Discrete mathematics /
Gallier, Jean H.
Discrete mathematics / Jean Gallier. - New York : Springer, c2011. - xiii, 465 p. : ill. (some col.), ports. ; 24 cm. - Universitext. .
Includes bibliographical references and indexes.
Mathematical reasoning, proof principles, and logic -- Relations, functions, partial functions -- Graphs, Part I: Basic notions -- Some counting problems; multinomial coefficients -- Partial orders, GCDs, RSA, Lattices -- Graphs, Part II: More advanced notions.
Summary: 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.
9781441980465 (pbk. : alk. paper) 9781441980472 (eISBN) 1441980466
2012419782
Mathematics.
Computer vision.
Number theory.
Engineering design.
QA76.9.M35 / G35 2011
510
Discrete mathematics / Jean Gallier. - New York : Springer, c2011. - xiii, 465 p. : ill. (some col.), ports. ; 24 cm. - Universitext. .
Includes bibliographical references and indexes.
Mathematical reasoning, proof principles, and logic -- Relations, functions, partial functions -- Graphs, Part I: Basic notions -- Some counting problems; multinomial coefficients -- Partial orders, GCDs, RSA, Lattices -- Graphs, Part II: More advanced notions.
Summary: 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.
9781441980465 (pbk. : alk. paper) 9781441980472 (eISBN) 1441980466
2012419782
Mathematics.
Computer vision.
Number theory.
Engineering design.
QA76.9.M35 / G35 2011
510