Discrete Mathematics

Written for undergraduates, this volume provides an introduction to discrete mathematics. The text begins with a presentation of the rules of logic as used in mathematics, and includes various examples of formal and informal proofs.

This books gives an introduction to discrete mathematics for beginning undergraduates. One of original features of this book is that it begins with a presentation of the rules of logic as used in mathematics. Many examples of formal and informal proofs are given. With this logical framework firmly in place, the book describes the major axioms of set theory and introduces the natural numbers. The rest of the book is more standard. 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 the correctness of the RSA scheme, as well as explicit algorithms to 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 the max flow min-cut theorem. We also discuss matchings, covering, bipartite graphs.

Summarizing the rules of mathematical reasoning and how to construct proofs Presents examples of formal and informal proofs Includes examples of proofs by induction Discusses public key cryptography, with a complete proof of the correctness of RSA Explicit, detailed algorithms for modular arithmetic Explores graph flows and the max-flow min-cut theorem Covers planar graphs Includes supplementary material: sn.pub/extras

Autorentext
Jean Gallier is a Professor in the Computer and Information Science Department, School of Engineering and Applied Science at the University of Pennsylvania.

Inhalt

Mathematical Reasoning, Proof Principles and Logic.- Relations, Functions, Partial Functions.- Graphs, Part I: Basic Notions.- Some Counting Problems; Multinomial Coefficients.- Partial Orders, GCD's, RSA, Lattices.- Graphs, Part II: More Advanced Notions.- Answers to Selected Problems.