Aspects of Combinatorics A Wide-ranging Introduction [Paperback]

Combinatorics is a broad and important area of mathematics, and this textbook provides the beginner with the ideal introduction to many of the different aspects of the subject.This textbook provides the beginner with the ideal introduction to many of the different aspects of the broad field of combinatorics by progressing from basic concepts and demonstrating the relationships between its various branches.This textbook provides the beginner with the ideal introduction to many of the different aspects of the broad field of combinatorics by progressing from basic concepts and demonstrating the relationships between its various branches.Building from basics and demonstrating the relationships among the various branches of combinatorics, Victor Bryant presents the results in a straightforward way. Numerous examples and exercises including hints and solutions are included throughout and serve to lead the reader to some of the deeper results of the subject, many of which are usually excluded from introductory texts.1. The binomial coefficients; 2. How many trees?; 3. The marriage theorem; 4. Three basic principles; 5. Latin squares; 6. The first theorem of graph theory; 7. Edge-colourings; 8. Harems and tournaments; 9. Minimax theorems; 10. Recurrence; 11. Vertex-colourings; 12. Rook polynomials; 13. Planar graphs; 14. Map-colourings; 15. Designs and codes; 16. Ramsey theory; Hints to exercises; Answers to exercises; Bibliography; Index. ...makes excellent reading for undergraduates who have already taken an introductory discrete mathematics course which covered counting methods, number theory, graph theory, and proof writing at an elementary level...I highly recommmend Aspects of Combinatorics as a great source of problems and examples that could supplement many upper division mathematics classes. Arthur Benjamin, SIAM Newsletter