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© 2014

Mathematical Methods in Biology and Neurobiology

Benefits

  • Develops the mathematical tools required for modern biology at all levels and scales

  • Provides a survey of mathematics, from graph theory and stochastic processes to dynamical systems and pattern formation

  • Contains biological examples from the molecular to the evolutionary and ecological levels

  • Contains concise, modern introduction to mathematical population genetics

  • Written by one of the most experienced and successful authors of advanced mathematical textbooks

Textbook

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-x
  2. Jürgen Jost
    Pages 1-4
  3. Jürgen Jost
    Pages 5-57
  4. Jürgen Jost
    Pages 59-88
  5. Jürgen Jost
    Pages 89-173
  6. Jürgen Jost
    Pages 175-198
  7. Jürgen Jost
    Pages 199-215
  8. Back Matter
    Pages 217-226

About this book

Introduction

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 recombination
• the interaction of species.

Written by one of the most experienced and successful authors of advanced mathematical textbooks, this book stands apart for the wide range of mathematical tools that are featured. It will be useful for graduate students and researchers in mathematics and physics that want a comprehensive overview and a working knowledge of the mathematical tools that can be applied in biology. It will also be useful for biologists with some mathematical background that want to learn more about the mathematical methods available to deal with biological structures and data.

Keywords

Branching Processes Coalescents Dynamical Systems in Biology FitzHugh-Nagumo Gene Genealogies Graph Theory Hodgkin-Huxley Mathematical Biology Mathematical Tools for Systems Biology Network Analysis Optimal Resource Allocation Pattern Formation Phylogenetic Reconstruction Population Genetics Reaction-Diffusion Systems Sexual Recombination Stochastic Processes Turing Mechanism Wright-Fisher

Authors and affiliations

  1. 1.Max Planck Institute for Mathematics in the SciencesLeipzigGermany

About the authors

Written by one of the most experienced and successful authors of advanced mathematical textbooks.

Bibliographic information

Industry Sectors
Energy, Utilities & Environment
Finance, Business & Banking

Reviews

From the book reviews:

“This book sets itself the task of highlighting the use of graph theory, stochastic methods and partial differential equations in current biology. … This book is ideal for someone with some mathematical expertise who wishes to put it to use at the current boundaries of biological exploration.” (Jeff Ibbotson, MAA Reviews, January, 2015)

“This is a very good discussion of the mathematical modeling of genetics, populational theory, and neurosciences. … I highly recommend this book to neuroscientists, students, fellows and neurobiologists alike.” (Joseph J. Grenier, Amazon.com, August, 2014)