Invitation to discrete mathematics - Jiri Matousek

This book is a clear and self-contained introduction to discrete mathematics, and in particular to combinatorics and graph theory. Aimed at undergraduate and early graduate students in mathematics and computer science, it is written with the goal of stimulating interest in mathematics and provides an active, problem-solving approach to the material. The reader is led to an understanding of the basic principles and methods of actually doing mathematics. It is more narrowly focusedthan many discrete mathematics textbooks and treats selected topics in unusual depth and from several points of view. The book reflects the conviction of the authors, active and internationally renowned mathematicians, that the most important gain from studying mathematics is the cultivation of clearand logical thinking and habits, invariably useful for attacking new problem. More than 400 exercises, ranging widely in difficulty and many accompanied by hints for solution, support this approach to teaching. Readers will appreciate the lively and informal style of the text, accompanied by more than 200 drawings and diagrams. Specialists in various parts of science with a basic mathematical education wishing to apply discrete mathematics in their field can use the book as a useful source, andeven experts in combinatorics may occasionally learn from pointers to research literature or from the presentation of recent results. Invitation to Discrete Mathematics should make delightful reading both for beginners and for mathematical professionals. The main topics include: elementary countingproblems, asymptotic estimates, basic graph theory and graph algorithms, finite projective planes, elementary probability and the probabilistic method, generating functions, and combinatorial applications of linear algebra. General mathematical notions beyond high-school level are thouroughly explained in the introductory chapter. An appendix summarizes the undergraduate algebra needed in some of the more advanced sections of the book.