CS533 | DISCRETE MATHEMATICAL STRUCTURES | 4-0-0-8 |
Pre-requisites : NIL |
Syllabus : 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, partitions, recurrences, generating functions Graph Theory: paths, connectivity, subgraphs, isomorphism, trees, complete graphs, bipartite graphs, matchings, colourability, planarity, digraphs Algebraic Structures: semigroups, groups, subgroups, homomorphisms, rings, integral domains, fields, lattices and boolean algebras. |
Texts : 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. |
References : 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. J P Tremblay and R P Manohar, Discrete Mathematics with Applications to Computer Science, Tata McGraw-Hill, 1997. |