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Author: Nicholas F. Britton Publisher: Springer Science & Business Media ISBN: 1447100492 Category : Mathematics Languages : en Pages : 347
Book Description
This self-contained introduction to the fast-growing field of Mathematical Biology is written for students with a mathematical background. It sets the subject in a historical context and guides the reader towards questions of current research interest. A broad range of topics is covered including: Population dynamics, Infectious diseases, Population genetics and evolution, Dispersal, Molecular and cellular biology, Pattern formation, and Cancer modelling. Particular attention is paid to situations where the simple assumptions of homogenity made in early models break down and the process of mathematical modelling is seen in action.
Author: Nicholas F. Britton Publisher: Springer Science & Business Media ISBN: 1447100492 Category : Mathematics Languages : en Pages : 347
Book Description
This self-contained introduction to the fast-growing field of Mathematical Biology is written for students with a mathematical background. It sets the subject in a historical context and guides the reader towards questions of current research interest. A broad range of topics is covered including: Population dynamics, Infectious diseases, Population genetics and evolution, Dispersal, Molecular and cellular biology, Pattern formation, and Cancer modelling. Particular attention is paid to situations where the simple assumptions of homogenity made in early models break down and the process of mathematical modelling is seen in action.
Author: G. Bard Ermentrout Publisher: Springer Science & Business Media ISBN: 0387877088 Category : Mathematics Languages : en Pages : 434
Book Description
This book applies methods from nonlinear dynamics to problems in neuroscience. It uses modern mathematical approaches to understand patterns of neuronal activity seen in experiments and models of neuronal behavior. The intended audience is researchers interested in applying mathematics to important problems in neuroscience, and neuroscientists who would like to understand how to create models, as well as the mathematical and computational methods for analyzing them. The authors take a very broad approach and use many different methods to solve and understand complex models of neurons and circuits. They explain and combine numerical, analytical, dynamical systems and perturbation methods to produce a modern approach to the types of model equations that arise in neuroscience. There are extensive chapters on the role of noise, multiple time scales and spatial interactions in generating complex activity patterns found in experiments. The early chapters require little more than basic calculus and some elementary differential equations and can form the core of a computational neuroscience course. Later chapters can be used as a basis for a graduate class and as a source for current research in mathematical neuroscience. The book contains a large number of illustrations, chapter summaries and hundreds of exercises which are motivated by issues that arise in biology, and involve both computation and analysis. Bard Ermentrout is Professor of Computational Biology and Professor of Mathematics at the University of Pittsburgh. David Terman is Professor of Mathematics at the Ohio State University.
Author: Robert J. Rosen Publisher: Academic Press ISBN: 1483271854 Category : Science Languages : en Pages : 431
Book Description
Foundations of Mathematical Biology, Volume III, is devoted to the treatment of behavior of whole organisms and groups of organisms. The viewpoint taken throughout the book is a holistic, phenomenological one. That is, the integrated behavior of these organisms and groups of organisms is not, in general, referred back to specific structural properties of interacting subunits (as in a reductionist scheme), but is rather treated on its own terms without invoking the properties of lower levels of organization. The book begins with an overview of organization and control in physiological systems, with emphasis on the mathematical techniques involved in more detailed investigations of specific physiological mechanisms. Separate chapters cover the cardiovascular system, with particular reference to blood flow; gross problems of organic form; a relational overview of physics, biology, and sociology; the automata theory in the context of the central nervous system; and populations of interacting organisms. The final chapter discusses the material presented in the entire work, some of its philosophical presuppositions and implications, and the possibility of constructing a unified theory of mathematical biology.
Author: Deviderjit Singh Sivia Publisher: OUP Oxford ISBN: 9780198504283 Category : Mathematics Languages : en Pages : 98
Book Description
This text spans a large range of mathematics, from basic algebra to calculus and Fourier transforms. Its tutorial style bridges the gap between school and university while its conciseness provides a useful reference for the professional.
Author: J. David Logan Publisher: John Wiley & Sons ISBN: 0470525878 Category : Science Languages : en Pages : 437
Book Description
A one-of-a-kind guide to using deterministic and probabilistic methods for solving problems in the biological sciences Highlighting the growing relevance of quantitative techniques in scientific research, Mathematical Methods in Biology provides an accessible presentation of the broad range of important mathematical methods for solving problems in the biological sciences. The book reveals the growing connections between mathematics and biology through clear explanations and specific, interesting problems from areas such as population dynamics, foraging theory, and life history theory. The authors begin with an introduction and review of mathematical tools that are employed in subsequent chapters, including biological modeling, calculus, differential equations, dimensionless variables, and descriptive statistics. The following chapters examine standard discrete and continuous models using matrix algebra as well as difference and differential equations. Finally, the book outlines probability, statistics, and stochastic methods as well as material on bootstrapping and stochastic differential equations, which is a unique approach that is not offered in other literature on the topic. In order to demonstrate the application of mathematical methods to the biological sciences, the authors provide focused examples from the field of theoretical ecology, which serve as an accessible context for study while also demonstrating mathematical skills that are applicable to many other areas in the life sciences. The book's algorithms are illustrated using MATLAB®, but can also be replicated using other software packages, including R, Mathematica®, and Maple; however, the text does not require any single computer algebra package. Each chapter contains numerous exercises and problems that range in difficulty, from the basic to more challenging, to assist readers with building their problem-solving skills. Selected solutions are included at the back of the book, and a related Web site features supplemental material for further study. Extensively class-tested to ensure an easy-to-follow format, Mathematical Methods in Biology is an excellent book for mathematics and biology courses at the upper-undergraduate and graduate levels. It also serves as a valuable reference for researchers and professionals working in the fields of biology, ecology, and biomathematics.
Author: Andreas Kremling Publisher: CRC Press ISBN: 1466567899 Category : Mathematics Languages : en Pages : 382
Book Description
Drawing on the latest research in the field, Systems Biology: Mathematical Modeling and Model Analysis presents many methods for modeling and analyzing biological systems, in particular cellular systems. It shows how to use predictive mathematical models to acquire and analyze knowledge about cellular systems. It also explores how the models are systematically applied in biotechnology. The first part of the book introduces biological basics, such as metabolism, signaling, gene expression, and control as well as mathematical modeling fundamentals, including deterministic models and thermodynamics. The text also discusses linear regression methods, explains the differences between linear and nonlinear regression, and illustrates how to determine input variables to improve estimation accuracy during experimental design. The second part covers intracellular processes, including enzymatic reactions, polymerization processes, and signal transduction. The author highlights the process–function–behavior sequence in cells and shows how modeling and analysis of signal transduction units play a mediating role between process and function. The third part presents theoretical methods that address the dynamics of subsystems and the behavior near a steady state. It covers techniques for determining different time scales, sensitivity analysis, structural kinetic modeling, and theoretical control engineering aspects, including a method for robust control. It also explores frequent patterns (motifs) in biochemical networks, such as the feed-forward loop in the transcriptional network of E. coli. Moving on to models that describe a large number of individual reactions, the last part looks at how these cellular models are used in biotechnology. The book also explains how graphs can illustrate the link between two components in large networks with several interactions.
Author: Matthias Dehmer Publisher: John Wiley & Sons ISBN: 3527339094 Category : Medical Languages : en Pages : 298
Book Description
This latest addition to the successful Network Biology series presents current methods for determining the entropy of networks, making it the first to cover the recently established Quantitative Graph Theory. An excellent international team of editors and contributors provides an up-to-date outlook for the field, covering a broad range of graph entropy-related concepts and methods. The topics range from analyzing mathematical properties of methods right up to applying them in real-life areas. Filling a gap in the contemporary literature this is an invaluable reference for a number of disciplines, including mathematicians, computer scientists, computational biologists, and structural chemists.
Author: Robert J. Rosen Publisher: Academic Press ISBN: 1483272133 Category : Science Languages : en Pages : 316
Book Description
Foundations of Mathematical Biology, Volume 1, Subcellular Systems, provides an introduction the place of mathematical biology in relation to the other biological, physical, and organizational sciences. It discusses the use of mathematical tools and techniques to solve biological problems. The book contains four chapters and begins with a discussion of the nature of hierarchical control in living matter. This is followed by a chapter on chemical kinetics and enzyme kinetics, covering the physicomathematical principles, models, and approximations underlying transition-state theory and the unimolecular reaction. Subsequent chapters deal with quantum genetics and membrane excitability.
Author: Raina Robeva Publisher: Academic Press ISBN: 0128012714 Category : Mathematics Languages : en Pages : 383
Book Description
Written by experts in both mathematics and biology, Algebraic and Discrete Mathematical Methods for Modern Biology offers a bridge between math and biology, providing a framework for simulating, analyzing, predicting, and modulating the behavior of complex biological systems. Each chapter begins with a question from modern biology, followed by the description of certain mathematical methods and theory appropriate in the search of answers. Every topic provides a fast-track pathway through the problem by presenting the biological foundation, covering the relevant mathematical theory, and highlighting connections between them. Many of the projects and exercises embedded in each chapter utilize specialized software, providing students with much-needed familiarity and experience with computing applications, critical components of the "modern biology" skill set. This book is appropriate for mathematics courses such as finite mathematics, discrete structures, linear algebra, abstract/modern algebra, graph theory, probability, bioinformatics, statistics, biostatistics, and modeling, as well as for biology courses such as genetics, cell and molecular biology, biochemistry, ecology, and evolution. - Examines significant questions in modern biology and their mathematical treatments - Presents important mathematical concepts and tools in the context of essential biology - Features material of interest to students in both mathematics and biology - Presents chapters in modular format so coverage need not follow the Table of Contents - Introduces projects appropriate for undergraduate research - Utilizes freely accessible software for visualization, simulation, and analysis in modern biology - Requires no calculus as a prerequisite - Provides a complete Solutions Manual - Features a companion website with supplementary resources
Author: Nicholas F. Britton
Author: Nicholas F. Britton
Author: G. Bard Ermentrout
Author: Robert J. Rosen
Author: Anthony William Fairbank Edwards
Author: Deviderjit Singh Sivia
Author: J. David Logan
Author: Andreas Kremling
Author: Matthias Dehmer
Author: Robert J. Rosen
Author: Raina Robeva