1. Logic - Introduction * Truth tables * Conditional propositions * Quantifiers * Types of proof * Mathematical induction * Project * Summary. 2. Sets - Introduction * Operations on sets * De Morgan's Laws * Power sets * Inclusion-exclusion * Products and partitions * Finite and infinite * Paradoxes * Projects * Summary. 3. Relations and Functions - Relations * Equivalence relations * Partial orders * Diagrams of relations * Functions * One-one and onto * Composition of functions * The inverse of a function * The pigeonhole principle * Projects * Summary. 4. Combinatorics - History * Sum and product * Premutations and combinations * Pascal's triangle * The binominal theorem * Multinominals and rearrangements * Projects * Summary 5. Probability - Introduction * Equally likely outcomes * Experiments with outcomes which are not equally likely * The sample space, outcomes and events * Conditional probability, independence and Bayes' theorem * Projects * Summary. 6. Graphs - Introduction * Definitions and examples * Representations of graphs and graph isomorphism * Paths, cycles and connectivity * Trees * Hamiltonian and Eulerian graphs * Planar graphs * Graph colouring * Projects * Summary * Glossary * Index.