Mathematics for the biological sciences

Written specifically to strengthen the quantitative skills of life science students, Mathematics for the Biological Sciences presents mathematical concepts with biological applications. Its nine chapters deal with a wide range of mathematics and, through worked examples, help students develop the ability to relate mathematics to biology. In its pages you will find: • Sound, in-depth coverage of essential finite mathematics, including discrete probability and matrices • Lucid explanations of Markov chains and game theory-Important in population ecology and in medical diagnosis and treatment • Detailed descriptions of discrete and continuous probability distributions important in biological applications • Development of difference equations-a vital tool in population genetics • A chapter devoted to developing skills in building mathematical models of biological processes • Presentation of parallel developments of difference and differential equations, with clear explanations of how both discrete and continuous models of biological processes can be constructed • 750 problem at various levels of difficulty that reinforce the mathematics of each chapter and suggest many biological applications. Organization is clear and logical. The first three chapters cover basic finite mathematics, and require only high school algebra. Sets, the binomial and multinomial theorems. discrete probability, vectors and matrices- all the concepts necessary for understanding the subsequent material are thoroughly presented. Three of the most important applications of vectors and matrices are examined in the following chapters: linear programming, Markov chains, and game theory. After this there is a complete discussion of difference equations. The next two chapters-differential equations and continuous probability-use calculus; students who lack a calculus background or who need to review calculus are provided with two complete appendices that present basic material. The final chapter is devoted to developing mathematical models of biological processes. The models examined all relate to the basic problems of the growth, survival, and extinction of populations. All material required for these models is developed in the preceding chapters. Just as the overall presentation is logically developed, so are the individual chapters. Each begins with the introduction of one or more interrelating mathematical concepts. that are illustrated by several examples. Frequently, a meaningful biological or medical problem is cited and then the mathematical tools necessary to analyze the problem are developed. A wide selection of problems concludes each chapter.