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

Norman L. Biggs , Professor of Mathematics, London School of Economics, University of London

`For the Second Edition: "... it is a wonderful book. Biggs' expository style is of the highest quality." ' Professor James Reid, University of Mississippi