Discrete Mathematics - Brossura

Gallier, Jean

Brossura

ISBN 10: 1441980466 ISBN 13: 9781441980465

Casa editrice: Springer, 2011

Riassunto

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.

Su questo libro

Informazioni sull?autore

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

Dalla quarta di copertina

<p>This book gives an introduction to discrete mathematics for beginning undergraduates and starts with a chapter on the rules of mathematical reasoning. </p><p> </p><p>This book  begins with a presentation of the rules of logic as used in mathematics where 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 deals with functions and relations, directed and undirected graphs and an introduction to combinatorics, partial orders and complete induction. 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 where Eulerian and Hamiltonian cycles are discussed. This book also includes network flows, matchings, covering, bipartite graphs, planar graphs and state the graph minor theorem of Seymour and Robertson. </p><p> </p><p>The book is highly illustrated  and each chapter ends with a list of problems of varying difficulty. Undergraduates in mathematics and computer science will find this book useful. </p><p> </p>

Dettagli dell?edizione

• Editore: Springer
• Data di pubblicazione: 2011
• Lingua: Inglese
• ISBN 10: 1441980466
• ISBN 13: 9781441980465
• Rilegatura: Copertina flessibile
• Numero di pagine: 480
• Contatto del produttore: non disponibile
• Persona responsabile: CMN Printpool Inh. Mathis Neumann; https://www.also.com/ec/cms5/en_6000/6000/index.jsp; ; Friedrich-Karl-Str. 9; Hamburg; Germania