Mathematical Concepts and Methods in Modern Biology
Using Modern Discrete Models
- 2nd Edition - December 1, 2025
- Latest edition
- Editor: Raina Robeva
- Language: English
Mathematical Concepts and Methods in Modern Biology: Using Modern Discrete Models, Second Edition presents an updated, quantitative framework for analyzing, predicting, and modula… Read more
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
Researchers in algebraic biology, mathematical and computational biology
Preface to the 2nd Edition
Preface to the 1st Edition
1. Modeling Gene Regulation Using Boolean Network Models
Raina Robeva, Bessie Kirkwood and Robin Davies
2. Bistability in Bacterial Genetic Networks: A Comparison of Differential Equations and Boolean Network Models
Raina Robeva and Necmettin Yildirim
3. Inferring the Topology of Gene Regulatory Networks: An Algebraic Approach to Reverse Engineering
Elena Dimitrova and Brandilyn Stigler
4. Stochastic Boolean Networks
David Murrugarra, Alan Veliz-Cuba and Daniel Plaugher
5. Global Dynamics Emerging from Local Interactions: Agent-Based Modeling for the Life Sciences
Holly Gaff
6. Agent-Based Models and Optimal Control in Biology: A Discrete Approach
Reinhard Laubenbacher, Franziska Hinkelmann and Matthew Oremland
7. Neuronal Networks: A Discrete Model
David Terman and Ann Sungwoo
8. Predicting Population Growth: Modeling with Projection Matrices
Janet C. Steven and James Kirkwood
9. Identifying CpG Islands: Sliding Windows and Using Hidden Markov Models Approaches
Raina Robeva, Robin Davies, Aaron Garrett and James Kirkwood
10. Phylogenetic Tree Reconstruction: Geometric Approaches
Ruriko Yoshida
11. Tropical Linear Algebra and its Applications to Phylogenomics
Ruriko Yoshida
Preface to the 1st Edition
1. Modeling Gene Regulation Using Boolean Network Models
Raina Robeva, Bessie Kirkwood and Robin Davies
2. Bistability in Bacterial Genetic Networks: A Comparison of Differential Equations and Boolean Network Models
Raina Robeva and Necmettin Yildirim
3. Inferring the Topology of Gene Regulatory Networks: An Algebraic Approach to Reverse Engineering
Elena Dimitrova and Brandilyn Stigler
4. Stochastic Boolean Networks
David Murrugarra, Alan Veliz-Cuba and Daniel Plaugher
5. Global Dynamics Emerging from Local Interactions: Agent-Based Modeling for the Life Sciences
Holly Gaff
6. Agent-Based Models and Optimal Control in Biology: A Discrete Approach
Reinhard Laubenbacher, Franziska Hinkelmann and Matthew Oremland
7. Neuronal Networks: A Discrete Model
David Terman and Ann Sungwoo
8. Predicting Population Growth: Modeling with Projection Matrices
Janet C. Steven and James Kirkwood
9. Identifying CpG Islands: Sliding Windows and Using Hidden Markov Models Approaches
Raina Robeva, Robin Davies, Aaron Garrett and James Kirkwood
10. Phylogenetic Tree Reconstruction: Geometric Approaches
Ruriko Yoshida
11. Tropical Linear Algebra and its Applications to Phylogenomics
Ruriko Yoshida
- Edition: 2
- Latest edition
- Published: December 1, 2025
- Language: English
RR
Raina Robeva
Raina Robeva was born in Sofia, Bulgaria. She holds a Ph.D. in Mathematics from the University of Virginia and is a Professor of Mathematics and a Karl E. Peace Fellow in Mathematics at Randolph-Macon College in the United States. Her current research is in the broad fields of mathematical and systems biology. In addition to editing this second edition, she has authored and edited several books, including A Bridge to Higher Mathematics (CRC Press, 2024), Algebraic and Combinatorial Computational Biology (Academic Press, 2019), and Algebraic and Discrete Mathematical Methods for Modern Biology (Academic Press, 2015). She has chaired the Advisory Board of the National Institute for Mathematical and Biological Synthesis (NIMBioS), led the Committee on Special Interest Groups of the Mathematical Association of America, and served for over a decade as the founding Editor-in-Chief of Frontiers in Systems Biology.
Affiliations and expertise
Professor of Mathematics, Karl E. Peace Fellow in Mathematics, Randolph-Macon College, VA USA