Discrete Mathematics (Universitext) 2011th Edition by Jean Gallier (PDF)

Description

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.

User’s Reviews

Editorial Reviews: Review 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) From the Back Cover This book gives an introduction to discrete mathematics for beginning undergraduates and starts with a chapter on the rules of mathematical reasoning. 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. 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. About the Author Jean Gallier is a Professor in the Computer and Information Science Department, School of Engineering and Applied Science at the University of Pennsylvania. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Discrete mathematics (so-called because it handles a bunch of seemingly “random” topics) is the red-headed stepchild of math; nearly every computer science student is required to take a course in it, but there is little glamor to it and so the textbooks about it are usually very wooden. Jean Gallier, who teaches at Penn, has tried to duplicate the flavor of an introductory yet high-powered course in this Springer Universitext; however, those of you who aren’t “Ivy Leaguers” will not be particularly well-served by his presentation. Gallier writes in an “engaging” style but four hundred and fifty pages later the reader is not yet particularly engaged; the topics covered in this way come across as a weird mix of very basic principles of modern math and highly abstract topics which are mostly gestured at.The book starts with a chapter on logic that is far too advanced; I cannot imagine that even an average computer science PhD will need to know Kripke’s semantics for intuitionistic logic. It is then followed by sections on set theory which are too primitive; it seems likely that even a four-year CS student will need to know several versions of the axiom of choice. The two chapters on graph theory are adequate, although too little care is taken in presenting the graph-theoretic algorithms programmers may very well have a need to use in practice; another chapter goes on about the RSA public-key cryptography system at length, then directs the reader to “more complete” discussions of the system in other books. (The section on lattices, a topic where a great deal of “pure” logic is naturally and neatly encapsulated in a properly “mathematical” structure, is the best of the bunch.)Color printing is used badly, for only a few of the diagrams in the book require it and the endless cavalcade of postage-stamp-sized portraits of (male) mathematicians is gratuitous *tout court*. For a person like me with limited knowledge of the “purer” mathematical topics addressed there is some value to this as a “starter”, but another book will be required to achieve an adequate mastery of the field.

⭐

Keywords

Free Download Discrete Mathematics (Universitext) 2011th Edition in PDF format
Discrete Mathematics (Universitext) 2011th Edition PDF Free Download
Download Discrete Mathematics (Universitext) 2011th Edition 2011 PDF Free
Discrete Mathematics (Universitext) 2011th Edition 2011 PDF Free Download
Download Discrete Mathematics (Universitext) 2011th Edition PDF
Free Download Ebook Discrete Mathematics (Universitext) 2011th Edition