Discrete Mathematics

This much-awaited new edition of Biggs' best-selling text includes new chapters on statements and proof, logical framework, and natural numbers and the integers, in addition to updated chapters, over 1000 tailored exercises and an accompanying website containing hints and solutions to all exercises. The text is designed explicitly for mathematicians and computer scientists seeking a first approach to this important topic.

Includes chapters on statements and proof, logical framework, and natural numbers and the integers. This edition also features over 1000 tailored exercises and an accompanying website containing hints and solutions to all exercises. It is suitable for mathematicians and computer scientists seeking a first approach to this topic.

... the ideal choice for introductory courses to discrete mathematicians.

Klappentext

This much-awaited new edition of Biggs' best-selling text includes new chapters on statements and proof, logical framework, and natural numbers and the integers, in addition to updated chapters, over 1000 tailored exercises and an accompanying website containing hints and solutions to all exercises. The text is designed explicitly for mathematicians and computer scientists seeking a first approach to this important topic.

Zusammenfassung
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.

Inhalt

• 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