This books gives an introduction todiscrete mathematics for beginning undergraduates.One of original features of this book is that it beginswith a presentation of the rules of logic as usedin mathematics. Many examples of formaland informal proofs are given. With this logical frameworkfirmly in place, the book describes the major axioms of set theoryand introduces the natural numbers. The rest of the book is morestandard. It deals with functions and relations, directed and undirected graphs,and an introduction to combinatorics. There is a section on public key cryptography and RSA,with complete proofs of Fermat's little theorem and thecorrectness of the RSA scheme, as well as explicit algorithmsto perform modular arithmetic. The last chapter provides more graph theory.Eulerian and Hamiltonian cycles are discussed.Then, we study flows and tensions and state and prove themax flow min-cut theorem.We also discuss matchings, covering, bipartite graphs.