Mathematical Concepts and Methods in Modern Biology

Using Modern Discrete Models

Edited by

  • Raina Robeva, Professor of Mathematical Sciences, Sweet Briar College, Sweet Briar, VA, USA
  • Terrell Hodge, Western Michigan University, Kalamazoo, MI, USA

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.

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Researchers, educators, and students engaged in Biological Research and Mathematics


Book information

  • Published: January 2013
  • ISBN: 978-0-12-415780-4


"Contributors in biology, in mathematics, and in bioinformatics introduce undergraduate students and their instructors to more applications of discrete mathematics to biology than can be found in standard textbooks. The goal is not to be comprehensive, but to open the door to more advanced and specialized resources."--Reference and Research Book News, August 2013

Table of Contents

Preface by Raina Robeva and Terrell Hodge
Chapter 1. Mechanisms for Gene Regulation: A Boolean Network Model of the Lac Operon
Chapter 2. Epigenetic Features of the Lac Operon: Comparing Boolean and Ordinary Differential Equations Models
Chapter 3. Inferring the Topology of Gene Regulatory Networks: An Algebraic Approach to Reverse Engineering
Chapter 4. Global Dynamics Emerging from Local Interactions: Agent-based Modeling for the Life Sciences
Chapter 5. Agent-based Models and Optimal Control in Biology: An Algebraic Approach
Chapter 6. Neuronal Networks: A Discrete Model
Chapter 7. Predicting Plant Population Growth: Modeling with Projection Matrices
Chapter 8. Metabolic Pathways Analysis: A Linear Algebraic Approach
Chapter 9. Identifying CpG Islands: Sliding Windows and Hidden Markov Models
Chapter 10. Codon Usage: From Elementary Probability to Algebraic Geometry
Chapter 11. Phylogenetic Tree Reconstruction: Geometric Approaches