A First Course in Discrete Mathematics

1. Front Matter

   Pages i-viii

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2. Counting and Binomial Coefficients

   • Ian Anderson

   Pages 1-18

3. Recurrence

   • Ian Anderson

   Pages 19-42

4. Introduction to Graphs

   • Ian Anderson

   Pages 43-67

5. Travelling Round a Graph

   • Ian Anderson

   Pages 69-87

6. Partitions and Colourings

   • Ian Anderson

   Pages 89-105

7. The Inclusion-Exclusion Principle

   • Ian Anderson

   Pages 107-119

8. Latin Squares and Hall’s Theorem

   • Ian Anderson

   Pages 121-136

9. Schedules and 1-Factorisations

   • Ian Anderson

   Pages 137-148

10. Introduction to Designs

    • Ian Anderson

    Pages 149-177

11. Back Matter

    Pages 179-200

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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 ménage problem, magic squares, Catalan and Stirling numbers, and tournament schedules.

• Combinatorial Mathematics
• Designs
• Discrete Mathematics
• Enumeration
• Graph
• Graph theory
• Hall's Theorem
• Hamiltonian cycle
• Latin Squares
• Partition

• Department of Mathematics, University of Glasgow, University Gardens, Glasgow, UK

  Ian Anderson

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