An Invitation To Mathematical Biology

The textbook is designed to provide a "non-intimidating" entry to the field of mathematical biology. It is also useful for those wishing to teach an introductory course. Although there are many good mathematical biology texts available, most books are too advanced mathematically for most biology majors. Unlike undergraduate math majors, most biology major students possess a limited math background. Given that computational biology is a rapidly expanding field, more students should be encouraged to familiarize themselves with this powerful approach to understand complex biological phenomena. Ultimately, our goal with this undergraduate textbook is to provide an introduction to the interdisciplinary field of mathematical biology in a way that does not overly terrify an undergraduate biology major, thereby fostering a greater appreciation for the role of mathematics in biology

Essential for all biology and biomathematics courses, this textbook provides students with a fresh perspective of quantitative techniques in biology in a field where virtually any advance in the life sciences requires a sophisticated mathematical approach. An Invitation to Biomathematics, expertly written by a team of experienced educators, offers students a solid understanding of solving biological problems with mathematical applications. This text succeeds in enabling students to truly experience advancements made in biology through mathematical models by containing computer-based hands-on laboratory projects with emphasis on model development, model validation, and model refinement. The supplementary work, Laboratory Manual of Biomathematics is available separately ISBN 0123740223, or as a set ISBN: 0123740290) * Provides a complete guide for development of quantification skills crucial for applying mathematical methods to biological problems * Includes well-known examples from across disciplines in the life sciences including modern biomedical research * Explains how to use data sets or dynamical processes to build mathematical models * Offers extensive illustrative materials * Written in clear and easy-to-follow language without assuming a background in math or biology * A laboratory manual is available for hands-on, computer-assisted projects based on material covered in the text

This textbook provides students with a fresh perspective of quantitative techniques in biology in a field where virtually any advance in the life sciences requires a sophisticated mathematical approach. It is written by a team of experienced educators, and offers students a solid understanding of solving biological problems with mathematical applications. It succeeds in enabling students to truly experience advancements made in biology through mathematical models by containing computer-based hands-on laboratory projects with emphasis on model development, model validation, and model refinement.

Laboratory Manual of Biomathematics is a companion to the textbook An Invitation to Biomathematics. This laboratory manual expertly aids students who wish to gain a deeper understanding of solving biological issues with computer programs. It provides hands-on exploration of model development, model validation, and model refinement, enabling students to truly experience advancements made in biology by mathematical models. Each of the projects offered can be used as individual module in traditional biology or mathematics courses such as calculus, ordinary differential equations, elementary probability, statistics, and genetics. Biological topics include: Ecology, Toxicology, Microbiology, Epidemiology, Genetics, Biostatistics, Physiology, Cell Biology, and Molecular Biology . Mathematical topics include Discrete and continuous dynamical systems, difference equations, differential equations, probability distributions, statistics, data transformation, risk function, statistics, approximate entropy, periodic components, and pulse-detection algorithms. It includes more than 120 exercises derived from ongoing research studies. This text is designed for courses in mathematical biology, undergraduate biology majors, as well as general mathematics. The reader is not expected to have any extensive background in either math or biology. Can be used as a computer lab component of a course in biomathematics or as homework projects for independent student work Biological topics include: Ecology, Toxicology, Microbiology, Epidemiology, Genetics, Biostatistics, Physiology, Cell Biology, and Molecular Biology Mathematical topics include: Discrete and continuous dynamical systems, difference equations, differential equations, probability distributions, statistics, data transformation, risk function, statistics, approximate entropy, periodic components, and pulse-detection algorithms Includes more than 120 exercises derived from ongoing research studies

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 treatments Presents important mathematical concepts and tools in the context of essential biology Features material of interest to students in both mathematics and biology Presents chapters in modular format so coverage need not follow the Table of Contents Introduces projects appropriate for undergraduate research Utilizes freely accessible software for visualization, simulation, and analysis in modern biology Requires no calculus as a prerequisite Provides a complete Solutions Manual Features a companion website with supplementary resources

Mathematics has always benefited from its involvement with developing sciences. Each successive interaction revitalises and enhances the field. Biomedical science is clearly the premier science of the foreseeable future. For the continuing health of their subject mathematicians must become involved with biology. With the example of how mathematics has benefited from and influenced physics, it is clear that if mathematicians do not become involved in the biosciences they will simply not be a part of what are likely to be the most important and exciting scientific discoveries of all time. Mathematical biology is a fast growing, well recognised, albeit not clearly defined, subject and is, to my mind, the most exciting modern application of mathematics. The increasing use of mathematics in biology is inevitable as biol ogy becomes more quantitative. The complexity of the biological sciences makes interdisciplinary involvement essential. For the mathematician, biology opens up new and exciting branches while for the biologist mathematical modelling offers another research tool commmensurate with a new powerful laboratory technique but only if used appropriately and its limitations recognised. However, the use of esoteric mathematics arrogantly applied to biological problems by mathemati cians who know little about the real biology, together with unsubstantiated claims as to how important such theories are, does little to promote the interdisciplinary involvement which is so essential. Mathematical biology research, to be useful and interesting, must be relevant biologically.

This self-contained introduction to the fast-growing field of Mathematical Biology is written for students with a mathematical background. It sets the subject in a historical context and guides the reader towards questions of current research interest. A broad range of topics is covered including: Population dynamics, Infectious diseases, Population genetics and evolution, Dispersal, Molecular and cellular biology, Pattern formation, and Cancer modelling. Particular attention is paid to situations where the simple assumptions of homogenity made in early models break down and the process of mathematical modelling is seen in action.

Mathematical Concepts and Methods in Modern Biology offers a quantitative framework for analyzing, predicting, and modulating the behavior of complex biological systems. The book presents important mathematical concepts, methods and tools in the context of essential questions raised in modern biology. Designed around the principles of project-based learning and problem-solving, the book considers biological topics such as neuronal networks, plant population growth, metabolic pathways, and phylogenetic tree reconstruction. The mathematical modeling tools brought to bear on these topics include Boolean and ordinary differential equations, projection matrices, agent-based modeling and several algebraic approaches. Heavy computation in some of the examples is eased by the use of freely available open-source software. Features self-contained chapters with real biological research examples using freely available computational tools Spans several mathematical techniques at basic to advanced levels Offers broad perspective on the uses of algebraic geometry/polynomial algebra in molecular systems biology