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Computer Science and Engineering  Discrete Mathematical Structures
Title: Discrete Mathematical Structures
Department: Computer Science and Engineering
Author: Prof. Kamala Krithivasan
University: IIT Madras
Type: WebLink
Abstract: Mathematical reasoning; propositions; negation disjunction and conjuction; implication and equivalence; truth tables; predicates; quantifiers; natural deduction; rules of Inference; methods of proofs; use in program proving; resolution principle; application to PROLOG. (10 lectures)

Set theory; Paradoxes in set theory; inductive definition of sets and proof by induction;
Peono postulates; Relations; representation of relations by graphs; properties of relations;equivalence relations and partitions; Partial orderings; Posets; Linear and well'ordered sets; (10 lectures)

Graph Theory; elements of graph theory, Euler graph, Hamiltonian path, trees, tree
traversals, spanning trees; (4 lectures)

Functions; mappings; injection and surjections; composition of functions; inverse functions;special functions; Peono postulates; pigeonhole principle; recursive function theory; (6 lectures)

Definition and elementary properties of groups, semigroups, monoids, rings, fields, vector
spaces and lattices; (4 lectures)

Elementary combinatorics; counting techniques; recurrence relation; generating functions; (6 lectures)
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