Book Companion
Algebraic and Discrete Mathematical Methods for Modern Biology
Edition 1
Welcome to the companion site for Robeva: Algebraic and Discrete Mathematical Methods for Modern Biology, 1st Edition.
Inspired by the national initiative toward a 'new biology,' this work offers a collection of modules introducing methods from modern discrete mathematics into the undergraduate math and biology curricula. Each module begins with a question from contemporary biology, followed by the description of mathematical methods and theory appropriate for the search of answers. Projects and exercises embedded in the text utilize freely-accessible or widely-available software for visualization, simulation, and analysis used in modern biology research. 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. The companion website includes solutions to all exercises and additional materials including tutorials, projects, data sets, and computer code.
Key Features
Examines significant questions in modern biology and their mathematical treatments
Presents important concepts and methods from discrete mathematics in the context of essential biology
Features material appropriate for both mathematics and biology courses
Presents chapters in modular format so coverage does not need to follow the Table of Contents
Introduces projects appropriate for undergraduate research
Requires no calculus as a prerequisite.
About the Author
Raina Robeva was born in Sofia, Bulgaria. She has a Ph.D. in Mathematics from the University of Virginia.
About This Book
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.
Table of Contents
Preface 1. Graph Theory for Systems Biology: Interval Graphs, Motifs, and Pattern RecognitionJohn R. Jungck and Rama Viswanathan 2. Food Webs and GraphsMargaret (Midge) Cozzens 3. Adaptation and Fitness GraphsKristina Crona and Emilie Wiesner 4. Signaling Networks: Asynchronous Boolean ModelsRéka Albert and Raina Robeva 5. Dynamics of Complex Boolean Networks: Canalization, Stability, and Criticality Qijun He, Matthew Macauley and Robin Davies 6. Steady State Analysis of Boolean Models: A Dimension Reduction ApproachAlan Veliz-Cuba and David Murrugarra 7. BioModel Engineering with Petri NetsMary Ann Blätke, Monika Heiner and Wolfgang Marwan 8. Transmission of Infectious Diseases: Data, Models, and SimulationsWinfried Just, Hannah Callender, M. Drew LaMar and Natalia Toporikova 9. Disease Transmission Dynamics on Networks: Network Structure Versus Disease DynamicsWinfried Just, Hannah Callender and M. Drew LaMar 10. Predicting Correlated Responses in Quantitative Traits Under Selection: A Linear Algebra ApproachJanet Steven and Bessie Kirkwood 11. Metabolic Analysis: Algebraic and Geometric MethodsTerrell L. Hodge, Blair R. Szymczyna and Todd J. Barkman 12. Reconstructing the Phylogeny: Computational MethodsGrady Weyenberg and Ruriko Yoshida 13. RNA Secondary Structures: Combinatorial Models and Folding AlgorithmsQijun He, Matthew Macauley and Robin Davies 14. RNA Secondary Structures: An Approach Through Pseudoknots and FatgraphsChristian M. Reidys
Chapters
Chapter 01: Graph Theory for Systems Biology: Interval graphs, motifs, and patterns recognition
John R. Jungck and Rama Viswanathan
Chapter 02: Food Webs and Graphs
Margaret (Midge) Cozzens
Chapter 03: Adaptation and Fitness Graphs
Kristina Crona and Emilie Wiesner
Chapter 04: Signaling Networks: Asynchronous Boolean models
Réka Albert and Raina Robeva
Chapter 05: Dynamics of Complex Boolean Networks: Canalization, stability, and criticality
Qijun He, Matthew Macauley and Robin Davies
Chapter 06: Steady State Analysis of Boolean Models: A dimension reduction approach
Alan Veliz-Cuba and David Murrugarra
Chapter 07: BioModel Engineering with Petri Nets
Mary Ann Blätke, Monika Heiner and Wolfgang Marwan
Chapter 08: Transmission of Infectious Diseases: Data, models, and simulations
Winfried Just, Hannah Callender, M. Drew LaMar and Natalia Toporikova
Chapter 09: Disease Transmission Dynamics on Networks: Network structure versus disease dynamics
Winfried Just, Hannah Callender and M. Drew LaMar
Chapter 10: Predicting Correlated Responses in Quantitative Traits Under Selection: A linear algebra approach
Janet Steven and Bessie Kirkwood
Chapter 11: Metabolic Analysis: Algebraic and geometric methods
Terrell L. Hodge, Blair R. Szymczyna and Todd J. Barkman
Chapter 12: Reconstructing the Phylogeny: Computational methods
Grady Weyenberg and Ruriko Yoshida
Chapter 13: RNA Secondary Structures: Combinatorial models and folding algorithms
Qijun He, Matthew Macauley and Robin Davies
Chapter 14: RNA Secondary Structures: An approach through pseudoknots and fatgraphs
Christian M. Reidys
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