Discrete Mathematics

MA6566
CSE

Unit 1

LOGIC AND PROOFS

Propositional Logic – Propositional equivalences - Predicates and Quantifiers – Nested Quantifiers – Rules of inference - Introduction to proofs – Proof methods and strategy.

Part A (2m) Part B (16m)

Unit 2

COMBINATORICS

Mathematical induction – Strong induction and well ordering – The basics of counting – The pigeonhole principle – Permutations and combinations – Recurrence relations – Solving linearrecurrence relations – Generating functions – Inclusion and exclusion principle and its applications.

Part A (2m) Part B (16m)

Unit 3

GRAPHS

Graphs and graph models – Graph terminology and special types of graphs – Matrix representation of graphs and graph isomorphism – Connectivity – Euler and Hamilton paths.

Part A (2m) Part B (16m)

Unit 4

ALGEBRAIC STRUCTURES

Algebraic systems – Semi groups and monoids - Groups – Subgroups – Homomorphism’s – Normal subgroup and cosets – Lagrange’s theorem – Definitions and examples of Rings and Fields.

Part A (2m) Part B (16m)

Unit 5

LATTICES AND BOOLEAN ALGEBRA

Partial ordering – Posets – Lattices as posets – Properties of lattices - Lattices as algebraic systems – Sub lattices – Direct product and homomorphism – Some special lattices – Boolean algebra.

Part A (2m) Part B (16m)
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