Discrete mathematics
著者
書誌事項
Discrete mathematics
American Mathematical Society, c2007
- タイトル別名
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Diskrete mathematik
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注記
Translation of: Diskrete Mathematik. 5. Aufl
Originally published: Wiesbaden : Friedr. Vieweg & Sohn, 2004
Includes bibliographical references and index
内容説明・目次
内容説明
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. 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 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.
目次
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.
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