original research and survey articles are presented; numerous illustrations support the text. The book will be of great interest to researchers in topology, geometry, and mathematical physics, graduate students specializing in knot theory, and cell biologists interested
Contemporary mathematical physics
Dobrushin, R L; Shubin, M A; Vershik, Anatoly M
1996-01-01
This first of a two-volume collection is a celebration of the scientific heritage of F. A. Berezin (1931-1980). Before his untimely death, Berezin had an important influence on physics and mathematics, discovering new ideas in mathematical physics, representation theory, analysis, geometry, and other areas of mathematics. His crowning achievements were the introduction of a new notion of deformation quantization, and Grassmannian analysis ("supermathematics"). Collected here are papers by his many of his colleagues and others who worked in related areas, representing a wide spectrum of topics
Troelstra, AS
1988-01-01
Studies in Logic and the Foundations of Mathematics, Volume 123: Constructivism in Mathematics: An Introduction, Vol. II focuses on various studies in mathematics and logic, including metric spaces, polynomial rings, and Heyting algebras.The publication first takes a look at the topology of metric spaces, algebra, and finite-type arithmetic and theories of operators. Discussions focus on intuitionistic finite-type arithmetic, theories of operators and classes, rings and modules, linear algebra, polynomial rings, fields and local rings, complete separable metric spaces, and located sets. The te
Mathematical modelling techniques
Aris, Rutherford
1995-01-01
""Engaging, elegantly written."" - Applied Mathematical ModellingMathematical modelling is a highly useful methodology designed to enable mathematicians, physicists and other scientists to formulate equations from a given nonmathematical situation. In this elegantly written volume, a distinguished theoretical chemist and engineer sets down helpful rules not only for setting up models but also for solving the mathematical problems they pose and for evaluating models.The author begins with a discussion of the term ""model,"" followed by clearly presented examples of the different types of mode
Sulley, Robert
2014-01-01
Achieve the best possible standard with this bestselling book of traditional practice and guidance - now in colour!. First Aid in Mathematics provides all the help and support needed for learning and practising Mathematics. It offers comprehensive coverage of core mathematical topics in clear and accessible language. It is suitable for both native English speakers and students of English as a second language and can be used in class, or as a reference and revision book. - Develops a strong basis of understanding with core topics covered in clear and accessible language. - Improves student's ab
Hollingdale, S. H
1989-01-01
Fascinating and highly readable, this book recounts the history of mathematics as revealed in the lives and writings of the most distinguished practitioners of the art: Archimedes, Descartes, Fermat, Pascal, Newton, Leibniz, Euler, Gauss, Hamilton, Einstein, and many more. Author Stuart Hollingdale introduces and explains the roles of these gifted and often colorful figures in the development of mathematics as well as the ways in which their work relates to mathematics as a whole.Although the emphasis in this absorbing survey is primarily biographical, Hollingdale also discusses major historic
Fundamentals of university mathematics
McGregor, C M; Stothers, W W
2010-01-01
The third edition of this popular and effective textbook provides in one volume a unified treatment of topics essential for first year university students studying for degrees in mathematics. Students of computer science, physics and statistics will also find this book a helpful guide to all the basic mathematics they require. It clearly and comprehensively covers much of the material that other textbooks tend to assume, assisting students in the transition to university-level mathematics.Expertly revised and updated, the chapters cover topics such as number systems, set and functions, differe
Mathematization in introductory physics
Brahmia, Suzanne M.
Mathematization is central to STEM disciplines as a cornerstone of the quantitative reasoning that characterizes these fields. Introductory physics is required for most STEM majors in part so that students develop expert-like mathematization. This dissertation describes coordinated research and curriculum development for strengthening mathematization in introductory physics; it blends scholarship in physics and mathematics education in the form of three papers. The first paper explores mathematization in the context of physics, and makes an original contribution to the measurement of physics students' struggle to mathematize. Instructors naturally assume students have a conceptual mastery of algebra before embarking on a college physics course because these students are enrolled in math courses beyond algebra. This paper provides evidence that refutes the validity of this assumption and categorizes some of the barriers students commonly encounter with quantification and representing ideas symbolically. The second paper develops a model of instruction that can help students progress from their starting points to their instructor's desired endpoints. Instructors recognize that the introductory physics course introduces new ideas at an astonishing rate. More than most physicists realize, however, the way that mathematics is used in the course is foreign to a large portion of class. This paper puts forth an instructional model that can move all students toward better quantitative and physical reasoning, despite the substantial variability of those students' initial states. The third paper describes the design and testing of curricular materials that foster mathematical creativity to prepare students to better understand physics reasoning. Few students enter introductory physics with experience generating equations in response to specific challenges involving unfamiliar quantities and units, yet this generative use of mathematics is typical of the thinking involved in
The Greatest Mathematical Discovery?
Bailey, David H.; Borwein, Jonathan M.
2010-05-12
What mathematical discovery more than 1500 years ago: (1) Is one of the greatest, if not the greatest, single discovery in the field of mathematics? (2) Involved three subtle ideas that eluded the greatest minds of antiquity, even geniuses such as Archimedes? (3) Was fiercely resisted in Europe for hundreds of years after its discovery? (4) Even today, in historical treatments of mathematics, is often dismissed with scant mention, or else is ascribed to the wrong source? Answer: Our modern system of positional decimal notation with zero, together with the basic arithmetic computational schemes, which were discovered in India about 500 CE.
a Discrete Mathematical Model to Simulate Malware Spreading
Del Rey, A. Martin; Sánchez, G. Rodriguez
2012-10-01
With the advent and worldwide development of Internet, the study and control of malware spreading has become very important. In this sense, some mathematical models to simulate malware propagation have been proposed in the scientific literature, and usually they are based on differential equations exploiting the similarities with mathematical epidemiology. The great majority of these models study the behavior of a particular type of malware called computer worms; indeed, to the best of our knowledge, no model has been proposed to simulate the spreading of a computer virus (the traditional type of malware which differs from computer worms in several aspects). In this sense, the purpose of this work is to introduce a new mathematical model not based on continuous mathematics tools but on discrete ones, to analyze and study the epidemic behavior of computer virus. Specifically, cellular automata are used in order to design such model.
Mathematical omnibus thirty lectures on classic mathematics
Fuchs, Dmitry; Fuchs, Dmitry
2007-01-01
The book consists of thirty lectures on diverse topics, covering much of the mathematical landscape rather than focusing on one area. The reader will learn numerous results that often belong to neither the standard undergraduate nor graduate curriculum and will discover connections between classical and contemporary ideas in algebra, combinatorics, geometry, and topology. The reader's effort will be rewarded in seeing the harmony of each subject. The common thread in the selected subjects is their illustration of the unity and beauty of mathematics. Most lectures contain exercises, and solutions or answers are given to selected exercises. A special feature of the book is an abundance of drawings (more than four hundred), artwork by an accomplished artist, and about a hundred portraits of mathematicians. Almost every lecture contains surprises for even the seasoned researcher.
Mathematics for the liberal arts
Bindner, Donald; Hemmeter, Joe
2014-01-01
Presents a clear bridge between mathematics and the liberal arts Mathematics for the Liberal Arts provides a comprehensible and precise introduction to modern mathematics intertwined with the history of mathematical discoveries. The book discusses mathematical ideas in the context of the unfolding story of human thought and highlights the application of mathematics in everyday life. Divided into two parts, Mathematics for the Liberal Arts first traces the history of mathematics from the ancient world to the Middle Ages, then moves on to the Renaissance and finishes with the development of modern mathematics. In the second part, the book explores major topics of calculus and number theory, including problem-solving techniques and real-world applications. This book emphasizes learning through doing, presents a practical approach, and features: A detailed explanation of why mathematical principles are true and how the mathematical processes workNumerous figures and diagrams as well as hundreds of worked example...
Mathematics, anxiety, and the brain.
Moustafa, Ahmed A; Tindle, Richard; Ansari, Zaheda; Doyle, Margery J; Hewedi, Doaa H; Eissa, Abeer
2017-05-24
Given that achievement in learning mathematics at school correlates with work and social achievements, it is important to understand the cognitive processes underlying abilities to learn mathematics efficiently as well as reasons underlying the occurrence of mathematics anxiety (i.e. feelings of tension and fear upon facing mathematical problems or numbers) among certain individuals. Over the last two decades, many studies have shown that learning mathematical and numerical concepts relies on many cognitive processes, including working memory, spatial skills, and linguistic abilities. In this review, we discuss the relationship between mathematical learning and cognitive processes as well as the neural substrates underlying successful mathematical learning and problem solving. More importantly, we also discuss the relationship between these cognitive processes, mathematics anxiety, and mathematics learning disabilities (dyscalculia). Our review shows that mathematical cognition relies on a complex brain network, and dysfunction to different segments of this network leads to varying manifestations of mathematical learning disabilities.
Mathematical Modeling in Mathematics Education: Basic Concepts and Approaches
Erbas, Ayhan Kürsat; Kertil, Mahmut; Çetinkaya, Bülent; Çakiroglu, Erdinç; Alacaci, Cengiz; Bas, Sinem
2014-01-01
Mathematical modeling and its role in mathematics education have been receiving increasing attention in Turkey, as in many other countries. The growing body of literature on this topic reveals a variety of approaches to mathematical modeling and related concepts, along with differing perspectives on the use of mathematical modeling in teaching and…
Mathematical Intelligence and Mathematical Creativity: A Causal Relationship
Tyagi, Tarun Kumar
2017-01-01
This study investigated the causal relationship between mathematical creativity and mathematical intelligence. Four hundred thirty-nine 8th-grade students, age ranged from 11 to 14 years, were included in the sample of this study by random cluster technique on which mathematical creativity and Hindi adaptation of mathematical intelligence test…
Elementary Mathematics Teachers' Perceptions and Lived Experiences on Mathematical Communication
Kaya, Defne; Aydin, Hasan
2016-01-01
Mathematical thinking skills and meaningful mathematical understanding are among the goals of current mathematics education. There is a wide consensus among scholars about the purpose of developing mathematical understanding and higher order thinking skills in students. However, how to develop those skills in classroom settings is an area that…
Using Mathematics in Science: Working with Your Mathematics Department
Lyon, Steve
2014-01-01
Changes to the mathematics and science curriculums are designed to increase rigour in mathematics, and place greater emphasis on mathematical content in science subjects at key stages 3, 4 and 5 (ages 11-18). One way to meet the growing challenge of providing increased emphasis on mathematics in the science curriculum is greater collaboration…
Mathematics Curriculum, the Philosophy of Mathematics and its ...
It is my observation that the current school mathematics curriculum in Ethiopia is not producing competent mathematics students. Many mathematicians in Ethiopia and other part of the world have often expressed grief that the majority of students do not understand mathematical concepts, or do not see why mathematical ...
Mathematical games, abstract games
Neto, Joao Pedro
2013-01-01
User-friendly, visually appealing collection offers both new and classic strategic board games. Includes abstract games for two and three players and mathematical games such as Nim and games on graphs.
Visualization and mathematics III
Polthier, Konrad
2003-01-01
This research book on Mathematical Visualization contains state of the art presentations on visualization problems in mathematics, on fundamental mathematical research in computer graphics, and on software frameworks for the application of visualization to real-world problems. All contributions were written by leading experts in the field and peer-refereed by an international editorial team. The book grew out of the third international workshop "Visualization and Mathematics", which was held from May 22-25, 2002 in Berlin. The themes of the book cover important recent developments on - Geometry and Combinatorics of Meshes - Discrete Vector Fields and Topology - Geometric Modelling - Image Based Visualization - Software Environments and Applications - Education and Communication The variety of topics makes the book a suitable resource for researchers, lecturers, and practitioners; http://www-sfb288.math.tu-berlin.de/vismath/
Refresher Course in Mathematics
at Department of Mathematics, Berhampur University, Berhampur 760007, Orissa ... Applications are invited. from University/College teachers and Researchers interested in ... Pre-requisites: A basic knowledge of analysis, topology, differential ...
Mathematical methods for physicists
Arfken, George B
2005-01-01
This best-selling title provides in one handy volume the essential mathematical tools and techniques used to solve problems in physics. It is a vital addition to the bookshelf of any serious student of physics or research professional in the field. The authors have put considerable effort into revamping this new edition.* Updates the leading graduate-level text in mathematical physics* Provides comprehensive coverage of the mathematics necessary for advanced study in physics and engineering* Focuses on problem-solving skills and offers a vast array of exercises * Clearly illustrates and proves mathematical relationsNew in the Sixth Edition:* Updated content throughout, based on users'' feedback * More advanced sections, including differential forms and the elegant forms of Maxwell''s equations* A new chapter on probability and statistics* More elementary sections have been deleted
Wickerhauser, Mladen Victor
2003-01-01
Mathematics and Multimedia focuses on the mathematics behind multimedia applications. This timely and thoroughly modern text is a rigorous survey of selected results from algebra and analysis, requiring only undergraduate math skills.The topics are `gems' chosen for their usefulness in understanding and creating application software for multimedia signal processing and communication.The book is aimed at a wide audience, including computer science and mathematics majors and those interested in employing mathematics in multimedia design and implementation. For the instructor, the material is divided into six chapters that may be presented in six lecture hours each. Thus, the entire text may be covered in one semester, with time left for examinations and student projects. For the student,there are more than 100 exercises with complete solutions, and numerous example programs in Standard C. Each chapter ends with suggestions for further reading. A companion website provides more insight for both instructors and s...
Applied Mathematics Seminar 1982
1983-01-01
This report contains the abstracts of the lectures delivered at 1982 Applied Mathematics Seminar of the DPD/LCC/CNPq and Colloquy on Applied Mathematics of LCC/CNPq. The Seminar comprised 36 conferences. Among these, 30 were presented by researchers associated to brazilian institutions, 9 of them to the LCC/CNPq, and the other 6 were given by visiting lecturers according to the following distribution: 4 from the USA, 1 from England and 1 from Venezuela. The 1981 Applied Mathematics Seminar was organized by Leon R. Sinay and Nelson do Valle Silva. The Colloquy on Applied Mathematics was held from october 1982 on, being organized by Ricardo S. Kubrusly and Leon R. Sinay. (Author) [pt
Mathematics for operations research
1994-01-01
Effective procedures for mathematical tasks in many fields: resolving linear independence, finding null spaces and factors of matrices; differentiating vectors and matrices by chain rule, many more. Techniques illustrated in examples. 1,300 problems. 1978 edition.
Mathematics for physical chemistry
Mortimer, Robert G
2005-01-01
Mathematics for Physical Chemistry, Third Edition, is the ideal text for students and physical chemists who want to sharpen their mathematics skills. It can help prepare the reader for an undergraduate course, serve as a supplementary text for use during a course, or serve as a reference for graduate students and practicing chemists. The text concentrates on applications instead of theory, and, although the emphasis is on physical chemistry, it can also be useful in general chemistry courses. The Third Edition includes new exercises in each chapter that provide practice in a technique immediately after discussion or example and encourage self-study. The first ten chapters are constructed around a sequence of mathematical topics, with a gradual progression into more advanced material. The final chapter discusses mathematical topics needed in the analysis of experimental data.* Numerous examples and problems interspersed throughout the presentations * Each extensive chapter contains a preview, objectives, and ...
Canuto, Claudio
2015-01-01
The purpose of the volume is to provide a support textbook for a second lecture course on Mathematical Analysis. The contents are organised to suit, in particular, students of Engineering, Computer Science and Physics, all areas in which mathematical tools play a crucial role. The basic notions and methods concerning integral and differential calculus for multivariable functions, series of functions and ordinary differential equations are presented in a manner that elicits critical reading and prompts a hands-on approach to concrete applications. The pedagogical layout echoes the one used in the companion text Mathematical Analysis I. The book’s structure has a specifically-designed modular nature, which allows for great flexibility in the preparation of a lecture course on Mathematical Analysis. The style privileges clarity in the exposition and a linear progression through the theory. The material is organised on two levels. The first, reflected in this book, allows students to grasp the essential ideas, ...
Farlow, Stanley J
2014-01-01
Students and puzzle enthusiasts will get plenty of enjoyment plus some painless mathematical instruction from 28 conundrums, including The Curve That Shook the World, Space Travel in a Wineglass, and Through Cantor's Looking Glass.
Fundamentals of scientific mathematics
Owen, George E
2003-01-01
Offering undergraduates a solid mathematical background (and functioning equally well for independent study), this rewarding, beautifully illustrated text covers geometry and matrices, vector algebra, analytic geometry, functions, and differential and integral calculus. 1961 edition.
Snow, D.R.
1975-01-01
This paper provides mathematicians and other persons interested in energy problems with some ideas of the kinds of mathematics being applied and a few ideas for further investigation both in the relevant mathematics and in mathematical modeling. This paper is not meant to be an extensive bibliography on the subject, but references are provided. The Conference emphasized large scale and economic considerations related to energy rather than specific technologies, but additional mathematical problems arising in current and future technologies are suggested. Several of the papers dealt with linear programming models of large scale systems related to energy. These included economic models, policy models, energy sector models for supply and demand and environmental concerns. One of the economic models utilized variational techniques including such things as the Hamiltonian, the Euler-Lagrange differential equation, transversality and natural boundary conditions
Manin, Yu I
1981-01-01
A bird's eye view of mathematics ; physical quantities, dimensions and constants : the source of numbers in physics ; a drop of milk : observer, observation, observable and unobservable ; space-time as a physical system ; action and symmetry.
Bronshtein, I N; Musiol, Gerhard; Mühlig, Heiner
2015-01-01
This guide book to mathematics contains in handbook form the fundamental working knowledge of mathematics which is needed as an everyday guide for working scientists and engineers, as well as for students. Easy to understand, and convenient to use, this guide book gives concisely the information necessary to evaluate most problems which occur in concrete applications. In the newer editions emphasis was laid on those fields of mathematics that became more important for the formulation and modeling of technical and natural processes, namely Numerical Mathematics, Probability Theory and Statistics, as well as Information Processing. Besides many enhancements and new paragraphs, new sections on Geometric and Coordinate Transformations, Quaternions and Applications, and Lie Groups and Lie Algebras were added for the sixth edition.
particularly to the mathematics decision viz., that of how to optimally combine making, otherwise known as operations evaluations of several experts on nonquan-. --------~-------- ... a short account of how the ratings of sports- persons are arrived ...
Mathematics for electronic technology
Howson, D P
1975-01-01
Mathematics for Electronic Technology is a nine-chapter book that begins with the elucidation of the introductory concepts related to use of mathematics in electronic engineering, including differentiation, integration, partial differentiation, infinite series, vectors, vector algebra, and surface, volume and line integrals. Subsequent chapters explore the determinants, differential equations, matrix analysis, complex variable, topography, graph theory, and numerical analysis used in this field. The use of Fourier method for harmonic analysis and the Laplace transform is also described. The ma
Mathematics and electromagnetism
Rodriguez Danta, M.
2000-01-01
Symbiosis between mathematics and electromagnetism is analyzed in a simple and concise manner by taking a historical perspective. The universal tool character of mathematical models allowed the transfer of models from several branches of physics into the realm of electromagnetism by drawing analogies. The mutual interdependence between covariant formulation and tensor calculus is marked. The paper focuses on the guiding idea of field theory and Maxwell's equations. Likewise, geometrization of interactions in connection with gauge fields is also noted. (Author)
Mathematical foundations of thermodynamics
Giles, R; Stark, M; Ulam, S
2013-01-01
Mathematical Foundations of Thermodynamics details the core concepts of the mathematical principles employed in thermodynamics. The book discusses the topics in a way that physical meanings are assigned to the theoretical terms. The coverage of the text includes the mechanical systems and adiabatic processes; topological considerations; and equilibrium states and potentials. The book also covers Galilean thermodynamics; symmetry in thermodynamics; and special relativistic thermodynamics. The book will be of great interest to practitioners and researchers of disciplines that deal with thermodyn
Landauer, C.; Bellman, K.L.
1996-12-31
In this paper, we study foundational issues that we believe will help us develop a theoretically sound approach to constructing complex systems. The two theoretical approaches that have helped us understand and develop computational systems in the past are mathematics and linguistics. We describe some differences and strengths of the approaches, and propose a research program to combine the richness of linguistic reasoning with the precision of mathematics.
Mathematical Optimiation in Economics
De Finetti, Bruno
2011-01-01
Preface by B. de Finetti.- G.Th. Guilbaud: Les equilibres dans les modeles economiques.-H.W. Kuhn: Locational problems and mathematical programming.- M. Morishima: The multi-sectoral theory of economic growth.- B. Martos, J. Kornai: Experiments in Hungary with industry-wide and economy wide programming.- A. Prekopa: Probability distribution problems concerning stochastic programming problems.- R. Frisch: General principles and mathematical techniques of macroeconomic programming.
[Building mathematics in imagination].
Patras, Frédéric
2015-01-01
The extraordinary quantitative achievements of contemporary science often hide their qualitative dimension. In mathematics, the understanding of fundamental theoretical phenomena we have got today goes much beyond that achieved in previous periods. This also holds when it comes to the theorisation of mathematical practice.Philosophically, these changes remain largely to be properly analyzed. The present article will address this issue from the point of view of Bachelard's epistemology.
International mathematical olympiad
Hanjš, Ž.
1999-01-01
Today mathematical competitions are very popular with primary and secondary school students and there are many countries all around the world where they are regularly organised. There are several rounds and a lot of students are included, especially at the beginning rounds. The best students from the previous round have the right to continue on the higher level of competition. The final level for the secondary school student competitors is the International Mathematical Olympiad (IMO). The te...
Understanding mathematical proof
Taylor, John
2014-01-01
Introduction The need for proof The language of mathematics Reasoning Deductive reasoning and truth Example proofs Logic and ReasoningIntroduction Propositions, connectives, and truth tables Logical equivalence and logical implication Predicates and quantification Logical reasoning Sets and Functions Introduction Sets and membership Operations on setsThe Cartesian product Functions and composite functions Properties of functions The Structure of Mathematical ProofsIntroduction Some proofs dissected An informal framework for proofs Direct proof A more formal framework Finding Proofs Direct proo
Ligomenides, Panos A.
2009-05-01
The power of mathematics is discussed as a way of expressing reasoning, aesthetics and insight in symbolic non-verbal communication. The human culture of discovering mathematical ways of thinking in the enterprise of exploring the understanding of the nature and the evolution of our world through hypotheses, theories and experimental affirmation of the scientific notion of algorithmic and non-algorithmic [`]computation', is examined and commended upon.
New mathematical cuneiform texts
Friberg, Jöran
2016-01-01
This monograph presents in great detail a large number of both unpublished and previously published Babylonian mathematical texts in the cuneiform script. It is a continuation of the work A Remarkable Collection of Babylonian Mathematical Texts (Springer 2007) written by Jöran Friberg, the leading expert on Babylonian mathematics. Focussing on the big picture, Friberg explores in this book several Late Babylonian arithmetical and metro-mathematical table texts from the sites of Babylon, Uruk and Sippar, collections of mathematical exercises from four Old Babylonian sites, as well as a new text from Early Dynastic/Early Sargonic Umma, which is the oldest known collection of mathematical exercises. A table of reciprocals from the end of the third millennium BC, differing radically from well-documented but younger tables of reciprocals from the Neo-Sumerian and Old-Babylonian periods, as well as a fragment of a Neo-Sumerian clay tablet showing a new type of a labyrinth are also discussed. The material is presen...
Boyer, Carl B
1989-01-01
"Boyer and Merzbach distill thousands of years of mathematics into this fascinating chronicle. From the Greeks to Godel, the mathematics is brilliant; the cast of characters is distinguished; the ebb and flow of ideas is everywhere evident. And, while tracing the development of European mathematics, the authors do not overlook the contributions of Chinese, Indian, and Arabic civilizations. Without doubt, this is--and will long remain--a classic one-volume history of mathematics and mathematicians who create it." --William Dunham Author, Journey Through Genius, The Great Theorems of Mathematics "When we read a book like A History of Mathematics, we get the picture of a mounting structure, ever taller and broader and more beautiful and magnificent--and with a foundation, moreover, that is as untainted and as functional now as it was when Thales worked out the first geometrical theorems nearly 26 centuries ago." --From the Foreword by Isaac Asimov "One of the most useful and comprehensive general introductions t...
Nuclear medicine and mathematics
Pedroso de Lima, J.J. [Dept. de Biofisica e Proc. de Imagem, IBILI - Faculdade de Medicina, Coimbra (Portugal)
1996-06-01
The purpose of this review is not to present a comprehensive description of all the mathematical tools used in nuclear medicine, but to emphasize the importance of the mathematical method in nuclear medicine and to elucidate some of the mathematical concepts currently used. We can distinguish three different areas in which mathematical support has been offered to nuclear medicine: Physiology, methodology and data processing. Nevertheless, the boundaries between these areas can be indistinct. It is impossible in a single article to give even an idea of the extent and complexity of the procedures currently usede in nuclear medicine, such as image processing, reconstruction from projections and artificial intelligence. These disciplines do not belong to nuclear medicine: They are already branches of engineering, and my interest will reside simply in revealing a little of the elegance and the fantastic potential of these new `allies` of nuclear medicine. In this review the mathematics of physiological interpretation and methodology are considered together in the same section. General aspects of data-processing methods, including image processing and artificial intelligence, are briefly analysed. The mathematical tools that are most often used to assist the interpretation of biological phenomena in nuclear medicine are considered; these include convolution and deconvolution methods, Fourier analysis, factorial analysis and neural networking. (orig.)
Nuclear medicine and mathematics
Pedroso de Lima, J.J.
1996-01-01
The purpose of this review is not to present a comprehensive description of all the mathematical tools used in nuclear medicine, but to emphasize the importance of the mathematical method in nuclear medicine and to elucidate some of the mathematical concepts currently used. We can distinguish three different areas in which mathematical support has been offered to nuclear medicine: Physiology, methodology and data processing. Nevertheless, the boundaries between these areas can be indistinct. It is impossible in a single article to give even an idea of the extent and complexity of the procedures currently usede in nuclear medicine, such as image processing, reconstruction from projections and artificial intelligence. These disciplines do not belong to nuclear medicine: They are already branches of engineering, and my interest will reside simply in revealing a little of the elegance and the fantastic potential of these new 'allies' of nuclear medicine. In this review the mathematics of physiological interpretation and methodology are considered together in the same section. General aspects of data-processing methods, including image processing and artificial intelligence, are briefly analysed. The mathematical tools that are most often used to assist the interpretation of biological phenomena in nuclear medicine are considered; these include convolution and deconvolution methods, Fourier analysis, factorial analysis and neural networking. (orig.)
Pontrjagin, Lev Semenovič
1984-01-01
Lev Semenovic Pontrjagin (1908) is one of the outstanding figures in 20th century mathematics. In a long career he has made fundamental con tributions to many branches of mathematics, both pure and applied. He has received every honor that a grateful government can bestow. Though in no way constrained to do so, he has through the years taught mathematics courses at Moscow State University. In the year 1975 he set himself the task of writing a series of books on secondary school and beginning university mathematics. In his own words, "I wished to set forth the foundations of higher mathematics in a form that would have been accessible to myself as a lad, but making use of all my experience as a scientist and a teacher, ac cumulated over many years. " The present volume is a translation of the first two out of four moderately sized volumes on this theme planned by Pro fessor Pontrjagin. The book begins at the beginning of modern mathematics, analytic ge ometry in the plane and 3-dimensional space. Refin...
Predicting Success in College Mathematics from High School Mathematics Preparation
Shepley, Richard A.
1983-01-01
The purpose of this study was to develop a model to predict the college mathematics courses a freshman could expect to pass by considering their high school mathematics preparation. The high school information that was used consisted of the student's sex, the student's grade point average in mathematics, the highest level of high school mathematics courses taken, and the number of mathematics courses taken in high school. The high school sample was drawn from graduated Seniors in the State...
Eibinger, Manuel; Zahel, Thomas; Ganner, Thomas; Plank, Harald; Nidetzky, Bernd
2016-01-01
Enzymatic hydrolysis of cellulose involves the spatiotemporally correlated action of distinct polysaccharide chain cleaving activities confined to the surface of an insoluble substrate. Because cellulases differ in preference for attacking crystalline compared to amorphous cellulose, the spatial distribution of structural order across the cellulose surface imposes additional constraints on the dynamic interplay between the enzymes. Reconstruction of total system behavior from single-molecule activity parameters is a longstanding key goal in the field. We have developed a stochastic, cellular automata-based modeling approach to describe degradation of cellulosic material by a cellulase system at single-molecule resolution. Substrate morphology was modeled to represent the amorphous and crystalline phases as well as the different spatial orientations of the polysaccharide chains. The enzyme system model consisted of an internally chain-cleaving endoglucanase (EG) as well as two processively acting, reducing and non-reducing chain end-cleaving cellobiohydrolases (CBHs). Substrate preference (amorphous: EG, CBH II; crystalline: CBH I) and characteristic frequencies for chain cleavage, processive movement, and dissociation were assigned from biochemical data. Once adsorbed, enzymes were allowed to reach surface-exposed substrate sites through "random-walk" lateral diffusion or processive motion. Simulations revealed that slow dissociation of processive enzymes at obstacles obstructing further movement resulted in local jamming of the cellulases, with consequent delay in the degradation of the surface area affected. Exploiting validation against evidence from atomic force microscopy imaging as a unique opportunity opened up by the modeling approach, we show that spatiotemporal characteristics of cellulose surface degradation by the system of synergizing cellulases were reproduced quantitatively at the nanometer resolution of the experimental data. This in turn gave
Mathematical points as didactical ideas
Mogensen, Arne
Mathematics teaching in Denmark was recently recommended better organized in sequences with clear mathematical pedagogical goals and a focus on mathematical points. In this paper I define a mathematical point and inform on coding of transcripts in a video based Danish research study on grade 8 te...
Mathematical Modeling: A Structured Process
Anhalt, Cynthia Oropesa; Cortez, Ricardo
2015-01-01
Mathematical modeling, in which students use mathematics to explain or interpret physical, social, or scientific phenomena, is an essential component of the high school curriculum. The Common Core State Standards for Mathematics (CCSSM) classify modeling as a K-12 standard for mathematical practice and as a conceptual category for high school…
MATHEMATICS EDUCATION FOR LOGISTICS ENGINEERING
BÉLA ILLÉS; GABRIELLA BOGNÁR
2012-01-01
Mathematics is a crucial language in all engineering courses and researches where mathematical modeling, simulation and manipulation are commonly used. Engineering Mathematics courses are considered difficult courses in engineering curricula. This is reflected in engineering students’ performance at the end of each semester for these courses. Our goal is to overview a few questions on mathematics as a core subject of engineering.
A Mathematics Software Database Update.
Cunningham, R. S.; Smith, David A.
1987-01-01
Contains an update of an earlier listing of software for mathematics instruction at the college level. Topics are: advanced mathematics, algebra, calculus, differential equations, discrete mathematics, equation solving, general mathematics, geometry, linear and matrix algebra, logic, statistics and probability, and trigonometry. (PK)
Remedial mathematics for quantum chemistry
Koopman, L.; Brouwer, N.; Heck, A.; Buma, W.J.
2008-01-01
Proper mathematical skills are important for every science course and mathematics-intensive chemistry courses rely on a sound mathematical pre-knowledge. In the first-year quantum chemistry course at this university, it was noticed that many students lack basic mathematical knowledge. To tackle the
Unlu, Melihan; Ertekin, Erhan; Dilmac, Bulent
2017-01-01
The purpose of the research is to investigate the relationships between self-efficacy beliefs toward mathematics, mathematics anxiety and self-efficacy beliefs toward mathematics teaching, mathematics teaching anxiety variables and testing the relationships between these variables with structural equation model. The sample of the research, which…
Measuring Developmental Students' Mathematics Anxiety
Ding, Yanqing
2016-01-01
This study conducted an item-level analysis of mathematics anxiety and examined the dimensionality of mathematics anxiety in a sample of developmental mathematics students (N = 162) by Multi-dimensional Random Coefficients Multinominal Logit Model (MRCMLM). The results indicate a moderately correlated factor structure of mathematics anxiety (r =…
Teacher's Guide to Secondary Mathematics.
Duval County Schools, Jacksonville, FL.
This is a teacher's guide to secondary school mathematics. Developed for use in the Duval County Public Schools, Jacksonville, Florida. Areas of mathematics covered are algebra, analysis, calculus, computer literacy, computer science, geometry, analytic geometry, general mathematics, consumer mathematics, pre-algebra, probability and statistics,…
Discrete Mathematics and Curriculum Reform.
Kenney, Margaret J.
1996-01-01
Defines discrete mathematics as the mathematics necessary to effect reasoned decision making in finite situations and explains how its use supports the current view of mathematics education. Discrete mathematics can be used by curriculum developers to improve the curriculum for students of all ages and abilities. (SLD)
Cellular-based preemption system
Bachelder, Aaron D. (Inventor)
2011-01-01
A cellular-based preemption system that uses existing cellular infrastructure to transmit preemption related data to allow safe passage of emergency vehicles through one or more intersections. A cellular unit in an emergency vehicle is used to generate position reports that are transmitted to the one or more intersections during an emergency response. Based on this position data, the one or more intersections calculate an estimated time of arrival (ETA) of the emergency vehicle, and transmit preemption commands to traffic signals at the intersections based on the calculated ETA. Additional techniques may be used for refining the position reports, ETA calculations, and the like. Such techniques include, without limitation, statistical preemption, map-matching, dead-reckoning, augmented navigation, and/or preemption optimization techniques, all of which are described in further detail in the above-referenced patent applications.
Novel Materials for Cellular Nanosensors
Sasso, Luigi
The monitoring of cellular behavior is useful for the advancement of biomedical diagnostics, drug development and the understanding of a cell as the main unit of the human body. Micro- and nanotechnology allow for the creation of functional devices that enhance the study of cellular dynamics...... modifications for electrochemical nanosensors for the detection of analytes released from cells. Two type of materials were investigated, each pertaining to the two different aspects of such devices: peptide nanostructures were studied for the creation of cellular sensing substrates that mimic in vivo surfaces...... and that offer advantages of functionalization, and conducting polymers were used as electrochemical sensor surface modifications for increasing the sensitivity towards relevant analytes, with focus on the detection of dopamine released from cells via exocytosis. Vertical peptide nanowires were synthesized from...
Admission Control Threshold in Cellular Relay Networks with Power Adjustment
Lee Ki-Dong
2009-01-01
Full Text Available Abstract In the cellular network with relays, the mobile station can benefit from both coverage extension and capacity enhancement. However, the operation complexity increases as the number of relays grows up. Furthermore, in the cellular network with cooperative relays, it is even more complex because of an increased dimension of signal-to-noise ratios (SNRs formed in the cooperative wireless transmission links. In this paper, we propose a new method for admission capacity planning in a cellular network using a cooperative relaying mechanism called decode-and-forward. We mathematically formulate the dropping ratio using the randomness of "channel gain." With this, we formulate an admission threshold planning problem as a simple optimization problem, where we maximize the accommodation capacity (in number of connections subject to two types of constraints. (1 A constraint that the sum of the transmit powers of the source node and relay node is upper-bounded where both nodes can jointly adjust the transmit power. (2 A constraint that the dropping ratio is upper-bounded by a certain threshold value. The simplicity of the problem formulation facilitates its solution in real-time. We believe that the proposed planning method can provide an attractive guideline for dimensioning a cellular relay network with cooperative relays.
Cooperative Handover Management in Dense Cellular Networks
Arshad, Rabe
2017-02-07
Network densification has always been an important factor to cope with the ever increasing capacity demand. Deploying more base stations (BSs) improves the spatial frequency utilization, which increases the network capacity. However, such improvement comes at the expense of shrinking the BSs\\' footprints, which increases the handover (HO) rate and may diminish the foreseen capacity gains. In this paper, we propose a cooperative HO management scheme to mitigate the HO effect on throughput gains achieved via cellular network densification. The proposed HO scheme relies on skipping HO to the nearest BS at some instances along the user\\'s trajectory while enabling cooperative BS service during HO execution at other instances. To this end, we develop a mathematical model, via stochastic geometry, to quantify the performance of the proposed HO scheme in terms of coverage probability and user throughput. The results show that the proposed cooperative HO scheme outperforms the always best connected based association at high mobility. Also, the value of BS cooperation along with handover skipping is quantified with respect to the HO skipping only that has recently appeared in the literature. Particularly, the proposed cooperative HO scheme shows throughput gains of 12% to 27% and 17% on average, when compared to the always best connected and HO skipping only schemes at user velocity ranging from 80 km/h to 160 Km/h, respectively.
Cooperative Handover Management in Dense Cellular Networks
Arshad, Rabe; Elsawy, Hesham; Sorour, Sameh; Al-Naffouri, Tareq Y.; Alouini, Mohamed-Slim
2017-01-01
Network densification has always been an important factor to cope with the ever increasing capacity demand. Deploying more base stations (BSs) improves the spatial frequency utilization, which increases the network capacity. However, such improvement comes at the expense of shrinking the BSs' footprints, which increases the handover (HO) rate and may diminish the foreseen capacity gains. In this paper, we propose a cooperative HO management scheme to mitigate the HO effect on throughput gains achieved via cellular network densification. The proposed HO scheme relies on skipping HO to the nearest BS at some instances along the user's trajectory while enabling cooperative BS service during HO execution at other instances. To this end, we develop a mathematical model, via stochastic geometry, to quantify the performance of the proposed HO scheme in terms of coverage probability and user throughput. The results show that the proposed cooperative HO scheme outperforms the always best connected based association at high mobility. Also, the value of BS cooperation along with handover skipping is quantified with respect to the HO skipping only that has recently appeared in the literature. Particularly, the proposed cooperative HO scheme shows throughput gains of 12% to 27% and 17% on average, when compared to the always best connected and HO skipping only schemes at user velocity ranging from 80 km/h to 160 Km/h, respectively.
Molecular processes in cellular arsenic metabolism
Thomas, David J.
2007-01-01
Elucidating molecular processes that underlie accumulation, metabolism and binding of iAs and its methylated metabolites provides a basis for understanding the modes of action by which iAs acts as a toxin and a carcinogen. One approach to this problem is to construct a conceptual model that incorporates available information on molecular processes involved in the influx, metabolism, binding and efflux of arsenicals in cells. This conceptual model is initially conceived as a non-quantitative representation of critical molecular processes that can be used as a framework for experimental design and prediction. However, with refinement and incorporation of additional data, the conceptual model can be expressed in mathematical terms and should be useful for quantitative estimates of the kinetic and dynamic behavior of iAs and its methylated metabolites in cells. Development of a quantitative model will be facilitated by the availability of tools and techniques to manipulate molecular processes underlying transport of arsenicals across cell membranes or expression and activity of enzymes involved in methylation of arsenicals. This model of cellular metabolism might be integrated into more complex pharmacokinetic models for systemic metabolism of iAs and its methylated metabolites. It may also be useful in development of biologically based dose-response models describing the toxic and carcinogenic actions of arsenicals
Cellular structures with interconnected microchannels
Shaefer, Robert Shahram; Ghoniem, Nasr M.; Williams, Brian
2018-01-30
A method for fabricating a cellular tritium breeder component includes obtaining a reticulated carbon foam skeleton comprising a network of interconnected ligaments. The foam skeleton is then melt-infiltrated with a tritium breeder material, for example, lithium zirconate or lithium titanate. The foam skeleton is then removed to define a cellular breeder component having a network of interconnected tritium purge channels. In an embodiment the ligaments of the foam skeleton are enlarged by adding carbon using chemical vapor infiltration (CVI) prior to melt-infiltration. In an embodiment the foam skeleton is coated with a refractory material, for example, tungsten, prior to melt infiltration.
DISCRETE MATHEMATICS/NUMBER THEORY
Mrs. Manju Devi*
2017-01-01
Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics such as integers, graphs, and statements do not vary smoothly in this way, but have distinct, separated values. Discrete mathematics therefore excludes topics in "continuous mathematics" such as calculus and analysis. Discrete objects can often be enumerated by ...
Mathematical problems for chemistry students
Pota, Gyorgy
2011-01-01
Mathematical Problems for Chemistry Students has been compiled and written (a) to help chemistrystudents in their mathematical studies by providing them with mathematical problems really occurring in chemistry (b) to help practising chemists to activate their applied mathematical skills and (c) to introduce students and specialistsof the chemistry-related fields (physicists, mathematicians, biologists, etc.) intothe world of the chemical applications.Some problems of the collection are mathematical reformulations of those in the standard textbooks of chemistry, others we
Finite mathematics models and applications
Morris, Carla C
2015-01-01
Features step-by-step examples based on actual data and connects fundamental mathematical modeling skills and decision making concepts to everyday applicability Featuring key linear programming, matrix, and probability concepts, Finite Mathematics: Models and Applications emphasizes cross-disciplinary applications that relate mathematics to everyday life. The book provides a unique combination of practical mathematical applications to illustrate the wide use of mathematics in fields ranging from business, economics, finance, management, operations research, and the life and social sciences.
Mathematical structures for computer graphics
Janke, Steven J
2014-01-01
A comprehensive exploration of the mathematics behind the modeling and rendering of computer graphics scenes Mathematical Structures for Computer Graphics presents an accessible and intuitive approach to the mathematical ideas and techniques necessary for two- and three-dimensional computer graphics. Focusing on the significant mathematical results, the book establishes key algorithms used to build complex graphics scenes. Written for readers with various levels of mathematical background, the book develops a solid foundation for graphics techniques and fills in relevant grap
Mathematics education a spectrum of work in mathematical sciences departments
Hsu, Pao-sheng; Pollatsek, Harriet
2016-01-01
Many in the mathematics community in the U.S. are involved in mathematics education in various capacities. This book highlights the breadth of the work in K-16 mathematics education done by members of US departments of mathematical sciences. It contains contributions by mathematicians and mathematics educators who do work in areas such as teacher education, quantitative literacy, informal education, writing and communication, social justice, outreach and mentoring, tactile learning, art and mathematics, ethnomathematics, scholarship of teaching and learning, and mathematics education research. Contributors describe their work, its impact, and how it is perceived and valued. In addition, there is a chapter, co-authored by two mathematicians who have become administrators, on the challenges of supporting, evaluating, and rewarding work in mathematics education in departments of mathematical sciences. This book is intended to inform the readership of the breadth of the work and to encourage discussion of its val...
Gaber, David; Schlimm, Dirk
2015-01-01
Mathematics is a powerful tool for describing and developing our knowledge of the physical world. It informs our understanding of subjects as diverse as music, games, science, economics, communications protocols, and visual arts. Mathematical thinking has its roots in the adaptive behavior of living creatures: animals must employ judgments about quantities and magnitudes in the assessment of both threats (how many foes) and opportunities (how much food) in order to make effective decisions, and use geometric information in the environment for recognizing landmarks and navigating environments. Correspondingly, cognitive systems that are dedicated to the processing of distinctly mathematical information have developed. In particular, there is evidence that certain core systems for understanding different aspects of arithmetic as well as geometry are employed by humans and many other animals. They become active early in life and, particularly in the case of humans, develop through maturation. Although these core systems individually appear to be quite limited in application, in combination they allow for the recognition of mathematical properties and the formation of appropriate inferences based upon those properties. In this overview, the core systems, their roles, their limitations, and their interaction with external representations are discussed, as well as possibilities for how they can be employed together to allow us to reason about more complex mathematical domains. © 2015 John Wiley & Sons, Ltd.
Cellular uptake of metallated cobalamins
Tran, Mai Thanh Quynh; Stürup, Stefan; Lambert, Ian Henry
2016-01-01
Cellular uptake of vitamin B12-cisplatin conjugates was estimated via detection of their metal constituents (Co, Pt, and Re) by inductively coupled plasma mass spectrometry (ICP-MS). Vitamin B12 (cyano-cob(iii)alamin) and aquo-cob(iii)alamin [Cbl-OH2](+), which differ in the β-axial ligands (CN...
Repaglinide at a cellular level
Krogsgaard Thomsen, M; Bokvist, K; Høy, M
2002-01-01
To investigate the hormonal and cellular selectivity of the prandial glucose regulators, we have undertaken a series of experiments, in which we characterised the effects of repaglinide and nateglinide on ATP-sensitive potassium ion (KATP) channel activity, membrane potential and exocytosis in ra...
Cellular automaton for surface reactions
Pechatnikov, E L [AN SSSR, Chernogolovka (Russian Federation). Otdelenie Inst. Khimicheskoj Fiziki; Frankowicz, A; Danielak, R [Uniwersytet Jagiellonski, Cracow (Poland)
1994-06-01
A new algorithm which overcomes some specific difficulties arising in modeling of heterogeneous catalytic processes by cellular automata (CA) technique is proposed. The algorithm was tested with scheme introduced by Ziff, Gulari and Barshad and showed a good agreement with their results. The problem of the physical adequacy and interpretation of the algorithm was discussed. (author). 10 refs, 4 figs.
Cellular Automata and the Humanities.
Gallo, Ernest
1994-01-01
The use of cellular automata to analyze several pre-Socratic hypotheses about the evolution of the physical world is discussed. These hypotheses combine characteristics of both rigorous and metaphoric language. Since the computer demands explicit instructions for each step in the evolution of the automaton, such models can reveal conceptual…
Cellular buckling in long structures
Hunt, G.W.; Peletier, M.A.; Champneys, A.R.; Woods, P.D.; Wadee, M.A.; Budd, C.J.; Lord, G.J.
2000-01-01
A long structural system with an unstable (subcritical)post-buckling response that subsequently restabilizes typically deformsin a cellular manner, with localized buckles first forming and thenlocking up in sequence. As buckling continues over a growing number ofcells, the response can be described
Hadley, Kristin M.; Dorward, Jim
2011-01-01
Many elementary teachers have been found to have high levels of mathematics anxiety but the impact on student achievement was unknown. Elementary teachers (N = 692) completed the modified Mathematics Anxiety Rating Scale-Revised (Hopko, 2003) along with a questionnaire probing anxiety about teaching mathematics and current mathematics instructional practices. Student mathematics achievement data were collected for the classrooms taught by the teachers. A positive relationship was found betwee...
A mathematical medley fifty easy pieces on mathematics
Szpiro, George G
2010-01-01
Szpiro's book provides a delightful, well-written, eclectic selection of mathematical tidbits that makes excellent airplane reading for anyone with an interest in mathematics, regardless of their mathematical background. Excellent gift material. -Keith Devlin, Stanford University, author of The Unfinished Game and The Language of Mathematics It is great to have collected in one volume the many varied, insightful and often surprising mathematical stories that George Szpiro has written in his mathematical columns for the newspapers through the years. -Marcus du Sautoy, Oxford University, author
Kinetic theory approach to modeling of cellular repair mechanisms under genome stress.
Jinpeng Qi
Full Text Available Under acute perturbations from outer environment, a normal cell can trigger cellular self-defense mechanism in response to genome stress. To investigate the kinetics of cellular self-repair process at single cell level further, a model of DNA damage generating and repair is proposed under acute Ion Radiation (IR by using mathematical framework of kinetic theory of active particles (KTAP. Firstly, we focus on illustrating the profile of Cellular Repair System (CRS instituted by two sub-populations, each of which is made up of the active particles with different discrete states. Then, we implement the mathematical framework of cellular self-repair mechanism, and illustrate the dynamic processes of Double Strand Breaks (DSBs and Repair Protein (RP generating, DSB-protein complexes (DSBCs synthesizing, and toxins accumulating. Finally, we roughly analyze the capability of cellular self-repair mechanism, cellular activity of transferring DNA damage, and genome stability, especially the different fates of a certain cell before and after the time thresholds of IR perturbations that a cell can tolerate maximally under different IR perturbation circumstances.
Kinetic theory approach to modeling of cellular repair mechanisms under genome stress.
Qi, Jinpeng; Ding, Yongsheng; Zhu, Ying; Wu, Yizhi
2011-01-01
Under acute perturbations from outer environment, a normal cell can trigger cellular self-defense mechanism in response to genome stress. To investigate the kinetics of cellular self-repair process at single cell level further, a model of DNA damage generating and repair is proposed under acute Ion Radiation (IR) by using mathematical framework of kinetic theory of active particles (KTAP). Firstly, we focus on illustrating the profile of Cellular Repair System (CRS) instituted by two sub-populations, each of which is made up of the active particles with different discrete states. Then, we implement the mathematical framework of cellular self-repair mechanism, and illustrate the dynamic processes of Double Strand Breaks (DSBs) and Repair Protein (RP) generating, DSB-protein complexes (DSBCs) synthesizing, and toxins accumulating. Finally, we roughly analyze the capability of cellular self-repair mechanism, cellular activity of transferring DNA damage, and genome stability, especially the different fates of a certain cell before and after the time thresholds of IR perturbations that a cell can tolerate maximally under different IR perturbation circumstances.
Mathematical methods in engineering
Machado, José
2014-01-01
This book presents a careful selection of the contributions presented at the Mathematical Methods in Engineering (MME10) International Symposium, held at the Polytechnic Institute of Coimbra- Engineering Institute of Coimbra (IPC/ISEC), Portugal, October 21-24, 2010. The volume discusses recent developments about theoretical and applied mathematics toward the solution of engineering problems, thus covering a wide range of topics, such as: Automatic Control, Autonomous Systems, Computer Science, Dynamical Systems and Control, Electronics, Finance and Economics, Fluid Mechanics and Heat Transfer, Fractional Mathematics, Fractional Transforms and Their Applications, Fuzzy Sets and Systems, Image and Signal Analysis, Image Processing, Mechanics, Mechatronics, Motor Control and Human Movement Analysis, Nonlinear Dynamics, Partial Differential Equations, Robotics, Acoustics, Vibration and Control, and Wavelets.
Mathematics difficulties & classroom leadership
Schmidt, Maria Christina Secher
2016-01-01
This article investigates possible links between inclusion, students, for whom mathematics is extensively difficult, and classroom leadership through a case study on teaching strategies and student participation in four classrooms at two different primary schools in Denmark. Three sets of results...... are presented: 1) descriptions of the teachers’ classroom leadership to include all their students in the learning community, 2) the learning community produced by stated and practiced rules for teaching and learning behavior, 3) the classroom behavior of students who experience difficulties with mathematics....... The findings suggest that the teachers’ pedagogical choices and actions support an active learning environment for students in diverse learning needs, and that the teachers practise dimensions of inclusive classroom leadership that are known to be successful for teaching mathematics to all students. Despite...
Advances in mathematical economics
Yamazaki, Akira
2005-01-01
A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories. The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research. The editorial board of this series comprises the following prominent economists and mathematicians: Managing Editors: S. Kusuoka (Univ. Tokyo), T. Maruyama (Keio Univ.). Editors: R. Anderson (U.C. Berkeley), C. Castaing (Univ. Montpellier), F.H. Clarke (Univ. Lyon I), G. Debreu (U.C. Berkeley), E. Dierker (Univ. Vienna), D. Duffie (Stanford Univ.), L.C. Evans (U.C. Berkeley), T. Fujimoto (Okayama Univ.), J.-M. Grandmont...
Mathematics for sustainability
Roe, John; Jamshidi, Sara
2018-01-01
Designed for the 21st century classroom, this textbook poses, refines, and analyzes questions of sustainability in a quantitative environment. Building mathematical knowledge in the context of issues relevant to every global citizen today, this text takes an approach that empowers students of all disciplines to understand and reason with quantitative information. Whatever conclusions may be reached on a given topic, this book will prepare the reader to think critically about their own and other people’s arguments and to support them with careful, mathematical reasoning. Topics are grouped in themes of measurement, flow, connectivity, change, risk, and decision-making. Mathematical thinking is at the fore throughout, as students learn to model sustainability on local, regional, and global scales. Exercises emphasize concepts, while projects build and challenge communication skills. With no prerequisites beyond high school algebra, instructors will find this book a rich resource for engaging all majors in the...
Mathematical grammar of biology
Yamagishi, Michel Eduardo Beleza
2017-01-01
This seminal, multidisciplinary book shows how mathematics can be used to study the first principles of DNA. Most importantly, it enriches the so-called “Chargaff’s grammar of biology” by providing the conceptual theoretical framework necessary to generalize Chargaff’s rules. Starting with a simple example of DNA mathematical modeling where human nucleotide frequencies are associated to the Fibonacci sequence and the Golden Ratio through an optimization problem, its breakthrough is showing that the reverse, complement and reverse-complement operators defined over oligonucleotides induce a natural set partition of DNA words of fixed-size. These equivalence classes, when organized into a matrix form, reveal hidden patterns within the DNA sequence of every living organism. Intended for undergraduate and graduate students both in mathematics and in life sciences, it is also a valuable resource for researchers interested in studying invariant genomic properties.
Mathematical tools for physicists
Trigg, G.L.
2005-01-01
Mathematical Tools for Physisists is a unique collection of 18 review articles, each one written by a renowned expert of its field. Their professional style will be beneficial for advanced students as well as for the scientist at work. The first may find a comprehensive introduction while the latter use it as a quick reference. Great attention was paid to ensuring fast access to the information, and each carefully reviewed article includes a glossary of terms and a guide to further reading. The contributions range from fundamental methods right up to the latest applications, including: - Algebraic Methods - Analytic Methods - Fourier and Other Mathematical Transforms - Fractal Geometry - Geometrical Methods - Green's Functions - Group Theory - Mathematical Modeling - Monte Carlo Methods - Numerical Methods - Perturbation Methods - Quantum Computation - Quantum Logic - Special Functions - Stochastic Processes - Symmetries and Conservation Laws - Topology - Variational Methods. (orig.)
Basic mathematics for biochemists
Cornish-Bowden, Athel
1981-01-01
Some teachers of biochemistry think it positively beneficial for students to struggle with difficult mathematics. I do not number myself among these people, although I have derived much personal pleasure from the study of mathematics and from applying it to problems that interest me in biochemistry. On the contrary, I think that students choose courses in biochemistry out of interest in biochemistry and that they should not be encumbered with more mathematics than is absolutely required for a proper understanding of biochemistry. This of course includes physical chemistry, because a biochemist ignorant of physical chemistry is no biochemist. I have been guided by these beliefs in writing this book. I have laid heavy emphasis on those topics, such as the use of logarithms, that play an important role in biochemistry and often cause problems in teaching; I have ignored others, such as trigonometry, that one can manage without. The proper treatment of statistics has been more difficult to decide. Although it cle...
Principles of mathematical modeling
Dym, Clive
2004-01-01
Science and engineering students depend heavily on concepts of mathematical modeling. In an age where almost everything is done on a computer, author Clive Dym believes that students need to understand and "own" the underlying mathematics that computers are doing on their behalf. His goal for Principles of Mathematical Modeling, Second Edition, is to engage the student reader in developing a foundational understanding of the subject that will serve them well into their careers. The first half of the book begins with a clearly defined set of modeling principles, and then introduces a set of foundational tools including dimensional analysis, scaling techniques, and approximation and validation techniques. The second half demonstrates the latest applications for these tools to a broad variety of subjects, including exponential growth and decay in fields ranging from biology to economics, traffic flow, free and forced vibration of mechanical and other systems, and optimization problems in biology, structures, an...
Frontiers in mathematical biology
1994-01-01
Volume 100, which is the final volume of the LNBM series serves to commemorate the acievements in two decades of this influential collection of books in mathematical biology. The contributions, by the leading mathematical biologists, survey the state of the art in the subject, and offer speculative, philosophical and critical analyses of the key issues confronting the field. The papers address fundamental issues in cell and molecular biology, organismal biology, evolutionary biology, population ecology, community and ecosystem ecology, and applied biology, plus the explicit and implicit mathematical challenges. Cross-cuttting issues involve the problem of variation among units in nonlinear systems, and the related problems of the interactions among phenomena across scales of space, time and organizational complexity.
Bird, John
2014-01-01
Introductory mathematics written specifically for students new to engineering Now in its sixth edition, Basic Engineering Mathematics is an established textbook that has helped thousands of students to succeed in their exams. John Bird's approach is based on worked examples and interactive problems. This makes it ideal for students from a wide range of academic backgrounds as the student can work through the material at their own pace. Mathematical theories are explained in a straightforward manner, being supported by practical engineering examples and applications in order to ensure that readers can relate theory to practice. The extensive and thorough topic coverage makes this an ideal text for introductory level engineering courses. This title is supported by a companion website with resources for both students and lecturers, including lists of essential formulae, multiple choice tests, full solutions for all 1,600 further questions contained within the practice exercises, and biographical information on t...
Persian architecture and mathematics
2012-01-01
This volulme features eight original papers dedicated to the theme “Persian Architecture and Mathematics,” guest edited by Reza Sarhangi. All papers were approved through a rigorous process of blind peer review and edited by an interdisciplinary scientific editorial committee. Topics range from symmetry in ancient Persian architecture to the elaborate geometric patterns and complex three-dimensional structures of standing monuments of historical periods, from the expression of mathematical ideas to architectonic structures, and from decorative ornament to the representation of modern group theory and quasi-crystalline patterns. The articles discuss unique monuments Persia, including domed structures and two-dimensional patterns, which have received significant scholarly attention in recent years. This book is a unique contribution to studies of Persian architecture in relation to mathematics.
Herbart's mathematical psychology.
Boudewijnse, G J; Murray, D J; Bandomir, C A
1999-08-01
J.F. Herbart (1824/1890b) provided a mathematical theory about how mental ideas (Vorstellungen) in consciousness at Time 1 (T1) could compete, possibly driving 1 or more Vorstellungen below a threshold of consciousness. At T1 a Vorstellung A could also fuse with another, B. If at a later T2, A resurfaced into consciousness, it could help B to re-resurface into consciousness. This article describes the historical and mathematical background of Herbart's theory, outlines the mathematical theory itself with the aid of computer graphics, and argues that the theory can be applied to the modern problem of predicting recognition latencies in short-term memory (Sternberg's task; Sternberg, 1966)
Zorich, Vladimir A
2015-01-01
VLADIMIR A. ZORICH is professor of mathematics at Moscow State University. His areas of specialization are analysis, conformal geometry, quasiconformal mappings, and mathematical aspects of thermodynamics. He solved the problem of global homeomorphism for space quasiconformal mappings. He holds a patent in the technology of mechanical engineering, and he is also known by his book Mathematical Analysis of Problems in the Natural Sciences . This second English edition of a very popular two-volume work presents a thorough first course in analysis, leading from real numbers to such advanced topics as differential forms on manifolds; asymptotic methods; Fourier, Laplace, and Legendre transforms; elliptic functions; and distributions. Especially notable in this course are the clearly expressed orientation toward the natural sciences and the informal exploration of the essence and the roots of the basic concepts and theorems of calculus. Clarity of exposition is matched by a wealth of instructive exercises, problems...
Mathematical olympiad challenges
Andreescu, Titu
2000-01-01
Mathematical Olympiad Challenges is a rich collection of problems put together by two experienced and well-known professors and coaches of the U.S. International Mathematical Olympiad Team. Hundreds of beautiful, challenging, and instructive problems from algebra, geometry, trigonometry, combinatorics, and number theory were selected from numerous mathematical competitions and journals. An important feature of the work is the comprehensive background material provided with each grouping of problems. The problems are clustered by topic into self-contained sections with solutions provided separately. All sections start with an essay discussing basic facts and one or two representative examples. A list of carefully chosen problems follows and the reader is invited to take them on. Additionally, historical insights and asides are presented to stimulate further inquiry. The emphasis throughout is on encouraging readers to move away from routine exercises and memorized algorithms toward creative solutions to open-e...
Heath, Thomas
2015-01-01
Originally published in 1949. This meticulously researched book presents a comprehensive outline and discussion of Aristotle's mathematics with the author's translations of the greek. To Aristotle, mathematics was one of the three theoretical sciences, the others being theology and the philosophy of nature (physics). Arranged thematically, this book considers his thinking in relation to the other sciences and looks into such specifics as squaring of the circle, syllogism, parallels, incommensurability of the diagonal, angles, universal proof, gnomons, infinity, agelessness of the universe, surface of water, meteorology, metaphysics and mechanics such as levers, rudders, wedges, wheels and inertia. The last few short chapters address 'problems' that Aristotle posed but couldn't answer, related ethics issues and a summary of some short treatises that only briefly touch on mathematics.
Engineering mathematics pocket book
Bird, John
2008-01-01
This compendium of essential formulae, definitions, tables and general information provides the mathematical information required by students, technicians, scientists and engineers in day-to-day engineering practice. A practical and versatile reference source, now in its fourth edition, the layout has been changed and the book has been streamlined to ensure the information is even more quickly and readily available - making it a handy companion on-site, in the office as well as for academic study. It also acts as a practical revision guide for those undertaking BTEC Nationals, Higher Nationals and NVQs, where engineering mathematics is an underpinning requirement of the course.All the essentials of engineering mathematics - from algebra, geometry and trigonometry to logic circuits, differential equations and probability - are covered, with clear and succinct explanations and illustrated with over 300 line drawings and 500 worked examples based in real-world application. The emphasis throughout the book is on ...
Perception determinants in learning mathematics
Mokhtar, Siti Fairus; Ali, Noor Rasidah; Rashid, Nurazlina Abdul
2015-05-01
This article described a statistical study of students' perception in mathematics. The objective of this study is to identify factors related to perception about learning mathematics among non mathematics' student. This study also determined the relationship between of these factors among non mathematics' student. 43 items questionnaires were distributed to one hundred students in UiTM Kedah who enrolled in the Business Mathematics course. These items were measured by using a semantic scale with the following anchors: 1 = strongly disagree to 7 = strongly agree. A factor analysis of respondents were identified into five factors that influencing the students' perception in mathematics. In my study, factors identified were attitude, interest, role of the teacher, role of peers and usefulness of mathematics that may relate to the perception about learning mathematics among non mathematics' student.
Mathematics for the liberal arts
Brown, Jason I
2014-01-01
The Math in Your Life Health, Safety, and Mathematics Found in Translation The Essentials of Conversion Making Sense of Your World with Statistics Summarizing Data with a Few Good Numbers Estimating Unknowns Leading You Down the Garden Path with Statistics Visualizing with Mathematics Seeing Data A Graph Is Worth a Thousand Words Money and Risk Money - Now or Later Risk Taking and Probability The Life in Your Math! Deciding to Make the Best Decisions Making the Right Choices for You Game Theory - Coming Out on Top Making Joint Decisions Art Imitating Math The Math that Makes the Art Believing What You See (or Not) The Mathematics of Sound (and the Sound of Mathematics) The Mathematics of Listening The Mathematics of Composing Solving Musical Mysteries with MSI (Math Scene Investigations) Late Night Mathematics - Humor and Philosophy Laughing with Mathematics The Limits of Mathematics Bibliography Index Review questions appear at the end of each chapter.
Agrachev, A.A.
2002-01-01
This volume is based on the lecture notes of the minicourses given in the frame of the school on Mathematical Control Theory held at the Abdus Salam ICTP from 3 to 28 September 2001. Mathematical Control Theory is a rapidly growing field which provides strict theoretical and computational tools for dealing with problems arising in electrical and aerospace engineering, automatics, robotics, applied chemistry, and biology etc. Control methods are also involved in questions pertaining to the development of countries in the South, such as wastewater treatment, agronomy, epidemiology, population dynamics, control of industrial and natural bio-reactors. Since most of these natural processes are highly nonlinear, the tools of nonlinear control are essential for the modelling and control of such processes. At present regular courses in Mathematical Control Theory are rarely included in the curricula of universities, and very few researchers receive enough background in the field. Therefore it is important to organize specific activities in the form of schools to provide the necessary background for those embarking on research in this field. The school at the Abdus Salam ICTP consisted of several minicourses intended to provide an introduction to various topics of Mathematical Control Theory, including Linear Control Theory (finite and infinite-dimensional), Nonlinear Control, and Optimal Control. The last week of the school was concentrated on applications of Mathematical Control Theory, in particular, those which are important for the development of non-industrialized countries. The school was intended primarily for mathematicians and mathematically oriented engineers at the beginning of their career. The typical participant was expected to be a graduate student or young post-doctoral researcher interested in Mathematical Control Theory. It was assumed that participants have sufficient background in Ordinary Differential Equations and Advanced Calculus. The volume
Mathematical analysis fundamentals
Bashirov, Agamirza
2014-01-01
The author's goal is a rigorous presentation of the fundamentals of analysis, starting from elementary level and moving to the advanced coursework. The curriculum of all mathematics (pure or applied) and physics programs include a compulsory course in mathematical analysis. This book will serve as can serve a main textbook of such (one semester) courses. The book can also serve as additional reading for such courses as real analysis, functional analysis, harmonic analysis etc. For non-math major students requiring math beyond calculus, this is a more friendly approach than many math-centric o
Concepts of modern mathematics
Stewart, Ian
1995-01-01
Some years ago, ""new math"" took the country's classrooms by storm. Based on the abstract, general style of mathematical exposition favored by research mathematicians, its goal was to teach students not just to manipulate numbers and formulas, but to grasp the underlying mathematical concepts. The result, at least at first, was a great deal of confusion among teachers, students, and parents. Since then, the negative aspects of ""new math"" have been eliminated and its positive elements assimilated into classroom instruction.In this charming volume, a noted English mathematician uses humor an
Computational mathematics in China
Shi, Zhong-Ci
1994-01-01
This volume describes the most significant contributions made by Chinese mathematicians over the past decades in various areas of computational mathematics. Some of the results are quite important and complement Western developments in the field. The contributors to the volume range from noted senior mathematicians to promising young researchers. The topics include finite element methods, computational fluid mechanics, numerical solutions of differential equations, computational methods in dynamical systems, numerical algebra, approximation, and optimization. Containing a number of survey articles, the book provides an excellent way for Western readers to gain an understanding of the status and trends of computational mathematics in China.
Agrachev, A A [Steklov Mathematical Institute, Moscow (Russian Federation); SISSA, Trieste [Italy; ed.
2002-07-15
This volume is based on the lecture notes of the minicourses given in the frame of the school on Mathematical Control Theory held at the Abdus Salam ICTP from 3 to 28 September 2001. Mathematical Control Theory is a rapidly growing field which provides strict theoretical and computational tools for dealing with problems arising in electrical and aerospace engineering, automatics, tics, applied chemistry, and biology etc. Control methods are also involved in questions pertaining to the development of countries in the South, such as wastewater treatment, agronomy, epidemiology, population dynamics, control of industrial and natural bio-reactors. Since most of these natural processes are highly nonlinear, the tools of nonlinear control are essential for the modelling and control of such processes. At present regular courses in Mathematical Control Theory are rarely included in the curricula of universities, and very few researchers receive enough background in the field. Therefore it is important to organize specific activities in the form of schools to provide the necessary background for those embarking on research in this field. The school at the Abdus Salam ICTP consisted of several minicourses intended to provide an introduction to various topics of Mathematical Control Theory, including Linear Control Theory (finite and infinite-dimensional), Nonlinear Control, and Optimal Control. The last week of the school was concentrated on applications of Mathematical Control Theory, in particular, those which are important for the development of non-industrialized countries. The school was intended primarily for mathematicians and mathematically oriented engineers at the beginning of their career. The typical participant was expected to be a graduate student or young post-doctoral researcher interested in Mathematical Control Theory. It was assumed that participants have sufficient background in Ordinary Differential Equations and Advanced Calculus. The volume contains
Mathematics Education: For Whom?
Mesquita, Mônica
2009-01-01
To rethink about our role as researchers of the mathematics education pro- cess could be a way to think about the relation between for what and why mathematics education exists. Some thoughts, that grew from my inner dia- logues as a researcher, teacher, student, and mother that I am, were devel- oped within practices inside multiple systems in which I was engaged, bring- ing some questions that became a paper from the necessity for sharing them in the Discussion Group 3 of the ICME environment
Mathematical models in radiogeochronology
Abril, J.M.; Garcia Leon, M.
1991-01-01
The study of activity vs. depth profiles in sediment cores of some man-made and natural ocurring radionuclides have shown to be a poweful tool for dating purposes. Nevertheless, in most cases, an adecuate interpretation of such profiles requires mathematical models. In this paper, by considering the sediment as a continuum, a general equation for diffusion of radionuclides through it is obtained. Consequentely, some previously published dating models are found to be particular solutions of such general advenction-diffusion problem. Special emphasis is given to the mathematical treatment of compactation effect and time dependent problems. (author)
Mathematical Astronomy in India
Plofker, Kim
Astronomy in South Asia's Sanskrit tradition, apparently originating in simple calendric computations regulating the timing of ancient ritual practices, expanded over the course of two or three millennia to include detailed spherical models, an endless variety of astrological systems, and academic mathematics in general. Assimilating various technical models, methods, and genres from the astronomy of neighboring cultures, Indian astronomers created new forms that were in turn borrowed by their foreign counterparts. Always recognizably related to the main themes of Eurasian geocentric mathematical astronomy, Indian astral science nonetheless maintained its culturally distinct character until Keplerian heliocentrism and Newtonian mechanics replaced it in colonial South Asia's academic mainstream.
Hartimo, Mirja
2010-01-01
During Edmund Husserl,s lifetime, modern logic and mathematics rapidly developed toward their current outlook and Husserl,s writings can be fruitfully compared and contrasted with both 19th century figures (Boole, Schroder, Weierstrass) as well as the 20th century characters (Heyting, Zermelo, Godel). Besides the more historical studies, the internal ones on Husserl alone and the external ones attempting to clarify his role in the more general context of the developing mathematics and logic, Husserl,s phenomenology offers also a systematically rich but little researched area of investigation.
Mathematical foundations of elasticity
Marsden, Jerrold E
1994-01-01
This advanced-level study approaches mathematical foundations of three-dimensional elasticity using modern differential geometry and functional analysis. It is directed to mathematicians, engineers and physicists who wish to see this classical subject in a modern setting with examples of newer mathematical contributions. Prerequisites include a solid background in advanced calculus and the basics of geometry and functional analysis.The first two chapters cover the background geometry ― developed as needed ― and use this discussion to obtain the basic results on kinematics and dynamics of con
Gaal, Lisl
2017-01-01
Embark on a playful mathematical tour, aided by Lisl Gaal's illustrations of familiar scenes and whimsical triggers for the imagination. Along the way, find fruit stands arranged using polynomial multiplication, checkerboard tablecloths sewed with patterns of primes in a two-dimensional number system, and deceptive cats revealing that simple counting is not always so simple. Grasping the mathematics in this book requires only a basic background in algebra and geometry, so while the ideas can be understood and enjoyed at a variety of levels, it is recommended for ages 13-99. Touching on topics in current research, this is a book to read and revisit, gaining new insights each time.
Insights into teaching mathematics
Orton, Anthony
2004-01-01
Providing essential guidance and background information about teaching mathematics, this book is intended particularly for teachers who do not regard themselves as specialists in mathematics. It deals with issues of learning and teaching, including the delivery of content and the place of problems and investigations. Difficulties which pupils encounter in connection with language and symbols form important sections of the overall discussion of how to enhance learning. The curriculum is considered in brief under the headings of number, algebra, shape and space, and data handling, and special at
Mathematics for the environment
Walter, Martin
2011-01-01
MATHEMATICS IS CONNECTED TO EVERYTHING ELSEEarth's Climate and Some Basic Principles One of the Greatest Crimes of the 20th Century Feedback Edison's Algorithm: Listening to Nature's Feedback Fuzzy Logic, Filters, the Bigger Picture Principle Consequences of the Crime: Suburbia's Topology A Toxic Consequence of the Crime Hubbert's Peak and the End of Cheap Oil Resource Wars: Oil and Water The CO2 Greenhouse Law of Svante ArrheniusEconomic Instability: Ongoing Causes Necessary Conditions for Economic Success The Mathematical Structure of Ponzi Schemes Dishonest Assessment of Risk One Reason Why
Applied mathematics made simple
Murphy, Patrick
1982-01-01
Applied Mathematics: Made Simple provides an elementary study of the three main branches of classical applied mathematics: statics, hydrostatics, and dynamics. The book begins with discussion of the concepts of mechanics, parallel forces and rigid bodies, kinematics, motion with uniform acceleration in a straight line, and Newton's law of motion. Separate chapters cover vector algebra and coplanar motion, relative motion, projectiles, friction, and rigid bodies in equilibrium under the action of coplanar forces. The final chapters deal with machines and hydrostatics. The standard and conte
Introduction to mathematical logic
Mendelson, Elliott
2015-01-01
The new edition of this classic textbook, Introduction to Mathematical Logic, Sixth Edition explores the principal topics of mathematical logic. It covers propositional logic, first-order logic, first-order number theory, axiomatic set theory, and the theory of computability. The text also discusses the major results of Gödel, Church, Kleene, Rosser, and Turing.The sixth edition incorporates recent work on Gödel's second incompleteness theorem as well as restoring an appendix on consistency proofs for first-order arithmetic. This appendix last appeared in the first edition. It is offered in th
Comprehensive basic mathematics
Veena, GR
2005-01-01
Salient Features As per II PUC Basic Mathematics syllabus of Karnataka. Provides an introduction to various basic mathematical techniques and the situations where these could be usefully employed. The language is simple and the material is self-explanatory with a large number of illustrations. Assists the reader in gaining proficiency to solve diverse variety of problems. A special capsule containing a gist and list of formulae titled ''REMEMBER! Additional chapterwise arranged question bank and 3 model papers in a separate section---''EXAMINATION CORNER''.
Concepts of mathematical modeling
Meyer, Walter J
2004-01-01
Appropriate for undergraduate and graduate students, this text features independent sections that illustrate the most important principles of mathematical modeling, a variety of applications, and classic models. Students with a solid background in calculus and some knowledge of probability and matrix theory will find the material entirely accessible. The range of subjects includes topics from the physical, biological, and social sciences, as well as those of operations research. Discussions cover related mathematical tools and the historical eras from which the applications are drawn. Each sec
Friedman, Mel
2012-01-01
Earn College Credit with REA's Test Prep for CLEP* College Mathematics Everything you need to pass the exam and get the college credit you deserve.CLEP* is the most popular credit-by-examination program in the country, accepted by more than 2,900 colleges and universities. For over 15 years, REA has helped students pass the CLEP* exam and earn college credit while reducing their tuition costs. Our test prep for CLEP* College Mathematics and the free online tools that come with it, allow you to create a personalized CLEP* study plan that can be customized to fit you: your schedule, your lea
Dennery, Philippe
1967-01-01
""A fine example of how to present 'classical' physical mathematics."" - American ScientistWritten for advanced undergraduate and graduate students, this volume provides a thorough background in the mathematics needed to understand today's more advanced topics in physics and engineering. Without sacrificing rigor, the authors develop the theoretical material at length, in a highly readable, and, wherever possible, in an intuitive manner. Each abstract idea is accompanied by a very simple, concrete example, showing the student that the abstraction is merely a generalization from easily understo
van Kerkhove, Bart
2007-01-01
Philosophy of mathematics today has transformed into a very complex network of diverse ideas, viewpoints, and theories. Sometimes the emphasis is on the ""classical"" foundational work (often connected with the use of formal logical methods), sometimes on the sociological dimension of the mathematical research community and the ""products"" it produces, then again on the education of future mathematicians and the problem of how knowledge is or should be transmitted from one generation to the next. The editors of this book felt the urge, first of all, to bring together the widest variety of aut
Early modern mathematical instruments.
Bennett, Jim
2011-12-01
In considering the appropriate use of the terms "science" and "scientific instrument," tracing the history of "mathematical instruments" in the early modern period is offered as an illuminating alternative to the historian's natural instinct to follow the guiding lights of originality and innovation, even if the trail transgresses contemporary boundaries. The mathematical instrument was a well-defined category, shared across the academic, artisanal, and commercial aspects of instrumentation, and its narrative from the sixteenth to the eighteenth century was largely independent from other classes of device, in a period when a "scientific" instrument was unheard of.
Discrete algorithmic mathematics
Maurer, Stephen B
2005-01-01
The exposition is self-contained, complemented by diverse exercises and also accompanied by an introduction to mathematical reasoning … this book is an excellent textbook for a one-semester undergraduate course and it includes a lot of additional material to choose from.-EMS, March 2006In a textbook, it is necessary to select carefully the statements and difficulty of the problems … in this textbook, this is fully achieved … This review considers this book an excellent one.-The Mathematical Gazette, March 2006
Beasley, John D
2006-01-01
""Mind-exercising and thought-provoking.""-New ScientistIf playing games is natural for humans, analyzing games is equally natural for mathematicians. Even the simplest of games involves the fundamentals of mathematics, such as figuring out the best move or the odds of a certain chance event. This entertaining and wide-ranging guide demonstrates how simple mathematical analysis can throw unexpected light on games of every type-games of chance, games of skill, games of chance and skill, and automatic games.Just how random is a card shuffle or a throw of the dice? Is bluffing a valid poker strat
Computer mathematics for programmers
Abney, Darrell H; Sibrel, Donald W
1985-01-01
Computer Mathematics for Programmers presents the Mathematics that is essential to the computer programmer.The book is comprised of 10 chapters. The first chapter introduces several computer number systems. Chapter 2 shows how to perform arithmetic operations using the number systems introduced in Chapter 1. The third chapter covers the way numbers are stored in computers, how the computer performs arithmetic on real numbers and integers, and how round-off errors are generated in computer programs. Chapter 4 details the use of algorithms and flowcharting as problem-solving tools for computer p
Biosensor Architectures for High-Fidelity Reporting of Cellular Signaling
Dushek, Omer; Lellouch, Annemarie C.; Vaux, David J.; Shahrezaei, Vahid
2014-01-01
Understanding mechanisms of information processing in cellular signaling networks requires quantitative measurements of protein activities in living cells. Biosensors are molecular probes that have been developed to directly track the activity of specific signaling proteins and their use is revolutionizing our understanding of signal transduction. The use of biosensors relies on the assumption that their activity is linearly proportional to the activity of the signaling protein they have been engineered to track. We use mechanistic mathematical models of common biosensor architectures (single-chain FRET-based biosensors), which include both intramolecular and intermolecular reactions, to study the validity of the linearity assumption. As a result of the classic mechanism of zero-order ultrasensitivity, we find that biosensor activity can be highly nonlinear so that small changes in signaling protein activity can give rise to large changes in biosensor activity and vice versa. This nonlinearity is abolished in architectures that favor the formation of biosensor oligomers, but oligomeric biosensors produce complicated FRET states. Based on this finding, we show that high-fidelity reporting is possible when a single-chain intermolecular biosensor is used that cannot undergo intramolecular reactions and is restricted to forming dimers. We provide phase diagrams that compare various trade-offs, including observer effects, which further highlight the utility of biosensor architectures that favor intermolecular over intramolecular binding. We discuss challenges in calibrating and constructing biosensors and highlight the utility of mathematical models in designing novel probes for cellular signaling. PMID:25099816
Mathematical Thinking and Creativity through Mathematical Problem Posing and Solving
María F. Ayllón
2016-04-01
Full Text Available This work shows the relationship between the development of mathematical thinking and creativity with mathematical problem posing and solving. Creativity and mathematics are disciplines that do not usually appear together. Both concepts constitute complex processes sharing elements, such as fluency (number of ideas, flexibility (range of ideas, novelty (unique idea and elaboration (idea development. These factors contribute, among others, to the fact that schoolchildren are competent in mathematics. The problem solving and posing are a very powerful evaluation tool that shows the mathematical reasoning and creative level of a person. Creativity is part of the mathematics education and is a necessary ingredient to perform mathematical assignments. This contribution presents some important research works about problem posing and solving related to the development of mathematical knowledge and creativity. To that end, it is based on various beliefs reflected in the literature with respect to notions of creativity, problem solving and posing.
Modeling integrated cellular machinery using hybrid Petri-Boolean networks.
Natalie Berestovsky
Full Text Available The behavior and phenotypic changes of cells are governed by a cellular circuitry that represents a set of biochemical reactions. Based on biological functions, this circuitry is divided into three types of networks, each encoding for a major biological process: signal transduction, transcription regulation, and metabolism. This division has generally enabled taming computational complexity dealing with the entire system, allowed for using modeling techniques that are specific to each of the components, and achieved separation of the different time scales at which reactions in each of the three networks occur. Nonetheless, with this division comes loss of information and power needed to elucidate certain cellular phenomena. Within the cell, these three types of networks work in tandem, and each produces signals and/or substances that are used by the others to process information and operate normally. Therefore, computational techniques for modeling integrated cellular machinery are needed. In this work, we propose an integrated hybrid model (IHM that combines Petri nets and Boolean networks to model integrated cellular networks. Coupled with a stochastic simulation mechanism, the model simulates the dynamics of the integrated network, and can be perturbed to generate testable hypotheses. Our model is qualitative and is mostly built upon knowledge from the literature and requires fine-tuning of very few parameters. We validated our model on two systems: the transcriptional regulation of glucose metabolism in human cells, and cellular osmoregulation in S. cerevisiae. The model produced results that are in very good agreement with experimental data, and produces valid hypotheses. The abstract nature of our model and the ease of its construction makes it a very good candidate for modeling integrated networks from qualitative data. The results it produces can guide the practitioner to zoom into components and interconnections and investigate them
Implementing a new mathematics curriculum: Mathematics teachers’ beliefs and practices
Ernest Ampadu
2013-01-01
Mathematics has become a ‘critical filter’ in the social, economic and professional development of individuals and forms a core component of the school curriculum in most countries. It is upon this utilitarian nature of mathematics to the individual and the society as a whole that the school mathematics curriculum has been undergoing a number of restructuring over the last three decades. In Ghana, a new mathematics curriculum was introduced in September 2007 which aims at shifting the teachin...
Celebrate Mathematical Curiosity
Redford, Christine
2011-01-01
Children's mathematical questions are often based in real-world experiences, as they instinctively make connections to the world around them. In teaching math methods courses, this author recently started to emphasize the importance of fostering curiosity in, and activating the thinking of, the students. In this article, she describes how to tap…
Continental Mathematics League.
Quartararo, Joseph
2002-01-01
This article describes the activities of the Continental Mathematics League, which offers a series of meets for children in grades 3 though 9. In addition, a Calculus League and a Computer Contest are offered. The league allows schools to participate by mail so that rural schools can participate. (CR)
Mankiewicz, Richard
2000-01-01
Questioning how mathematics has evolved over the centuries and for what reasons; how human endeavour and changes in the way we live have been dependent on mathematics, this book tells the story of the impact this intellectual activity has had across cultures and civilizations. It shows how, far from being just the obsession of an elite group of philosophers, priests and scientists, mathematics has in some shape or other entered every area of human activity. The mysterious tally sticks of prehistoric peoples and the terrestial maps used for trade, exploration and warfare; the perennial fascination with the motions of heavenly bodies and changing perspectives on the art and science of vision; all are testament to a mathematics at the heart of history. The path of this changing discipline is marked by a wealth of images, from medieval manuscripts to the unsettling art of Dali or Duchamp, from the austere beauty of Babylonian clay tablets to the delicate complexity of computer-generated images. The text encompass...
Problematising Mathematics Education
Begg, Andy
2015-01-01
We assume many things when considering our practice, but our assumptions limit what we do. In this theoretical/philosophical paper I consider some assumptions that relate to our work. My purpose is to stimulate a debate, a search for alternatives, and to help us improve mathematics education by influencing our future curriculum documents and…
Høyrup, Jens
The paper discusses the question “what is mathematics” from a point of view inspired by anthropology. In this perspective, the character of mathematical thinking and argument is strongly affected – almost essentially determined, indeed – by the dynamics of the specific social, mostly professional...
Strategy Instruction in Mathematics.
Goldman, Susan R.
1989-01-01
Experiments in strategy instruction for mathematics have been conducted using three models (direct instruction, self-instruction, and guided learning) applied to the tasks of computation and word problem solving. Results have implications for effective strategy instruction for learning disabled students. It is recommended that strategy instruction…
Research in Mathematics Education
Schoenfeld, Alan H.
2016-01-01
As one of the three Rs, "'rithmetic" has always been central to education and education research. By virtue of that centrality, research in mathematics education has often reflected and at times led trends in education research. This chapter provides some deep background on epistemological and other issues that shape current research,…
Barger, Rita H.; Jarrah, Adeeb M.
2012-01-01
March 14 is special because it is Pi Day. Mathematics is celebrated on that day because the date, 3-14, replicates the first three digits of pi. Pi-related songs, websites, trivia facts, and more are at the fingertips of interested teachers and students. Less celebrated, but still fairly well known, is National Metric Day, which falls on October…
Putting Foundations Into Mathematics
Hubbard, G. L.
1972-01-01
For meaningful learning of mathematics, a learning set is required which demands that all things accepted as true should be demonstrable in terms of a paradigm appropriate to the child's cognitive development: preparatory, concrete-particular, concrete-general, formal-abstract. Future teachers should experience all paradigms to become aware that…
Admin
2012-09-07
Sep 7, 2012 ... of public–private partnership in research and education in India. The Institute receives major private funding, side by side with substantial .... We are writing this to say that students who fail to do well in Mathematics Olympiad have no reason to get disheartened and to think that they are not good enough to ...
Cartier, Pierre; Heinzmann, Gerhard; Villani, Cédric
2016-01-01
This book challenges the views put forward by Pierre Cartier, one of the anchors of the famous Bourbaki group, and Cédric Villani, one of the most brilliant mathematicians of his generation, who received the Fields Medal in 2010. Jean Dhombres, mathematician and science historian, and Gerhard Heinzmann, philosopher of science and also a specialist in mathematics engage in a fruitful dialogue with the two mathematicians, prompting readers to reflect on mathematical activity and its social consequences in history as well as in the modern world. Cédric Villani’s popular success proves once again that a common awareness has developed, albeit in a very confused way, of the major role of mathematics in the construction and efficiency of natural sciences, which are at the origin of our technologies. Despite this, the idea that mathematics cannot be shared remains firmly entrenched, a perceived failing that has even been branded a lack of culture by vocal forces in the media as well as cultural and political esta...
December 2004-November 2007 Denmark, Hungary, Lithuania, the Netherlands, Norway, Slovenia and Spain have cooperated in the project Mathematics in Action (MiA). The MiA project is supported by the Grundtvig action in the Socrates program of the European Commission. The aim of the project...
Assessment Mathematics Teacher's Competencies
Alnoor, A. G.; Yuanxiang, Guo; Abudhuim, F. S.
2007-01-01
This paper aimed to identifying the professional efficiencies for the intermediate schools mathematics teachers and tries to know at what level the math teachers experience those competencies. The researcher used a descriptive research approach, the study data collected from specialist educators and teacher's experts and previous studies to…
New Technologies in Mathematics.
Sarmiento, Jorge
An understanding of past technological advancements can help educators understand the influence of new technologies in education. Inventions such as the abacus, logarithms, the slide rule, the calculating machine, computers, and electronic calculators have all found their place in mathematics education. While new technologies can be very useful,…
Elementary School Mathematics Priorities
Wilson, W. Stephen
2009-01-01
This article first describes some of the basic skills and knowledge that a solid elementary school mathematics foundation requires. It then elaborates on several points germane to these practices. These are then followed with a discussion and conclude with final comments and suggestions for future research. The article sets out the five…
Lee, Ji-Eun; Kim, Kyoung-Tae
2007-01-01
This article proposes an instructional idea where students can figure out an individual's secret personal information using the power of mathematics, particularly the power of algebraic thinking. The proposed examples in this article start with a personalized context that other people do not know and end up with generalized patterns of solutions.…
Vision in elementary mathematics
Sawyer, W W
2003-01-01
Sure-fire techniques of visualizing, dramatizing, and analyzing numbers promise to attract and retain students' attention and understanding. Topics include basic multiplication and division, algebra, word problems, graphs, negative numbers, fractions, many other practical applications of elementary mathematics. 1964 ed. Answers to Problems.
Foundations of mathematical logic
Curry, Haskell B
2010-01-01
Written by a pioneer of mathematical logic, this comprehensive graduate-level text explores the constructive theory of first-order predicate calculus. It covers formal methods, including algorithms and epitheory, and offers a brief treatment of Markov's approach to algorithms, explains elementary facts about lattices and similar algebraic systems, and more. 1963 edition.
Learning Mathematics through Games
Gough, John
2015-01-01
When considering the use of games for teaching mathematics, educators should distinguish between an "activity" and a "game". Gough (1999) states that "A 'game' needs to have two or more players, who take turns, each competing to achieve a 'winning' situation of some kind, each able to exercise some choice about how to move…
Bureau of Naval Personnel, Washington, DC.
The second of three volumes of a mathematics training course for Navy personnel, this document contains material primarily found at the college level. Beginning with logarithms and trigonometry, the text moves into vectors and static equilibrium (physics). Coordinate geometry, conic sections, and the tangents, normals, and slopes of curves follow.…
Stoddard, Edward
1994-01-01
Entertaining, easy-to-follow suggestions for developing greater speed and accuracy in doing mathematical calculations. Surefire methods for multiplying without carrying, dividing with half the pencil work of long division, plus advice on how to add and subtract rapidly, master fractions, work quickly with decimals, handle percentages, and much more.
Mathematical methods in neutronics
Planchard, J.
1995-01-01
This book presents the mathematical theory of nuclear reactors. It applies to engineers in neutronics and applied mathematicians. After a recall of the elementary notions of neutronics and of diffusion-type partial derivative equations, the theory of reactors criticality calculation is described. (J.S.)
The Constructivist Mathematics Classroom
Jones, Karrie; Jones, Jennifer L.; Vermette, Paul J.
2010-01-01
By examining how people learn, the educational theories of Dewey, Piaget, Vygotsky and Bruner can be synthesized to give this set of core Constructivist principles. Principles of effective mathematics teaching: (1) allows learning that is "active" and "reflective". Students are required to transfer key concepts to new situations; (2) allows…
Zack, Laurie; Fuselier, Jenny; Graham-Squire, Adam; Lamb, Ron; O'Hara, Karen
2015-01-01
Our study compared a flipped class with a standard lecture class in four introductory courses: finite mathematics, precalculus, business calculus, and calculus 1. The flipped sections watched video lectures outside of class and spent time in class actively working on problems. The traditional sections had lectures in class and did homework outside…
Mathematics for quantum chemistry
Anderson, Jay Martin
2005-01-01
This concise volume offers undergraduates an introduction to mathematical formalism in problems of molecular structure and motion. The main topics cover the calculus of orthogonal functions, algebra of vector spaces, and Lagrangian and Hamiltonian formulation of classical mechanics and applications to molecular motion. Answers to problems. 1966 edition.
De Luca, R; Faella, O
2014-01-01
Mathematical fireworks are reproduced in two dimensions by means of simple notions in kinematics and Newtonian mechanics. Extension of the analysis in three dimensions is proposed and the geometric figures the falling tiny particles make on the ground after explosion are determined. (paper)
Towards mathematical philosophy
Hendricks, Vincent F
2008-01-01
Logical investigations in cognitive science have successfully utilized methods and systems of belief revision, non-monotonic logic and dynamic epistemic logic. This title deals with focal issues of belief revision. It contains a collection of articles applying methods of logic or, more generally, of mathematics to solve problems.
Simulating physics with cellular automata
Vichniac, G Y
1984-01-01
Cellular automata are dynamical systems where space, time, and variables are discrete. They are shown on two-dimensional examples to be capable of non-numerical simulations of physics. They are useful for faithful parallel processing of lattice models. At another level, they exhibit behaviours and illustrate concepts that are unmistakably physical, such as non-ergodicity and order parameters, frustration, relaxation to chaos through period doublings, a conspicuous arrow of time in reversible microscopic dynamics, causality and light-cone, and non-separability. In general, they constitute exactly computable models for complex phenomena and large-scale correlations that result from very simple short-range interactions. The author studies their space, time, and intrinsic symmetries and the corresponding conservation laws, with an emphasis on the conservation of information obeyed by reversible cellular automata. 60 references.
Mathematical Modeling: Challenging the Figured Worlds of Elementary Mathematics
Wickstrom, Megan H.
2017-01-01
This article is a report on a teacher study group that focused on three elementary teachers' perceptions of mathematical modeling in contrast to typical mathematics instruction. Through the theoretical lens of figured worlds, I discuss how mathematics instruction was conceptualized across the classrooms in terms of artifacts, discourse, and…
Mathematics Teachers' Ideas about Mathematical Models: A Diverse Landscape
Bautista, Alfredo; Wilkerson-Jerde, Michelle H.; Tobin, Roger G.; Brizuela, Bárbara M.
2014-01-01
This paper describes the ideas that mathematics teachers (grades 5-9) have regarding mathematical models of real-world phenomena, and explores how teachers' ideas differ depending on their educational background. Participants were 56 United States in-service mathematics teachers. We analyzed teachers' written responses to three open-ended…
Racial Differences in Mathematics Test Scores for Advanced Mathematics Students
Minor, Elizabeth Covay
2016-01-01
Research on achievement gaps has found that achievement gaps are larger for students who take advanced mathematics courses compared to students who do not. Focusing on the advanced mathematics student achievement gap, this study found that African American advanced mathematics students have significantly lower test scores and are less likely to be…
"Mathematics Is Like a Lion": Elementary Students' Beliefs about Mathematics
Markovits, Zvia; Forgasz, Helen
2017-01-01
The aim of this study was to explore the beliefs of elementary school students about mathematics and about themselves as mathematics learners. The participants, Israeli grade 4 and grade 6 students, completed questionnaires. Using an "animal metaphor" to tap beliefs, some students perceived mathematics as difficult and complicated, while…
Mathematical Thinking and Creativity through Mathematical Problem Posing and Solving
Ayllón, María F.; Gómez, Isabel A.; Ballesta-Claver, Julio
2016-01-01
This work shows the relationship between the development of mathematical thinking and creativity with mathematical problem posing and solving. Creativity and mathematics are disciplines that do not usually appear together. Both concepts constitute complex processes sharing elements, such as fluency (number of ideas), flexibility (range of ideas),…
Mathematics and Engineering in Real Life through Mathematical Competitions
More, M.
2018-01-01
We bring out an experience of organizing mathematical competitions that can be used as a medium to motivate the student and teacher minds in new directions of thinking. This can contribute to fostering research, innovation and provide a hands-on experience of mathematical concepts with the real world. Mathematical competitions can be used to build…
Mathematical Models of Elementary Mathematics Learning and Performance. Final Report.
Suppes, Patrick
This project was concerned with the development of mathematical models of elementary mathematics learning and performance. Probabilistic finite automata and register machines with a finite number of registers were developed as models and extensively tested with data arising from the elementary-mathematics strand curriculum developed by the…
Middle School Mathematics Students' Perspectives on the Study of Mathematics
Vaughn, Christy H.
2012-01-01
This qualitative study addressed the perceptions toward the study of mathematics by middle school students who had formerly been in a remedial mathematics program. The purpose of the study was to explore the past experiences of nine students in order to determine what is needed for them to feel successful in mathematics. The conceptual framework…
Cellular Adhesion and Adhesion Molecules
SELLER, Zerrin
2014-01-01
In recent years, cell adhesion and cell adhesion molecules have been shown to be important for many normal biological processes, including embryonic cell migration, immune system functions and wound healing. It has also been shown that they contribute to the pathogenesis of a large number of common human disorders, such as rheumatoid arthritis and tumor cell metastasis in cancer. In this review, the basic mechanisms of cellular adhesion and the structural and functional features of adhes...
Cellular automata with voting rule
Makowiec, D.
1996-01-01
The chosen local interaction - the voting (majority) rule applied to the square lattice is known to cause the non ergodic cellular automata behaviour. Presented computer simulation results verify two cases of non ergodicity. The first one is implicated by the noise introduced to the local interactions and the second one follows properties of the initial lattice configuration selected at random. For the simplified voting rule - non symmetric voting, the critical behaviour has been explained rigorously. (author)
Theological Metaphors in Mathematics
Krajewski Stanisław
2016-03-01
Full Text Available Examples of possible theological influences upon the development of mathematics are indicated. The best known connection can be found in the realm of infinite sets treated by us as known or graspable, which constitutes a divine-like approach. Also the move to treat infinite processes as if they were one finished object that can be identified with its limits is routine in mathematicians, but refers to seemingly super-human power. For centuries this was seen as wrong and even today some philosophers, for example Brian Rotman, talk critically about “theological mathematics”. Theological metaphors, like “God’s view”, are used even by contemporary mathematicians. While rarely appearing in official texts they are rather easily invoked in “the kitchen of mathematics”. There exist theories developing without the assumption of actual infinity the tools of classical mathematics needed for applications (For instance, Mycielski’s approach. Conclusion: mathematics could have developed in another way. Finally, several specific examples of historical situations are mentioned where, according to some authors, direct theological input into mathematics appeared: the possibility of the ritual genesis of arithmetic and geometry, the importance of the Indian religious background for the emergence of zero, the genesis of the theories of Cantor and Brouwer, the role of Name-worshipping for the research of the Moscow school of topology. Neither these examples nor the previous illustrations of theological metaphors provide a certain proof that religion or theology was directly influencing the development of mathematical ideas. They do suggest, however, common points and connections that merit further exploration.
Cellular communications a comprehensive and practical guide
Tripathi, Nishith
2014-01-01
Even as newer cellular technologies and standards emerge, many of the fundamental principles and the components of the cellular network remain the same. Presenting a simple yet comprehensive view of cellular communications technologies, Cellular Communications provides an end-to-end perspective of cellular operations, ranging from physical layer details to call set-up and from the radio network to the core network. This self-contained source forpractitioners and students represents a comprehensive survey of the fundamentals of cellular communications and the landscape of commercially deployed
The practice of teaching mathematics
Hefendehl-Hebeker, Lisa
1998-01-01
The practice of teaching mathematics : experimental conditions of change. - In: The culture of the mathematics classroom / ed. by Falk Seeger .... - Cambridge u.a. : Cambridge Univ. Press, 1998. - S. 104-124
Soundoff: Mathematics Is Getting Easier.
Usiskin, Zalman
1984-01-01
Teaching mathematics in hard ways, rather than using easier methods or technology, is described. Employing the most efficient means possible to solve a problem is the essence of good mathematics, rather than wasting time in practicing obsolete skills. (MNS)
Algorithmic Principles of Mathematical Programming
Faigle, Ulrich; Kern, Walter; Still, Georg
2002-01-01
Algorithmic Principles of Mathematical Programming investigates the mathematical structures and principles underlying the design of efficient algorithms for optimization problems. Recent advances in algorithmic theory have shown that the traditionally separate areas of discrete optimization, linear
How to solve mathematical problems
Wickelgren, Wayne A
1995-01-01
Seven problem-solving techniques include inference, classification of action sequences, subgoals, contradiction, working backward, relations between problems, and mathematical representation. Also, problems from mathematics, science, and engineering with complete solutions.
Pedoe, Dan
2012-01-01
This lighthearted work uses a variety of practical applications and puzzles to take a look at today's mathematical trends. In nine chapters, Professor Pedoe covers mathematical games, chance and choice, automatic thinking, and more.
Mathematics Education and Language Diversity
Moschkovich, Judit; Planas, Nuria
This book examines multiple facets of language diversity and mathematics education. It features renowned authors from around the world and explores the learning and teaching of mathematics in contexts that include multilingual classrooms, indigenous education, teacher education, blind and deaf...
Mathematics Alive and in Action
Hansen, Vagn Lundsgaard
2005-01-01
This chapter addresses two main questions: What do mathematicians do? What is mathematics good for? With focus on recent times, a panorama of mathematical contributions to civilization is presented and the intellectual drive by which they were perceived is described.......This chapter addresses two main questions: What do mathematicians do? What is mathematics good for? With focus on recent times, a panorama of mathematical contributions to civilization is presented and the intellectual drive by which they were perceived is described....
Gender, culture, and mathematics performance
Hyde, Janet S.; Mertz, Janet E.
2009-01-01
Using contemporary data from the U.S. and other nations, we address 3 questions: Do gender differences in mathematics performance exist in the general population? Do gender differences exist among the mathematically talented? Do females exist who possess profound mathematical talent? In regard to the first question, contemporary data indicate that girls in the U.S. have reached parity with boys in mathematics performance, a pattern that is found in some other nations as well. Focusing on the ...
Panel Debate: Technics and technology in mathematics and mathematics education
Misfeldt, Morten
2015-01-01
The use of computer technology for teaching and learning of mathematics has several consequences and does sometimes give rise to both controversies and misunderstandings. We address these problems by both a philosophical and a historical approach, investigating what it actually is that goes on when...... guidelines and conclusions regarding the use of computer technology in mathematics education....... new technologies enter mathematics as a discipline and mathematics education as a societal practice. Our analysis suggests a focus on continuities in time and place in the sense that it is necessary to understand the history of “tool use” in mathematics and the various ways that scholastic and non...
The Magic of Mathematics Discovering the Spell of Mathematics
Pappas, Theoni
2011-01-01
Delves into the world of ideas, explores the spell mathematics casts on our lives, and helps you discover mathematics where you least expect it. Be spellbound by the mathematical designs found in nature. Learn how knots may untie the mysteries of life. Be mesmerized by the computer revolution. Discover how the hidden forces of mathematics hold architectural structures together connect your telephone calls help airplanes get off the ground solve the mysteries of the living cell. See how some artists use a mathematical palette in their works and how many writers draw upon the wealth of its ideas
The pragmatics of mathematics education vagueness and mathematical discourse
Rowland, Tim
2003-01-01
Drawing on philosophy of language and recent linguistic theory, Rowland surveys several approaches to classroom communication in mathematics. Are students intimidated by the nature of mathematics teaching? Many students appear fearful of voicing their understanding - is fear of error part of the linguistics of mathematics? The approaches explored here provide a rationale and a method for exploring and understanding speakers'' motives in classroom mathematics talk. Teacher-student interactions in mathematics are analysed, and this provides a toolkit that teachers can use to respond to the intellectual vulnerability of their students.
A Primer for Mathematical Modeling
Sole, Marla
2013-01-01
With the implementation of the National Council of Teachers of Mathematics recommendations and the adoption of the Common Core State Standards for Mathematics, modeling has moved to the forefront of K-12 education. Modeling activities not only reinforce purposeful problem-solving skills, they also connect the mathematics students learn in school…
Sriraman, Bharath, Ed.
2012-01-01
The interaction of the history of mathematics and mathematics education has long been construed as an esoteric area of inquiry. Much of the research done in this realm has been under the auspices of the history and pedagogy of mathematics group. However there is little systematization or consolidation of the existing literature aimed at…
Experimental Mathematics and Computational Statistics
Bailey, David H.; Borwein, Jonathan M.
2009-04-30
The field of statistics has long been noted for techniques to detect patterns and regularities in numerical data. In this article we explore connections between statistics and the emerging field of 'experimental mathematics'. These includes both applications of experimental mathematics in statistics, as well as statistical methods applied to computational mathematics.