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Discrete Mathematical Structures

Discrete Mathematical Structures. Instructor: Dr. Kamala Krithivasan, Department of Computer Science and Engineering, IIT Madras. This course deals with topics about discrete mathematical structures. Discrete Mathematics is a study of discrete structures which are abstract mathematical models dealing with discrete objects and their relationship between them. This course covers lessons in logic, sets, relations, functions, graphs, combinatorics, recurrence relations, algebras and finite state automaton. The aim of this course is not only make people learn about these topics, but also help them to develop the habit of thinking mathematically. (from nptel.ac.in)

Lecture 06 - Resolution Principles and Application to PROLOG

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Lecture 01 - Propositional Logic

Lecture 02 - Propositional Logic (cont.)

Lecture 03 - Predicates and Quantifiers

Lecture 04 - Predicates and Quantifiers (cont.)

Lecture 05 - Logical Inference

Lecture 06 - Resolution Principles and Application to PROLOG

Lecture 07 - Methods of Proof

Lecture 08 - Normal Forms

Lecture 09 - Proving Programs Correct

Lecture 10 - Sets

Lecture 11 - Induction

Lecture 12 - Set Operations on Strings over an Alphabet

Lecture 13 - Relations

Lecture 14 - Graphs

Lecture 15 - Graphs (cont.)

Lecture 16 - Trees

Lecture 17 - Trees and Graphs

Lecture 18 - Special Properties of Relations

Lecture 19 - Closure of Relations

Lecture 20 - Closure Properties of Relations

Lecture 21 - Order Relations

Lecture 22 - Order Relations and Equivalence Relations

Lecture 23 - Equivalence Relations and Partitions

Lecture 24 - Functions

Lecture 25 - Functions (cont.)

Lecture 26 - Functions (cont.)

Lecture 27 - Pigeonhole Principle

Lecture 28 - Permutations and Combinations

Lecture 29 - Permutations and Combinations (cont.)

Lecture 30 - Generating Functions

Lecture 31 - Generating Functions (cont.)

Lecture 32 - Recurrence Relations

Lecture 33 - Recurrence Relations (cont.)

Lecture 34 - Recurrence Relations (cont.)

Lecture 35 - Algebras

Lecture 36 - Algebras (cont.)

Lecture 37 - Algebras (cont.)

Lecture 38 - Finite State Automaton

Lecture 39 - Finite State Automaton (cont.)

Lecture 40 - Lattices