Universitext

Discrete Mathematics

Authors: Gallier, Jean

  • 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
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eBook $54.99
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  • ISBN 978-1-4419-8047-2
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  • Immediate eBook download after purchase
Softcover $74.95
price for USA
  • ISBN 978-1-4419-8046-5
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Rent the ebook  
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About this Textbook

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 authors

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

Reviews

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)


Table of contents (6 chapters)

  • Mathematical Reasoning, Proof Principles, and Logic

    Gallier, Jean

    Pages 1-100

  • Relations, Functions, Partial Functions

    Gallier, Jean

    Pages 101-164

  • Graphs, Part I: Basic Notions

    Gallier, Jean

    Pages 165-203

  • Some Counting Problems; Multinomial Coefficients, The Principle of Inclusion–Exclusion, Sylvester’s Formula, The Sieve Formula

    Gallier, Jean

    Pages 205-255

  • Partial Orders, Lattices, Well-Founded Orderings, Unique Prime Factorization in ℤ and GCDs, Equivalence Relations, Fibonacci and Lucas Numbers, Public Key Cryptography and RSA, Distributive Lattices, Boolean Algebras, Heyting Algebras

    Gallier, Jean

    Pages 257-363

Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-1-4419-8047-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $74.95
price for USA
  • ISBN 978-1-4419-8046-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Discrete Mathematics
Authors
Series Title
Universitext
Copyright
2011
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media, LLC
eBook ISBN
978-1-4419-8047-2
DOI
10.1007/978-1-4419-8047-2
Softcover ISBN
978-1-4419-8046-5
Series ISSN
0172-5939
Edition Number
1
Number of Pages
XIV, 466
Number of Illustrations and Tables
200 b/w illustrations, 20 illustrations in colour
Topics