Mathematical Concepts and Methods in Modern Biology

Using Modern Discrete Models

Raina Robeva

• Publisher: Academic Press
• Year: 2026
• Edition: 2
• eBook ISBN:
  9780443296536
• Topic: Biological Sciences
• Subtopic: Biology
• Index: Biological Sciences

Mathematical Concepts and Methods in Modern Biology: Using Modern Discrete Models, Second Edition presents an updated, quantitative framework for analyzing, predicting, and modulating complex biological systems. Structured around project-based learning and problem-solving, it integrates essential mathematical concepts and methods in the context of key biological questions. Topics include gene regulatory and neuronal networks, CpG islands, plant population growth, interacting populations, phylogenetics, and phylogenomics. Modeling tools span discrete dynamical systems (including deterministic and stochastic Boolean networks), ordinary differential equations, projection matrices, agent-based modeling, polynomial ideals, Gröbner bases, tropical algebra, and other algebraic approaches. Computation is supported by a range of software tools, including some developed for this book, as well as open source, freely available, and proprietary platforms. Updated code examples and step-by-step instructions illustrate software use, making this a valuable resource for health professionals, scientists, researchers, and students in related fields. - Provides fully updated and expanded content, examples, exercises, and projects on applications of modern discrete mathematics and algebraic statistics to pressing problems in modern biology. - Introduces discrete and algebraic methods in the context of important biological questions. - Emphasizes the use of specialized software as a core element of the modern biology skill set by integrating open-source tools, freely available applications, and mainstream proprietary software. - Prepares readers – through examples, exercises, and carefully selected projects – to transition successfully into student research and engagement with the research literature.

Table of contents

• Title of Book
• Chapter 1. Modeling gene regulation using Boolean network models∗
• Chapter 2. Bistability in bacterial genetic networks: A comparison of differential equations and Boolean network models∗
• Chapter 3. Inferring the topology of gene regulatory networks: An algebraic approach to reverse engineering∗
• Chapter 4. Stochastic Boolean Networks∗
• Chapter 5. Global dynamics emerging from local interactions: Agent-based modeling for the life sciences∗
• Chapter 6. Agent-based models and optimal control in biology: A discrete approach∗
• Chapter 7. Neuronal networks: A discrete model∗
• Chapter 8. Predicting population growth: Modeling with projection matrices∗
• Chapter 9. Identifying CpG islands: Sliding window and hidden Markov model approaches
• Chapter 10. Phylogenetic tree reconstruction: Geometric approaches∗
• Chapter 11. Tropical linear algebra and its applications to phylogenomics∗
• Index