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Gallier, Jean

Discrete Mathematics (Kartoniert / Broschiert / Paperback)

Reihe: Universitext

Springer-Verlag GmbH, Springer US, März 2011

465 S. - Sprache: Englisch - 200 schwarz-weiße und 20 farbige Abbildungen, 5 schwarz-weiße Tabellen - 237x159x29 mm Book

ISBN: 1441980466 EAN: 9781441980465

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.

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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 theoremCovers planar graphs


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.

Über den Autor

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


From the reviews:"This well-written, highly illustrated book will be very useful and interesting to students in both mathematics and computer science. ... Attractive features of this book include clear presentations, end-of-chapter summaries and references, a useful set of problems of varying difficulty, and a symbol as well as a subject index. Summing Up: Highly recommended. Upper-division undergraduates, graduate students, and professionals/practitioners." (D. V. Chopra, Choice, Vol. 48 (11), July, 2011)"This book is intended to be a textbook for students in Computer Science, covering basic areas of Discrete Mathematics. ... lots of references to supplementary or more advanced literature are provided, and less basic and more sophisticated problems as well as connections to other areas of science are given. Each chapter closes with a rich collection of exercises, which often include hints to their solution and further explanations." (Martina Kubitzke, Zentralblatt MATH, Vol. 1227, 2012)"This book provides a rigorous introduction to standard topics in the field: logical reasoning, sets, functions, graphs and counting techniques. Its intended audience is computer science undergraduate students, but could also be used in a course for mathematics majors. ... Each chapter has a summary and a generous number of exercises ... . The exposition is structured as a series of propositions and theorems that are proved clearly and in detail. Historical remarks and an abundance of photographs of mathematicians enliven the text." (Gabriella Pinter, The Mathematical Association of America, February, 2012)

ISBN 1-441980-46-6, ISBN 1-44-198046-6, ISBN 1-44198-046-6, ISBN 1-441-98046-6, ISBN 1-4419-8046-6

ISBN 978-1-441980-46-5, ISBN 978-1-44-198046-5, ISBN 978-1-44198-046-5, ISBN 978-1-441-98046-5, ISBN 978-1-4419-8046-5

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