DISCRETE MATHEMATICS
Combinatorics: Basic counting techniques. Principle of inclusion and exclusion. Recurrence relations and generating functions. Pigeon-hole principle, Ramsey theory. Standard counting numbers, Polya enumeration theorem. Graph Theory: Elementary notions, Shortest path problems. Eulerian and Hamiltonian graphs, The Chinese postman problem. Matchings, the personal assignment prolem. Colouring or Graphs. Number Theory: Divisibility Arithmetic functions. Congruences. Diophantine equations. Fermat’s big theorem, Quadratic reciprocity laws. Primitive roots.
Books
- Bondy, J. A. and Muirty, U. S. R., Graph theory with applications, Elsevier- North Holland, 1976.
- Burton, D. Elementary Number Theory, Mc Graw Hill, 1997.
- Clark, J. and Holton, D. A., A first book at Graph Theory, World Scientific Cp., 1991.
- Polya G. D., Tarjan, R. E. and Woods, D. R., Notes on Introductory Combinations, Springer-Verlag, 1990.