Algebraic and Discrete Mathematical Methods for Modern Biology

Written by experts in both mathematics and biology, Algebraic and Discrete Mathematical Methods for Modern Biology offers a bridge between math and biology, providing a framework for simulating, analyzing, predicting, and modulating the behavior of complex biological systems. Each chapter begins with a question from modern biology, followed by the description of certain mathematical methods and theory appropriate in the search of answers. Every topic provides a fast-track pathway through the problem by presenting the biological foundation, covering the relevant mathematical theory, and highlighting connections between them. Many of the projects and exercises embedded in each chapter utilize specialized software, providing students with much-needed familiarity and experience with computing applications, critical components of the "modern biology" skill set. This book is appropriate for mathematics courses such as finite mathematics, discrete structures, linear algebra, abstract/modern algebra, graph theory, probability, bioinformatics, statistics, biostatistics, and modeling, as well as for biology courses such as genetics, cell and molecular biology, biochemistry, ecology, and evolution.

Examines significant questions in modern biology and their mathematical treatmentsPresents important mathematical concepts and tools in the context of essential biologyFeatures material of interest to students in both mathematics and biologyPresents chapters in modular format so coverage need not follow the Table of ContentsIntroduces projects appropriate for undergraduate researchUtilizes freely accessible software for visualization, simulation, and analysis in modern biologyRequires no calculus as a prerequisiteProvides a complete Solutions ManualFeatures a companion website with supplementary resources

Preface 1. Graph Theory for Systems Biology: Interval graphs, motifs, and patterns recognition 2. Food Webs and Graphs 3. Adaptation and Fitness Graphs 4. Signaling Networks: Asynchronous Boolean models 5. Dynamics of Complex Boolean Networks: Canalization, stability, and criticality 6. Steady State Analysis of Boolean Models: A dimension reduction approach 7. BioModel Engineering with Petri Nets 8. Transmission of Infectious Diseases: Data, models, and simulations 9. Disease Transmission Dynamics on Networks: Network structure versus disease dynamics 10. Predicting Correlated Responses in Quantitative Traits Under Selection: A linear algebra approach 11. Metabolic Analysis: Algebraic and geometric methods 12. Reconstructing the Phylogeny: Computational methods 13. RNA Secondary Structures: Combinatorial models and folding algorithms 14. RNA Secondary Structures: An approach through pseudoknots and fatgraphs