This book introduces modeling real life situations with difference equations, matrices, Markov chains, linear programming, sets, and probability using Excel. An emphasis on the use of graphical and numerical techniques, rather than theoretical one, is utilized to investigate and analyze the behavior of solutions of the mathematical models. The author investigates interesting linear and nonlinear models, models represented by systems of linear and non-linear difference equations, and systems of linear equations from diverse disciplines. Linear optimization models are investigated by utilizing linear programming, sets and counting techniques are introduced and utilized in probability, and probabilistic models are explored. T he models represent real life situations in business, finance, economics, biology, ecology, environment, and the social sciences. The use of computers and cooperative learning techniques are integrated to create an interactive learning environment. and lab time are devoted to discussions on carefully prepared activities where students work in small groups to discuss and reflect on the results of their work. An emphasis on real world problems and computers promotes a conceptual understanding and to motivate students to expand that experience to a host of other real life situations. Readers are guided in this discovery method by exploring concepts and topics in mathematics that are useful and relevant to them. Topical coverage includes an introduction to mathematical modeling; modeling with first-order linear difference equations; modeling with first-order nonlinear difference equations; modeling with matrices and systems of first-order linear difference equations; modeling with systems of nonlinear difference equations; modeling with second-order difference equations; optimization models; sets and counting in modeling; probability models; and the basics of Excel spreadsheets.
