ABSTRACT
Discrete means “individually separated or distinct.” When used in the context of mathematics, it is the opposite of continuous. Thus whereas continuous mathematics is the study of the real line (the continuum), continuous functions on the line, the calculus of such functions, and the generalizations of these notions, discrete mathematics is the study of finite sets, sequences, recurrence relations, and other related notions. This chapter introduces some of the major topics in discrete mathematics, including elementary combinatorics, recurrence relations, and the analysis of algorithms. A combinatorial identity is an identity involving combinatorial objects such as permutations and combinations. Usually a combinatorial identity can be proved in several ways. One way involves the definition of permutations or combinations as ratios of factorials and copious tedious algebra. The chapter illustrates some of the most famous combinatorial identities. It also develops a method for solving some more complicated recurrence relations.
