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. 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 Günter M. Ziegler has been an international success with translations into 12 languages.
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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
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5.0 out of 5 stars
advanced book on discrete mathematics,
This review is from: Discrete Mathematics (Hardcover)
This is an advanced book on discrete mathematics. The concepts, theorems and proofs are given clearly and concisely with no frills. It is an accurate, well-written book but readers need to be familiar with the basics of discrete mathematics to appreciate this book. Beginners should start with a more elementary text such as Discrete Mathematics and Its Applications by Rosen. Another highly recommended book by Aigner is Proofs from the BOOK. You should take a look at this one.
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We would like to present here some fundamental rules on which all counting is based. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
counting coefficients, admissible flow, rising factorials, optimal vertex, integer partitions, logical net, cycle indicator, repetition code, vert ices, admissible solutions, parity check matrix, increasing path, pigeonhole principle, vertex cover, current vertex, cyclic codes, dual program, cycle representation, internal vertices Key Phrases - Capitalized Phrases (CAPs): (learn more)
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We would like to present here some fundamental rules on which all counting is based. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
counting coefficients, admissible flow, rising factorials, optimal vertex, integer partitions, logical net, cycle indicator, repetition code, vert ices, admissible solutions, parity check matrix, increasing path, pigeonhole principle, vertex cover, current vertex, cyclic codes, dual program, cycle representation, internal vertices Key Phrases - Capitalized Phrases (CAPs): (learn more)
Boolean Algebras New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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