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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)
List of lectures
Lecture 1 Propositional Logic 56:47 mins
Lecture 2 Propositional Logic (Contd.) 57:35 mins
Lecture 3 Predicates & Quantifiers 57:53 mins
Lecture 4 Predicates & Quantifiers (Contd.) 59:24 mins
Lecture 5 Logical Inference 59:14 mins
Lecture 6 Resolution Principles & Application to PROLOG 54:29 mins
Lecture 7 Methods of Proof 54:56 mins
Lecture 8 Normal Forms 58:08 mins
Lecture 9 Proving programs correct 54:08 mins
Lecture 10 Sets 55:12 mins
Lecture 11 Induction 53:19 mins
Lecture 12 Set Operations on Strings Over an Alphabet 58:21 mins
Lecture 13 Relations 57:56 mins
Lecture 14 Graphs 55:36 mins
Lecture 15 Graphs (Contd.) 55:46 mins
Lecture 16 Trees 57:22 mins
Lecture 17 Trees and Graphs 56:44 mins
Lecture 18 Special Properties of Relations 57:04 mins
Lecture 19 Closure of Relations 56:50 mins
Lecture 20 Closure of Relations (Contd.) 56:59 mins
Lecture 21 Order Relations 55:52 mins
Lecture 22 Order and Relations and Equivalence Relations 57:12 mins
Lecture 23 Equivalence relations and partitions 56:19 mins
Lecture 24 Functions 55:01 mins
Lecture 25 Functions (Contd.) 56:08 mins
Lecture 26 Functions (Contd.) 57:49 mins
Lecture 27 Permutations and Combinations 56:57 mins
Lecture 28 Permutations and combinations 57:17 mins
Lecture 29 Permutations and Combinations(Contd...) 59:51 mins
Lecture 30 Generating Functions 58:13 mins
Lecture 31 Generating Functions 56:18 mins
Lecture 32 Recurrence Relations 57:20 mins
Lecture 33 Recurrence Relations 55:57 mins
Lecture 34 Recurrence Relations(contd..) 54:18 mins
Lecture 35 Algebras 57:07 mins
Lecture 36 Algebras(contd...) 57:26 mins
Lecture 38 Finite state automaton 57:17 mins
Lecture 40 lattices 57:02 mins