Set theory: sets, relations, functions, countability; Logic: formulae, interpretations, methods of proof, soundness and completeness in propositional and predicate logic; Number theory: division algorithm, Euclid's algorithm, fundamental theorem of arithmetic, Chinese remainder theorem, special numbers like Catalan, Fibonacci, harmonic and Stirling; Combinatorics: permutations, combinations, pigeonhole principle, inclusion and exclusion principle, partitions, recurrence relations, generating functions; Graph Theory: paths, connectivity, subgraphs, isomorphism, trees, complete graphs, bipartite graphs, matchings, colourability, planarity, digraphs, Eulerian cycle and Hamiltonian cycle, adjacency and incidence matrices. |
Reference Books:
- Liu C. L. Elements of Discrete Mathematics, Tata McGraw-Hill
- Grimaldi R. P. Discrete and Combinatorial Mathematics, Pearson Education
- Penner R. C., Discrete Mathematics: Proof Techniques and Mathematical Structures, World Scientific
- Graham R. L., Knuth D. E. and Patashnik O. Concrete Mathematics, , Addison-Wesley
- Hein J. L. Discrete Structures, Logic, and Computability, Jones and Bartlett
- Burton D. M. Elementary Number Theory, McGraw Hill
- Deo N. Graph Theory, Prentice Hall of India
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