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
This edition of Biggs' 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 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
This edition of Biggs' 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.
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 arepresented 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, andmiscellaneous exercises are presented throughout, providing the student with over 1000 individual tailored exercises. This edition is accompanied by a website 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.
“This is a new edition of a successful textbook ... this revision is particularly welcome ... The text is written in a fluent but rigorous style and should appeal to sixthformers and undergraduates who are alienated by more formal presentations. There are plenty of approachable exercises, ranging from easy riders to establish technique to more challenging problems which introduce new ideas, and a bonus is that all the answers are available on a companion web-site. I can thoroughly recommend this text.”
For the Second Edition:"... it is a wonderful book. Biggs' expository style is of the highest quality." 'Professor James Reid, University of Mississippi
"... a well written book by a world-renowned expert. The explanations go to the heart of the matter and the proofsgiven are elegant." 'Professor Mohan Shrikhande, University of Michigan" the material is well written in a clear and lucid style ... " 'Dr Jim Renshaw, University of Southampton
the new chapters are elegantly written'Dr Peter Robinson, University of CambridgeFrom recent reviews of the first edition:"Biggs' book ... a timely and important addition to the literature ... stands out for its clarity of exposition, its careful organization, and for the way in which it reduces unnecessary abstraction to a minimum ... The range of topics covered is astonishing ... and ... it is written with humour and a lightness of touch which make it a pleasure to read." 'Times Higher Education Supplemement
"It seems to me that the book is as comprehensive as one could hope. I strongly recommend it" 'Bulletin of the London Mathematical Society`"the comprehensive course of discrete mathematics" 'L'Enseignement Mathematique, t.36, fasc.1-2, 1990
Norman L. Biggs is Professor of Mathematics, London School of Economics, University of London
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 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.
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