The advent of fast computers and the search for efficient algorithms revolutionized combinatorics and brought about the field of discrete mathematics. This book is an introduction to the main ideas and results of discrete mathematics, and with its emphasis on algorithms it should be interesting to mathematicians and computer scientists alike. The book is organized into three parts: enumeration, graphs and algorithms, and algebraic systems. There are 600 exercises with hints and solutions to about half of them. The only prerequisites for understanding everything in the book are linear algebra and calculus at the undergraduate level.
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Praise for the German edition ... ""This book is a well-written introduction to discrete mathematics and is highly recommended to every student of mathematics and computer science as well as to teachers of these topics."" - Konrad Engel for MathSciNet
""Aigner offers a very enjoyable review of discrete mathematics at the graduate level."" - Choice Reviews
""This book gives a leisurely and clear exposition of the main topics of discrete mathematics."" - Allen Stenger for MAA Reviews
Counting: Fundamentals
Summation
Generating functions
Counting patterns
Asymptotic analysis
Bibliography for Part 1
Graphs and algorithms: Graphs
Trees
Matchings and networks
Searching and sorting
General optimization methods
Bibliography for Part 2
Algebraic systems: Boolean algebras
Modular arithmetic
Coding
Cryptography
Linear optimization
Bibliography for Part 3
Solutions to selected exercises
Index
Martin Aigner is a professor of mathematics at the Free University of Berlin. He received his PhD at the University of Vienna and has held a number of positions in the USA and Germany before moving to Berlin. He is the author of several books on discrete mathematics, graph theory, and the theory of search. The Monthly article Turan's graph theorem earned him a 1995 Lester R. Ford Prize of the MAA for expository writing, and his book Proofs from the BOOK with Gunter M. Ziegler has been an international success with translations into 12 languages.
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