Pre-requisites : NIL
Review of sets, functions, relations Logic: formulae, interpretations, methods of proof in propositional and predicate logic Number theory: division algorithm, Euclid's algorithm, fundamental theorem of arithmetic, Chinese remainder theorem Combinatorics: permutations, combinations, partitions, recurrences, generating functions Graph Theory: isomorphism, complete graphs, bipartite graphs, matchings, colourability, planarity Algebraic Structures: semigroups, groups, subgroups, homomorphisms, rings, integral domains, fields, lattices and boolean algebras Linear algebra: system of linear equations, matrices, vector spaces, linear transformations, Eigen vectors, diagonalization Probability: conditional probability, random variables, probability distributions, Markov's inequality, Chebyshev and Chernoff Bounds.
.1. C L Liu, Elements of Discrete Mathematics, 2/e, Tata McGraw-Hill, 2000.
2. R C Penner, Discrete Mathematics: Proof Techniques and Mathematical Structures, World Scientific, 1999
1. R L Graham, D E Knuth, and O Patashnik, Concrete Mathematics, 2/e, Addison-Wesley, 1994.
2. K H Rosen, Discrete Mathematics & its Applications, 6/e, Tata McGraw-Hill, 2007.
3. J L Hein, Discrete Structures, Logic, and Computability, 3/e, Jones and Bartlett, 2010.
4. N Deo, Graph Theory, Prentice Hall of India, 1974.
5. S Lipschutz and M L Lipson, Schaum's Outline of Theory and Problems of Discrete Mathematics, 2/e, Tata McGraw-Hill, 1999.
6. Kishor S Trivedi, Probability & Statistics With Reliability, Queuing And Computer Science Applications, Prentice Hall of India.
7. Michael Mitzenmacher and Eli Upfal, Probability and Computing- Randomized Algorithms and Probabilistic Analysis.
8. Serge Lang, Introduction to Linear Algebra, Springer.