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Combinatorial mathematics

By: Material type: TextTextPublication details: Cambridge University Press 2021 CambridgeDescription: xx, 969p.: ill. Includes bibliographical references & subject indexISBN:
  • 9781107058583
Subject(s): DDC classification:
  • 511.6 W3C6
Summary: 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 https://www.cambridge.org/in/academic/subjects/mathematics/discrete-mathematics-information-theory-and-coding/combinatorial-mathematics?format=HB&isbn=9781107058583
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Item type Current library Item location Collection Shelving location Call number Status Date due Barcode
Books Vikram Sarabhai Library Rack 28-A / Slot 1359 (0 Floor, East Wing) Non-fiction General Stacks 511.6 W3C6 (Browse shelf(Opens below)) Available 205243

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.


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

https://www.cambridge.org/in/academic/subjects/mathematics/discrete-mathematics-information-theory-and-coding/combinatorial-mathematics?format=HB&isbn=9781107058583

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