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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.
List of contents
Preface to the 2nd Edition
Preface to the 1st Edition
1. Modeling Gene Regulation Using Boolean Network Models
2. Bistability in Bacterial Genetic Networks: A Comparison of Differential Equations and Boolean Network Models
3. Inferring the Topology of Gene Regulatory Networks: An Algebraic Approach to Reverse Engineering
4. Stochastic Boolean Networks
5. Global Dynamics Emerging from Local Interactions: Agent-Based Modeling for the Life Sciences
6. Agent-Based Models and Optimal Control in Biology: A Discrete Approach
7. Neuronal Networks: A Discrete Model
8. Predicting Population Growth: Modeling with Projection Matrices
9. Identifying CpG Islands: Sliding Windows and Using Hidden Markov Models Approaches
10. Phylogenetic Tree Reconstruction: Geometric Approaches
11. Tropical Linear Algebra and its Applications to Phylogenomics
About the author
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.
