Textbook:  Peter J. Cameron's "Combinatorics: Topics, Techniques, Algorithms,"
Cambridge University Press, 1994.

Comments on textbook:

The text contains far more material than can be studied in a semester, especially
at the pace which evolved. The text is dense, written at a high level, and is
seemingly too mathematical for the tastes of many of the students enrolled in the
course.  Much background on algebra and number theory is provided, and it proved
helpful to cover that background rather thoroughly.  I would happily use this
outstanding text in a future course.


Syllabus

1.   What is Combinatorics? Sample problems Ð How to use this book Ð What you
need to know Ð Exercises

2.  On number and counting Natural numbers and arithmetic Ð Induction Ð Some
useful functions Ð Orders of magnitude Ð Different ways of counting Ð Double
counting Ð Appendix on set notation Ð Exercises

3.  Subsets, partitions, permutations Subsets Ð Subsets of fixed size _ The
Binomial Theorem and Pascal's Triangle Ð Project: Congruences of binomial
coefficients Ð Permutations Ð Estimates for factorials Ð Selections Ð Equivalence
and order _ Project: Finite topologies Ð Project: Cayley's Theorem on trees Ð
Bell numbers Ð Generating combinatorial objects Ð Exercises

4.  Recurrence relations and generating functions Fibonacci numbers Ð Aside on
formal power series Ð Linear recurrence relations with constant coefficients Ð
Derangements and involutions Ð Catalan and Bell numbers Ð Computing solutions to
recurrence relations Ð Project: Finite fields and QUICKSORT Ð Exercises

9.  Finite geometry Linear algebra over finite fields Ð Gaussian coefficients

17.  Error-correcting codes Finding out a liar Ð Definitions Ð Probabilistic
considerations Ð Some bounds Ð Linear codes; Hamming codes Ð Perfect codes Ð
Linear codes and projective spaces Ð Exercises