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Course content |
There are four modules in the course:
- Proofs and structures
Introduction, propositions, predicates, examples of theorems and proofs, types of proof techniques, Axioms, Mathematical Induction, Well-ordering principle, Strong Induction, Sets, Russell’s paradox, infinite sets, functions, Countable and uncountable sets, Cantor’s diagonalization technique, Relations, Equivalence relations, partitions of a set. - Counting and Combinatorics
Permutations, combinations, binomial theorem, pigeon hole principle, principles of inclusion and exclusion, double counting. Recurrence relations, solving recurrence relations. - Elements of graph theory
Graph models, representations, connectivity. Euler and Hamiltonian paths, planar graphs. Trees and tree traversals. - Introduction to abstract algebra and number theory
Semigroups, monoids, groups, homomorphisms, normal subgroups, congruence relations. Ceiling, floor functions, divisibility. Modular arithmetic, prime numbers, primary theorems.
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Texts/References |
- Discrete Mathematics and its applications with Combinatorics and graph theory, 7th edition, by Kenneth H Rosen. Special Indian Edition published by McGraw-Hill Education, 2017.
- Introduction to Graph Theory, 2nd Edition, by Douglas B West. Eastern Economy Edition published by PHI Learning Pvt. Ltd, 2002.
- Discrete Mathematics, 2nd Edition, by Norman L Biggs. Indian Edition published by Oxford University Press, 2003.
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