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基本説明
Introduces the various aspects of discrete mathematics including enumeration, graph theory and configurations or arrangements.
Full Description
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.
Contents
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 Hall's Theorem.- 8. Schedules and 1-Factorisations.- 9. Introduction to Designs.- Solutions.- Further Reading.
