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COMBINATORIAL MATHEMATICS 2020 (H)
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This long-awaited textbook is the most comprehensive introduction to a broad swath of combinatorial and discrete mathematics. The text covers enumeration, graphs, sets, and methods, and it includes both classical results and more recent developments. Assuming no prior exposure to combinatorics, it explains the basic material for graduate-level students in mathematics and computer science. Optional more advanced material also makes it valuable as a research reference. Suitable for a one-year course or a one-semester introduction, this textbook prepares students to move on to more advanced material. It is organized to emphasize connections among the topics, and facilitate instruction, self-study, and research, with more than 2200 exercises (many accompanied by hints) at various levels of difficulty. Consistent notation and terminology are used throughout, allowing for a discussion of diverse topics in a unified language. The thorough bibliography, containing thousands of citations, makes this a valuable source for students and researchers alike.
> Can be used as a text for a one-year sequence, or as a one-semester introduction leading to an advanced course, with a complete solutions manual available online for instructors
> Contains more than 2200 exercises at various levels. Especially instructive, interesting, or valuable exercises are marked with a diamond symbol
> Includes several thousand references (with pointers to pages where cited) and many exercises, theorems, and proofs that have not previously appeared in textbooks
Table of Contents
Introduction
Part I. Enumeration:
1. Combinatorial arguments
2. Recurrence relations
3. Generating functions
4. Further topics
Part II. Graphs:
5. First concepts for graphs
6. Matchings
7. Connectivity and cycles
8. Coloring
9. Planar graphs
Part III. Sets:
10. Ramsey theory
11. Extremal problems
12. Partially ordered sets
13. Combinatorial designs
Part IV. Methods:
14. The probabilistic method
15. Linear algebra
16. Geometry and topology
Appendix. Hints to selected exercises
References
Author index
Notation index
Subject index. |
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Springer 國外現貨
  
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