Lecture Notes || SNS Courseware

Subject Details

Dept : IT

Sem : 5

Regul : R2019

Faculty : Sathya .S

phone : NIL

E-mail : sathyas.snsctmaths@gmail.com

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Lecture Notes

UNIT 1:

Propositional Logic

Propositional equivalences

Predicates and Quantifiers

Nested Quantifiers

Rules of inference

Introduction to proofs

Proof methods and strategy

UNIT 2:

Mathematical induction

Strong induction and well ordering

The basics of counting – The pigeonhole principle

Permutations and combinations

Recurrence relations

Solving linear recurrence relations

Generating functions

Inclusion and exclusion principle and its applications.

UNIT 3:

Graphs and graph models

Graph terminology and special types of graphs

Matrix representation of graphs and graph isomorphism

Connectivity

Euler and Hamilton paths

UNIT 4:

Algebraic systems

Semi groups and monoids

Groups

Subgroups

Homomorphism’s

Normal subgroup and cosets

Lagrange’s theorem

UNIT 5:

Partial ordering – Posets

Lattices as posets

Properties of lattices

Lattices as algebraic systems

Sub lattices

Direct product and homomorphism

Some special lattices

Boolean algebra

Sub lattices

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