- Title: Discrete 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)