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A First Course in Discrete Mathematics (Springer Undergraduate Mathematics Series)by Ian Anderson
Synopses & Reviews
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.
The place of discrete mathematics in the curriculum is now well established but many of the textbooks on the subject are directed towards computer science students. This book is written primarily for students of mathematics in the first or second year of their degree and introduces the key ideas, techniques and results.
Drawing on many years'experience of teaching discrete mathem atics to students of all levels, Anderson introduces such as pects as enumeration, graph theory and configurations or arr angements. Starting with an introduction to counting and rel ated problems, he moves on to the basic ideas of graph theor y with particular emphasis on trees and planar graphs. He de scribes the inclusion-exclusion principle followed by partit ions of sets which in turn leads to a study of Stirling and Bell numbers. Then follows a treatment of Hamiltonian cycles, Eulerian circuits in graphs, and Latin squares as well as proof of Hall's theorem. He concludes with the constructions of schedules and a brief introduction to block designs. Each chapter is backed by a number of examples, with straightforw ard applications of ideas and more challenging problems.
Includes bibliographical references (p. 197-198) and index.
Table of Contents
Counting and Binomial Coefficients.- Recurrence.- Introduction to Graphs.- Travelling Round a Graph.- Partitions and Colourings.- The Inclusion-Exclusion Principle.- Latin Squares and Hall's Theorem.- Schedules and One-Factorisations.- Introduction to Designs.- Appendix.- Solutions.- Further Reading.- Bibliography
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