Getting Started in Mathematical Life Sciences PDF Download

Author: Makoto Sato
Publisher: Springer Nature
ISBN: 9811982570
Category : Mathematics
Languages : en
Pages : 211

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Book Description
This book helps the reader make use of the mathematical models of biological phenomena starting from the basics of programming and computer simulation. Computer simulations based on a mathematical model enable us to find a novel biological mechanism and predict an unknown biological phenomenon. Mathematical biology could further expand the progress of modern life sciences. Although many biologists are interested in mathematical biology, they do not have experience in mathematics and computer science. An educational course that combines biology, mathematics, and computer science is very rare to date. Published books for mathematical biology usually explain the theories of established mathematical models, but they do not provide a practical explanation for how to solve the differential equations included in the models, or to establish such a model that fits with a phenomenon of interest. MATLAB is an ideal programming platform for the beginners of computer science. This book starts from the very basics about how to write a programming code for MATLAB (or Octave), explains how to solve ordinary and partial differential equations, and how to apply mathematical models to various biological phenomena such as diabetes, infectious diseases, and heartbeats. Some of them are original models, newly developed for this book. Because MATLAB codes are embedded and explained throughout the book, it will be easy to catch up with the text. In the final chapter, the book focuses on the mathematical model of the proneural wave, a phenomenon that guarantees the sequential differentiation of neurons in the brain. This model was published as a paper from the author’s lab (Sato et al., PNAS 113, E5153, 2016), and was intensively explained in the book chapter “Notch Signaling in Embryology and Cancer”, published by Springer in 2020. This book provides the reader who has a biological background with invaluable opportunities to learn and practice mathematical biology.

Author: Erin N. Bodine
Publisher: Princeton University Press
ISBN: 0691150729
Category : Mathematics
Languages : en
Pages : 630

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Book Description
An accessible undergraduate textbook on the essential math concepts used in the life sciences The life sciences deal with a vast array of problems at different spatial, temporal, and organizational scales. The mathematics necessary to describe, model, and analyze these problems is similarly diverse, incorporating quantitative techniques that are rarely taught in standard undergraduate courses. This textbook provides an accessible introduction to these critical mathematical concepts, linking them to biological observation and theory while also presenting the computational tools needed to address problems not readily investigated using mathematics alone. Proven in the classroom and requiring only a background in high school math, Mathematics for the Life Sciences doesn't just focus on calculus as do most other textbooks on the subject. It covers deterministic methods and those that incorporate uncertainty, problems in discrete and continuous time, probability, graphing and data analysis, matrix modeling, difference equations, differential equations, and much more. The book uses MATLAB throughout, explaining how to use it, write code, and connect models to data in examples chosen from across the life sciences. Provides undergraduate life science students with a succinct overview of major mathematical concepts that are essential for modern biology Covers all the major quantitative concepts that national reports have identified as the ideal components of an entry-level course for life science students Provides good background for the MCAT, which now includes data-based and statistical reasoning Explicitly links data and math modeling Includes end-of-chapter homework problems, end-of-unit student projects, and select answers to homework problems Uses MATLAB throughout, and MATLAB m-files with an R supplement are available online Prepares students to read with comprehension the growing quantitative literature across the life sciences A solutions manual for professors and an illustration package is available

Author: Gerda de Vries
Publisher: SIAM
ISBN: 0898716128
Category : Mathematics
Languages : en
Pages : 307

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Book Description
This is the only book that teaches all aspects of modern mathematical modeling and that is specifically designed to introduce undergraduate students to problem solving in the context of biology. Included is an integrated package of theoretical modeling and analysis tools, computational modeling techniques, and parameter estimation and model validation methods, with a focus on integrating analytical and computational tools in the modeling of biological processes. Divided into three parts, it covers basic analytical modeling techniques; introduces computational tools used in the modeling of biological problems; and includes various problems from epidemiology, ecology, and physiology. All chapters include realistic biological examples, including many exercises related to biological questions. In addition, 25 open-ended research projects are provided, suitable for students. An accompanying Web site contains solutions and a tutorial for the implementation of the computational modeling techniques. Calculations can be done in modern computing languages such as Maple, Mathematica, and MATLAB?.

Author: Yasuhiro Takeuchi
Publisher: Springer Science & Business Media
ISBN: 3540344268
Category : Mathematics
Languages : en
Pages : 232

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Book Description
The purpose of this volume is to present and discuss the many rich properties of the dynamical systems that appear in life science and medicine. It provides a fascinating survey of the theory of dynamical systems in biology and medicine. Each chapter will serve to introduce students and scholars to the state-of-the-art in an exciting area, to present new results, and to inspire future contributions to mathematical modeling in life science and medicine.

Author: Glenn Ledder
Publisher: MAA
ISBN: 0883851911
Category : Biomathematics
Languages : en
Pages : 228

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Book Description
There is a gap between the extensive mathematics background that is beneficial to biologists and the minimal mathematics background biology students acquire in their courses. The result is an undergraduate education in biology with very little quantitative content. New mathematics courses must be devised with the needs of biology students in mind. In this volume, authors from a variety of institutions address some of the problems involved in reforming mathematics curricula for biology students. The problems are sorted into three themes: Models, Processes, and Directions. It is difficult for mathematicians to generate curriculum ideas for the training of biologists so a number of the curriculum models that have been introduced at various institutions comprise the Models section. Processes deals with taking that great course and making sure it is institutionalized in both the biology department (as a requirement) and in the mathematics department (as a course that will live on even if the creator of the course is no longer on the faculty). Directions looks to the future, with each paper laying out a case for pedagogical developments that the authors would like to see.

Author: Frederic Y M Wan
Publisher: World Scientific Publishing Company
ISBN: 9813143355
Category : Mathematics
Languages : en
Pages : 400

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Book Description
Broadly speaking, there are two general approaches to teaching mathematical modeling: 1) the case study approach, and 2) the method based approach (that teaches mathematical techniques with applications to relevant mathematical models). This text emphasizes instead the scientific issues for modeling different phenomena. For the natural or harvested growth of a fish population, we may be interested in the evolution of the population, whether it reaches a steady state (equilibrium or cycle), stable or unstable with respect to a small perturbation from equilibrium, or whether a small change in the environment would cause a catastrophic change, etc. Each scientific issue requires an appropriate model and a different set of mathematical tools to extract information from the model. Models examined are chosen to help explain or justify empirical observations such as cocktail drug treatments are more effective and regenerations after injuries or illness are fast-tracked (compared to original developments). Volume I of this three-volume set limits its scope to phenomena and scientific issues that are modeled by ordinary differential equations (ODE). Scientific issues such as signal and wave propagation, diffusion, and shock formation involving spatial dynamics to be modeled by partial differential equations (PDE) will be treated in Vol. II. Scientific issues involving randomness and uncertainty are examined in Vol. III. Request Inspection Copy Contents: Mathematical Models and the Modeling CycleGrowth of a Population:Evolution and EquilibriumStability and BifurcationInteracting Populations:Linear InteractionsNonlinear Autonomous InteractionsHIV Dynamics and Drug TreatmentsIndex Theory, Bistability and FeedbackOptimization:The Economics of GrowthOptimization over a Planning PeriodModifications of the Basic ProblemBoundary Value Problems are More ComplexConstraints and Control:"Do Your Best" and the Maximum PrincipleChlamydia TrachomatisGenetic Instability and CarcinogenesisMathematical Modeling RevisitedAppendices:First Order ODEBasic Numerical MethodsAssignments Readership: Undergraduates in mathematical biology, mathematical modeling of dynamical systems, optimization and control, viral dynamics (infectious diseases), oncology.

Author: Alexandra V. Antoniouk
Publisher: Walter de Gruyter
ISBN: 3110288532
Category : Mathematics
Languages : en
Pages : 328

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Book Description
The book provides a unique collection of in-depth mathematical, statistical, and modeling methods and techniques for life sciences, as well as their applications in a number of areas within life sciences. It also includes a range of new ideas that represent emerging frontiers in life sciences where the application of such quantitative methods and techniques is becoming increasingly important. The book is aimed at researchers in academia, practitioners and graduate students who want to foster interdisciplinary collaborations required to meet the challenges at the interface of modern life sciences and mathematics.

Author: N. G. Cogan
Publisher: CRC Press
ISBN: 1000646955
Category : Mathematics
Languages : en
Pages : 209

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Book Description
The purpose of this unique textbook is to bridge the gap between the need for numerical solutions to modeling techniques through computer simulations to develop skill in employing sensitivity analysis to biological and life sciences applications. The underpinning mathematics is minimalized. The focus is on the consequences, implementation, and application. Historical context motivates the models. An understanding of the earliest models provides insight into more complicated ones. While the text avoids getting mired in the details of numerical analysis, it demonstrates how to use numerical methods and provides core codes that can be readily altered to fit a variety of situations. Numerical scripts in both Python and MATLAB® are included. Python is compiled in Jupyter Notebook to aid classroom use. Additionally, codes are organized and available online. One of the most important skills requiring the use of computer simulations is sensitivity analysis. Sensitivity analysis is increasingly used in biomathematics. There are numerous pitfalls to using sensitivity analysis and therefore a need for exposure to worked examples in order to successfully transfer their use from mathematicians to biologists. The interconnections between mathematics and the life sciences have an extensive history. This book offers a new approach to using mathematics to model applications using computers, to employ numerical methods, and takes students a step further into the realm of sensitivity analysis. With some guidance and practice, the reader will have a new and incredibly powerful tool to use. https://www.math.fsu.edu/~cogan/Book/Codes/Codes.html

Author: Glenn Ledder
Publisher: Springer Science & Business Media
ISBN: 1461472768
Category : Mathematics
Languages : en
Pages : 431

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Book Description
​ ​​ Mathematics for the Life Sciences provides present and future biologists with the mathematical concepts and tools needed to understand and use mathematical models and read advanced mathematical biology books. It presents mathematics in biological contexts, focusing on the central mathematical ideas, and providing detailed explanations. The author assumes no mathematics background beyond algebra and precalculus. Calculus is presented as a one-chapter primer that is suitable for readers who have not studied the subject before, as well as readers who have taken a calculus course and need a review. This primer is followed by a novel chapter on mathematical modeling that begins with discussions of biological data and the basic principles of modeling. The remainder of the chapter introduces the reader to topics in mechanistic modeling (deriving models from biological assumptions) and empirical modeling (using data to parameterize and select models). The modeling chapter contains a thorough treatment of key ideas and techniques that are often neglected in mathematics books. It also provides the reader with a sophisticated viewpoint and the essential background needed to make full use of the remainder of the book, which includes two chapters on probability and its applications to inferential statistics and three chapters on discrete and continuous dynamical systems. The biological content of the book is self-contained and includes many basic biology topics such as the genetic code, Mendelian genetics, population dynamics, predator-prey relationships, epidemiology, and immunology. The large number of problem sets include some drill problems along with a large number of case studies. The latter are divided into step-by-step problems and sorted into the appropriate section, allowing readers to gradually develop complete investigations from understanding the biological assumptions to a complete analysis.

Author: Ronald W. Shonkwiler
Publisher: Springer Science & Business Media
ISBN: 0387709843
Category : Science
Languages : en
Pages : 552

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Book Description
This text presents mathematical biology as a field with a unity of its own, rather than only the intrusion of one science into another. The book focuses on problems of contemporary interest, such as cancer, genetics, and the rapidly growing field of genomics.