Course: MAT 483 2.0 Combinatorics (Optional)
Course content:
Permutations & Combinations, Pigeonhole Principle, Generalized Pigeonhole Principle-Ramsey Theory, Binomial coefficients, Pascal triangle, Binomial Theorem, Multinomial Theorem, Inclusion Exclusion Principle, Derangements, Permutations with Forbidden positions, Recurrence relation & Generating functions, Fibonacci Lucas Sequences, Exponential generating functions, Counting numbers, Catalan, Sterling, Bell numbers , Partition numbers, Integer partition , Ferrer diagrams, pentagonal number theorem, Ramanujan Congruences , Combinatorics with graph theory, Eulerian trials, Hamiltonian Paths & cycles, Bipartite Multi graphs, Trees, Chromatic number.
Recommended Readings:
- Brualdi, introductory combinatoric. Prentice-Hall, 2004
- Bona. A walkthrough combinatorics-An introduction to Enumeration and Graph Theory, World Scientific Publication Company, 2002