Quantifying life : a sympiosis of computational, mathematics, and biology
Dimitry A. Kondrashov
Chicago : University Of Chicago Press, 2016
xvi, 417 pages ; 24 cm
Quantifying life offers an accessible introduction to the breadth of mathematical modeling used in biology today. Assuming only a foundation in high school mathematics, it takes an innovative computation approach to developing mathematical skills and intuition. Through lessons illustrated with copious examples, mathematical and programming exercises, literature discussion questions, and computational projects of various degrees of difficulty, students build and analyze models based on current research papers and learn to implement them in the R programming language. This interplay of mathematical ideas, systematically developed programming skills, and a broad selection of biological research topics make Quantifying Life an invaluable guide for seasoned life scientists and the next generation of biologists alike.
Describing single variables : Arithmetic and variables: the lifeblood of modeling ; Functiona and their graphs ; Describing data sets ; Random variables and distributions -- Estimation form a random sample -- Relationship between two variables : Independence of random variables ; Bayes' amazing formula ; Linear regression and correlation ; Nonlinear data fitting -- Chains of random variables : Markov models with discrete states ; Probability distributions of Markov chains ; Stationary distributions of Markov chains ; Dynamics of Markov models -- Variations that change with time : Linear difference equations ; Linear ordinary differential equations ; Graphical analysis of ordinary differential equations ; Chaos and bifuractions in difference equations