Mathematical Concepts and Methods in Modern Biology

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.