## Combinatorics |

## an upper-level introductory course in enumeration, graph theory, and design theory |

## by Joy Morris |

This free undergraduate text book provides an introduction to enumeration, graph theory, and design theory. It is aimed
at upper-level undergraduate students and the exercises expect some mathematical sophistication, including a reasonable
ability to construct proofs.
The text is designed to be used in an undergraduate course, but could be suitable for independent study by a student with
some mathematical background and understanding of proofs. It does not assume any background knowledge of combinatorics.

The book is being released online with a Creative Commons license (Attribution-NonCommercial-ShareAlike 2.0).
It has already been used as a textbook for several semesters by 2 different instructors
at the University of Lethbridge, as well as at a number of other universities. Version 2.0 (July 2021) includes
several optional new sections, a web-based format, an appendix on complex numbers and an appendix containing biographies of
mathematicians whose work is referenced.

Click here for the web-based format of the July 2021 version (produced using PreTeXt).
Click here for a pdf file of the July 2021 version (approximately 350 pages and 1.5 MB)

The LaTeX source files are available by request. E-mail the author to request these.

2. Basic Counting Techniques

3. Permutations, Combinations, and the Binomial Theorem

4. Bijections and Combinatorial Proofs

5. Counting with Repetitions

6. Induction and Recursion

7. Generating Functions

8. Generating Functions and Recursion

9. Some Important Recursively-Defined Sequences

10. Other Basic Counting Techniques

11. Basics of Graph Theory

12. Moving Through Graphs

13. Euler and Hamilton

14. Graph Colouring

15. Planar Graphs

16. Latin Squares

17. Designs

18. More Designs

19. Designs and Codes

Appendix A: Complex Numbers

Appendix C: Biographical Briefs

Appendix C: Solutions to Selected Exercises

List of Notation

Index