Discrete mathematics has now established its place in most undergraduate mathematics courses. This textbook provides a concise, readable and accessible introduction to a number of topics in this area, such as enumeration, graph theory, Latin squares and designs. It is aimed at second-year undergraduate mathematics students, and provides them with many of the basic techniques, ideas and results. It contains many worked examples, and each chapter ends with a large number of exercises, with hints or solutions provided for most of them. As well as including standard topics such as binomial coefficients, recurrence, the inclusion-exclusion principle, trees, Hamiltonian and Eulerian graphs, Latin squares and finite projective planes, the text also includes material on the mรฉnage problem, magic squares, Catalan and Stirling numbers, and tournament schedules
CONTENT
1. Counting and Binomial Coefficients -- 2. Recurrence -- 3. Introduction to Graphs -- 4. Travelling Round a Graph -- 5. Partitions and Colourings -- 6. The Inclusion Exclusion Principle -- 7. Latin Squares and Hallโ{128}{153}s Theorem -- 8. Schedules and 1-Factorisations -- 9. Introduction to Designs -- Solutions -- Further Reading
