Discrete Mathematics: Elementary and Beyond

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Springer Science & Business Media, Jan 27, 2003 - Mathematics - 284 pages
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Discrete mathematics is quickly becoming one of the most important areas of mathematical research, with applications to cryptography, linear programming, coding theory and the theory of computing. This book is aimed at undergraduate mathematics and computer science students interested in developing a feeling for what mathematics is all about, where mathematics can be helpful, and what kinds of questions mathematicians work on. The authors discuss a number of selected results and methods of discrete mathematics, mostly from the areas of combinatorics and graph theory, with a little number theory, probability, and combinatorial geometry. Wherever possible, the authors use proofs and problem solving to help students understand the solutions to problems. In addition, there are numerous examples, figures and exercises spread throughout the book.

László Lovász is a Senior Researcher in the Theory Group at Microsoft Corporation. He is a recipient of the 1999 Wolf Prize and the Gödel Prize for the top paper in Computer Science. József Pelikán is Professor of Mathematics in the Department of Algebra and Number Theory at Eötvös Loránd University, Hungary. In 2002, he was elected Chairman of the Advisory Board of the International Mathematical Olympiad. Katalin Vesztergombi is Senior Lecturer in the Department of Mathematics at the University of Washington.

 

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The book is awesome and I was impressed by the lucid treatment by the authors.
The prerequisite to read and understand this book is the knowledge of high school mathematics, but the reader must also
refer other papers and books to get the in depth knowledge for some of the proofs and concept.
Overall I will give it 5/5.
 

Contents

Lets Count
1
Combinatorial Tools
25
Binomial Coefficients and Pascals Triangle
43
Fibonacci Numbers
65
Combinatorial Probability
77
Integers Divisors and Primes
87
Graphs
125
Trees
141
Matchings in Graphs
165
Combinatorics in Geometry
179
Eulers Formula
189
Coloring Maps and Graphs
197
Finite Geometries Codes Latin Squares and Other Pretty Creatures
211
A Glimpse of Complexity and Cryptography
239
Answers to Exercises
251
Copyright

Finding the Optimum
157

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About the author (2003)

 László Lovász is a Senior Researcher in the Theory Group at Microsoft Corporation. He is a recipient of the 1999 Wolf Prize and the Gödel Prize for the top paper in Computer Science. József Pelikán is Professor of Mathematics in the Department of Algebra and Number Theory at Eötvös Loránd University, Hungary. In 2002, he was elected Chairman of the Advisory Board of the International Mathematical Olympiad. Katalin Vesztergombi is Senior Lecturer in the Department of Mathematics at the University of Washington.

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