Synopses & Reviews
Invitation to Discrete Mathematics is at once an introduction and a thoroughly comprehensive textbook for courses in combinatorics and graph theory. It also contains introductory chapters for more specialized courses such as probabilistic methods, applied linear algebra, combinatorial enumeration, and operations research. A lively and entertaining style is combined with rigorous mathematics, and the many illustrations, examples and exercises make the book particularly accessible and user-friendly.
Review
"Offers an introduction to nonlinear chemical dynamics written especially for chemists, covering oscillating reactions, chaos, and chemical pattern formation. Begins with a brief history of nonlinear chemical dynamics and a review of necessary mathematics and chemistry, then provides an overview of nonlinear dynamics, starting with the flow reactor and moving on to a detailed discussion of chemical oscillators. Later chapters cover advanced topics such as biological systems, polymers, and interactions between fields and waves. Includes a series of classroom-tested demonstrations and experiments appropriate for an undergraduate laboratory. Assumes an undergraduate knowledge of chemistry. Epstein is a professor of chemistry at Brandeis University. Pojman is a professor of chemistry and biochemistry at the University of Southern Mississippi."--SciTech Book News
"In current parlance, 'discrete mathematics' simply means all the mathematics that a computer scientist ought to master. Since only a fuzzy border separates theoretical computer science from mathematics anyway, one may either construe discrete mathematics broadly (so that it includes topics such as logic, formal languages, automata, recursive function theory, and algorithm analysis) or narrowly (so that it concentrates only on, say, combinatorics and graph theory). Matousek and Nesetril's book reflects the narrow interpretation, but the authors still take care that the book should nevertheless serve the needs of computer science students. . . . This book has the outstanding feature of focusing on overarching problem-solving principles and methods of proof without sacrificing too much the depth of treatment of its many particular topics. Thoughtfully and carefully constructed throughout with the student reader in mind. Recommended for college libraries."--Choice
"The primary aim of the book, as stated in the preface, is 'to lead the student to understand and appreciate mathematical notions, definitions, and proofs, to solve problems requiring more than just standard recipes, and to express mathematical thought precisely and rigorously.' The book delivers what it promises. From the opening chapter, which sets the mathematical and pedagogical tone for the book, to the last, on linear algebra applications to graph theory, Invitation to Discrete Mathematics is an honest, detailed, and mathematically rigorous text. All 451 exercises are classified according to difficulty. Most of them involve mathematical argumentation, and hints are given for many. Included in the exercise sets are frequent 'fun' problems that are only loosely related to the preceding textual material. These problems help build the student's mathematical sophistication and facility in conjecture, proof, and refutation."--Mathematics Teacher
Table of Contents
1. Introduction and basic concepts
2. Combinatorial counting
3. Graphs: an introduction
4. Trees
5. Drawing graphs in the place
6. Double-counting
7. The number of spanning trees
8. Finite projective planes
9. Probability and probabilistic proofs
10. Generating functions
11. Applications of linear algebra
Appendix: A summary of algebra
Bibliography
Hints to selected exercises
Index