This text surveys many of the topics taught in discrete and finite mathematics
courses. The topics chosen are widely applied in present-day
industry and, at the same time, are mathematically elegant. Chapter 1
begins with such preliminaries as sets, mathematical induction, functions,
and the division algorithm of algebra. Chapters 2 and 3 present
combinatorics and probability. Chapter 4 introduces the modern approach
to finance; it presents the concept of arbitrage and the arbitrage
theorem and then uses them to analyze the no-arbitrage costs of options.
Chapters 5 and 6 deal with graphs and their many applications. Chapter
7 introduces linear programming. Among other applications, we use
the duality theorem to derive the arbitrage theorem as well as the minimax
theorem of game theory. Chapter 8 presents sorting and searching
techniques that are useful in computer science. Chapter 9 introduces the
subject matter of statistics, presenting both its descriptive and inferential
side. Chapter 10 deals with groups and permutations