Discrete Mathematics SECOND EDITION

The long-awaited second edition of Norman Bigg's best-selling Discrete Mathematics, includes new chapters on statements and proof, logical framework, natural numbers, and the integers, in addition to updated chapters from the previous edition. Carefully structured, coherent and comprehensive, each chapter contains tailored exercises and solutions to selected questions, and miscellaneous exercises are presented throughout. This is an invaluable text for students seeking a clear introduction to discrete mathematics, graph theory, combinatorics, number theory and abstract algebra.

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.

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
10 - Principles of counting
11 - Subsets and designs
12 - Partition, classification and distribution
13 - Modular arithmetic
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
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