Discrete mathematics

Norman L. Biggs

The new edition of this text includes additional chapters on statements and proof, logical framework, and natural numbers and the integers. The updated chapters offer over 1000 tailored exercises, and an accompanying website contains hints and solutions to all exercises. The text is designed explicitly for mathematicians and computer scientists seeking a first approach to this important topic.

「Nielsen BookData」より

Biggs' Discrete Mathematics has been a best-selling textbook since the first and revised editions were published in 1986 and 1990, respectively. This second edition has been developed in response to undergraduate course changes and changes in students' needs. New to this edition are chapters on statements and proof, logical framework, and natural numbers and the integers, in addition to updated chapters from the previous edition. The new chapters are presented at a level suitable for mathematics and computer science students seeking a first approach to this broad and highly relevant topic. Each chapter contains newly developed tailored exercises, and miscellaneous exercises are presented throughout, providing the student with over 1000 individual tailored exercises. This edition is accompanied by a website www.oup.com/mathematics/discretemath containing hints and solutions to all exercises presented in the text, providing an invaluable resource for students and lecturers alike. The book is carefully structured, coherent and comprehensive, and is the ideal text for students seeking a clear introduction to discrete mathematics, graph theory, combinatorics, number theory, coding theory and abstract algebra.

「Nielsen BookData」より

[目次]

  • THE LANGUAGE OF MATHEMATICS
  • 1. Statements and proofs
  • 2. Set notation
  • 3. The logical framework
  • 4. Natural numbers
  • 5. Functions
  • 6. How to count
  • 7. Integers
  • 8. Divisibility and prime numbers
  • 9. Fractions and real numbers
  • TECHNIQUES
  • 10. Principles of counting
  • 11. Subsets and designs
  • 12. Partition, classification and distribution
  • 13. Modular arithmetic
  • ALGORITHMS AND GRAPHS
  • 14. Algorithms and their efficiency
  • 15. Graphs
  • 16. Trees, sorting and searching
  • 17. Bipartite graphs and matching problems
  • 18. Digraphs, networks and flows
  • 19. Recursive techniques
  • ALGEBRAIC METHODS
  • 20. Groups
  • 21. Groups of permutations
  • 22. Rings, fields and polynomials
  • 23. Finite fields and some applications
  • 24. Error-correcting codes
  • 25. Generating functions
  • 26. Partitions of a positive integer
  • 27. Symmetry and counting

「Nielsen BookData」より

[目次]

  • THE LANGUAGE OF MATHEMATICS
  • 1. Statements and proofs
  • 2. Set notation
  • 3. The logical framework
  • 4. Natural numbers
  • 5. Functions
  • 6. How to count
  • 7. Integers
  • 8. Divisibility and prime numbers
  • 9. Fractions and real numbers
  • TECHNIQUES
  • 10. Principles of counting
  • 11. Subsets and designs
  • 12. Partition, classification and distribution
  • 13. Modular arithmetic
  • ALGORITHMS AND GRAPHS
  • 14. Algorithms and their efficiency
  • 15. Graphs
  • 16. Trees, sorting and searching
  • 17. Bipartite graphs and matching problems
  • 18. Digraphs, networks and flows
  • 19. Recursive techniques
  • ALGEBRAIC METHODS
  • 20. Groups
  • 21. Groups of permutations
  • 22. Rings, fields and polynomials
  • 23. Finite fields and some applications
  • 24. Error-correcting codes
  • 25. Generating functions
  • 26. Partitions of a positive integer
  • 27. Symmetry and counting

「Nielsen BookData」より

この本の情報

書名 Discrete mathematics
著作者等 Biggs, Norman L.
Biggs Norman
出版元 Oxford University Press
刊行年月 2004
版表示 2nd ed., repr. with corrections
ページ数 xiv, 425 p.
大きさ 25 cm
ISBN 0198507178
0198507186
NCID BA77029993
※クリックでCiNii Booksを表示
言語 英語
出版国 イギリス
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