Mathematical Concepts And Methods In Modern Biology
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Mathematical Concepts And Methods In Modern Biology
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Author : Raina Robeva
language : en
Publisher: Academic Press
Release Date : 2013-02-26
Mathematical Concepts And Methods In Modern Biology written by Raina Robeva and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-26 with Mathematics categories.
Mathematical Concepts and Methods in Modern Biology offers a quantitative framework for analyzing, predicting, and modulating the behavior of complex biological systems. The book presents important mathematical concepts, methods and tools in the context of essential questions raised in modern biology.Designed around the principles of project-based learning and problem-solving, the book considers biological topics such as neuronal networks, plant population growth, metabolic pathways, and phylogenetic tree reconstruction. The mathematical modeling tools brought to bear on these topics include Boolean and ordinary differential equations, projection matrices, agent-based modeling and several algebraic approaches. Heavy computation in some of the examples is eased by the use of freely available open-source software. - Features self-contained chapters with real biological research examples using freely available computational tools - Spans several mathematical techniques at basic to advanced levels - Offers broad perspective on the uses of algebraic geometry/polynomial algebra in molecular systems biology
Algebraic And Discrete Mathematical Methods For Modern Biology
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Author : Raina Robeva
language : en
Publisher: Academic Press
Release Date : 2015-05-09
Algebraic And Discrete Mathematical Methods For Modern Biology written by Raina Robeva and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-09 with Mathematics categories.
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
Mathematics And The Natural Sciences The Physical Singularity Of Life
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Author : Giuseppe Longo
language : en
Publisher: World Scientific
Release Date : 2011-03-04
Mathematics And The Natural Sciences The Physical Singularity Of Life written by Giuseppe Longo and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-04 with Science categories.
This book identifies the organizing concepts of physical and biological phenomena by an analysis of the foundations of mathematics and physics. Our aim is to propose a dialog between different conceptual universes and thus to provide a unification of phenomena. The role of “order” and symmetries in the foundations of mathematics is linked to the main invariants and principles, among them the geodesic principle (a consequence of symmetries), which govern and confer unity to various physical theories. Moreover, an attempt is made to understand causal structures, a central element of physical intelligibility, in terms of both symmetries and symmetry breakings. A distinction between the principles of (conceptual) construction and of proofs, both in physics and in mathematics, guides most of the work.The importance of mathematical tools is also highlighted to clarify differences in the models for physics and biology that are proposed by continuous and discrete mathematics, such as computational simulations.Since biology is particularly complex and not as well understood at a theoretical level, we propose a “unification by concepts” which in any case should precede mathematization. This constitutes an outline for unification also based on highlighting conceptual differences, complex points of passage and technical irreducibilities of one field to another. Indeed, we suppose here a very common monist point of view, namely the view that living objects are “big bags of molecules”. The main question though is to understand which “theory” can help better understand these bags of molecules. They are, indeed, rather “singular”, from the physical point of view. Technically, we express this singularity through the concept of “extended criticality”, which provides a logical extension of the critical transitions that are known in physics. The presentation is mostly kept at an informal and conceptual level./a
Mathematics For The Life Sciences
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Author : Erin N. Bodine
language : en
Publisher: Princeton University Press
Release Date : 2014-08-17
Mathematics For The Life Sciences written by Erin N. Bodine and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-17 with Mathematics categories.
An accessible undergraduate textbook on the essential math concepts used in the life sciences The life sciences deal with a vast array of problems at different spatial, temporal, and organizational scales. The mathematics necessary to describe, model, and analyze these problems is similarly diverse, incorporating quantitative techniques that are rarely taught in standard undergraduate courses. This textbook provides an accessible introduction to these critical mathematical concepts, linking them to biological observation and theory while also presenting the computational tools needed to address problems not readily investigated using mathematics alone. Proven in the classroom and requiring only a background in high school math, Mathematics for the Life Sciences doesn't just focus on calculus as do most other textbooks on the subject. It covers deterministic methods and those that incorporate uncertainty, problems in discrete and continuous time, probability, graphing and data analysis, matrix modeling, difference equations, differential equations, and much more. The book uses MATLAB throughout, explaining how to use it, write code, and connect models to data in examples chosen from across the life sciences. Provides undergraduate life science students with a succinct overview of major mathematical concepts that are essential for modern biology Covers all the major quantitative concepts that national reports have identified as the ideal components of an entry-level course for life science students Provides good background for the MCAT, which now includes data-based and statistical reasoning Explicitly links data and math modeling Includes end-of-chapter homework problems, end-of-unit student projects, and select answers to homework problems Uses MATLAB throughout, and MATLAB m-files with an R supplement are available online Prepares students to read with comprehension the growing quantitative literature across the life sciences A solutions manual for professors and an illustration package is available
Modern Mathematical Methods For Scientists And Engineers
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Author : A. S. Fokas
language : en
Publisher: World Scientific Publishing Europe Limited
Release Date : 2023
Modern Mathematical Methods For Scientists And Engineers written by A. S. Fokas and has been published by World Scientific Publishing Europe Limited this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023 with Mathematical analysis categories.
"Partial differential equations (PDEs) are the mathematical cornerstone for describing an astonishingly wide range of phenomena, from quantum mechanics and ocean waves, to the diffusion of heat in matter and the behavior of financial markets. Despite the efforts of many famous mathematicians, physicists and engineers, the solution of partial differential equations remains a challenge. This book's authors introduce a novel method, the unified transform, which greatly facilitates this challenge. Two and a half centuries after Jean d'Alembert formulated the wave equation and presented a solution for solving a simple problem for this equation, this book introduces a generalization of the d'Alembert solution, which is valid for general boundary value problems. Moreover, two centuries after Joseph Fourier introduced the classical tool of the Fourier series for solving the heat equation, it offers a new solution of this problem, which has important analytical and numerical advantages in comparison to the classical solutions. The authors present the unified transform pedagogically, building all the necessary background, including functions of real and of complex variables and the Fourier transform, illustrating the method with numerous examples. Modern Mathematical Methods for Scientists and Engineers is a modern introduction to basic topics in mathematics at the undergraduate level, with emphasis on explanations and applications to real-life problems. There are also "Application" sections at the end of each chapter, with topics drawn from a variety of areas, including neural networks, fluid dynamics, and the behavior of put and call options in financial markets. In addition to the unified transform, the book presents several modern important and computationally efficient topics, including feed-forward neural networks, wavelets, generalized functions, stochastic optimization methods, and numerical methods. Broad in scope, but pedagogical in style and content, the book is an introduction to powerful mathematical concepts and modern tools for students in science and engineering"--
Mathematical Models In Biology
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Author : Leah Edelstein-Keshet
language : en
Publisher: SIAM
Release Date : 1988-01-01
Mathematical Models In Biology written by Leah Edelstein-Keshet and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-01-01 with Mathematics categories.
Mathematical Models in Biology is an introductory book for readers interested in biological applications of mathematics and modeling in biology. A favorite in the mathematical biology community, it shows how relatively simple mathematics can be applied to a variety of models to draw interesting conclusions. Connections are made between diverse biological examples linked by common mathematical themes. A variety of discrete and continuous ordinary and partial differential equation models are explored. Although great advances have taken place in many of the topics covered, the simple lessons contained in this book are still important and informative. Audience: the book does not assume too much background knowledge--essentially some calculus and high-school algebra. It was originally written with third- and fourth-year undergraduate mathematical-biology majors in mind; however, it was picked up by beginning graduate students as well as researchers in math (and some in biology) who wanted to learn about this field.
The Mathematics And Mechanics Of Biological Growth
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Author : Alain Goriely
language : en
Publisher: Springer
Release Date : 2017-05-29
The Mathematics And Mechanics Of Biological Growth written by Alain Goriely and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-29 with Mathematics categories.
This monograph presents a general mathematical theory for biological growth. It provides both a conceptual and a technical foundation for the understanding and analysis of problems arising in biology and physiology. The theory and methods are illustrated on a wide range of examples and applications. A process of extreme complexity, growth plays a fundamental role in many biological processes and is considered to be the hallmark of life itself. Its description has been one of the fundamental problems of life sciences, but until recently, it has not attracted much attention from mathematicians, physicists, and engineers. The author herein presents the first major technical monograph on the problem of growth since D’Arcy Wentworth Thompson’s 1917 book On Growth and Form. The emphasis of the book is on the proper mathematical formulation of growth kinematics and mechanics. Accordingly, the discussion proceeds in order of complexity and the book is divided into five parts. First, a general introduction on the problem of growth from a historical perspective is given. Then, basic concepts are introduced within the context of growth in filamentary structures. These ideas are then generalized to surfaces and membranes and eventually to the general case of volumetric growth. The book concludes with a discussion of open problems and outstanding challenges. Thoughtfully written and richly illustrated to be accessible to readers of varying interests and background, the text will appeal to life scientists, biophysicists, biomedical engineers, and applied mathematicians alike.
Modern Infectious Disease Epidemiology
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Author : Alexander Krämer
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-01-23
Modern Infectious Disease Epidemiology written by Alexander Krämer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-01-23 with Medical categories.
Hardly a day goes by without news headlines concerning infectious disease threats. Currently the spectre of a pandemic of influenza A|H1N1 is raising its head, and heated debates are taking place about the pro’s and con’s of vaccinating young girls against human papilloma virus. For an evidence-based and responsible communication of infectious disease topics to avoid misunderstandings and overreaction of the public, we need solid scientific knowledge and an understanding of all aspects of infectious diseases and their control. The aim of our book is to present the reader with the general picture and the main ideas of the subject. The book introduces the reader to methodological aspects of epidemiology that are specific for infectious diseases and provides insight into the epidemiology of some classes of infectious diseases characterized by their main modes of transmission. This choice of topics bridges the gap between scientific research on the clinical, biological, mathematical, social and economic aspects of infectious diseases and their applications in public health. The book will help the reader to understand the impact of infectious diseases on modern society and the instruments that policy makers have at their disposal to deal with these challenges. It is written for students of the health sciences, both of curative medicine and public health, and for experts that are active in these and related domains, and it may be of interest for the educated layman since the technical level is kept relatively low.
Quantitative Biology
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Author : Michael E. Wall
language : en
Publisher: CRC Press
Release Date : 2012-08-25
Quantitative Biology written by Michael E. Wall and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-25 with Science categories.
Quantitative methods are revolutionizing modern molecular and cellular biology. Groundbreaking technical advances are fueling the rapid expansion in our ability to observe, as seen in multidisciplinary studies that integrate theory, computation, experimental assays, and the control of microenvironments. Integrating new experimental and theoretical methods, Quantitative Biology: From Molecular to Cellular Systems gives both new and established researchers a solid foundation for starting work in this field. The book is organized into three sections: Fundamental Concepts covers bold ideas that inspire novel approaches in modern quantitative biology. It offers perspectives on evolutionary dynamics, system design principles, chance and memory, and information processing in biology. Methods describes recently developed or improved techniques that are transforming biological research. It covers experimental methods for studying single-molecule biochemistry, small-angle scattering from biomolecules, subcellular localization of proteins, and single-cell behavior. It also describes theoretical methods for synthetic biology and modeling random variations among cells. Molecular and Cellular Systems focuses on specific biological systems where modern quantitative biology methods are making an impact. It incorporates case studies of biological systems for which new concepts or methods are increasing our understanding. Examples include protein kinase at the molecular level, the genetic switch of phage lambda at the regulatory system level, and Escherichia coli chemotaxis at the cellular level. In short, Quantitative Biology presents practical tools for the observation, modeling, design, and manipulation of biological systems from the molecular to the cellular levels.
Concepts Of Modern Mathematics
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Author : Ian Stewart
language : en
Publisher: Courier Corporation
Release Date : 2012-05-23
Concepts Of Modern Mathematics written by Ian Stewart and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-23 with Mathematics categories.
In this charming volume, a noted English mathematician uses humor and anecdote to illuminate the concepts of groups, sets, subsets, topology, Boolean algebra, and other mathematical subjects. 200 illustrations.