Lecture Notes || SNS Courseware

Subject Details

Dept : IT

Sem : 5

Regul : 2019

Faculty : Saranya C

phone : NIL

E-mail : saranya.c.math@snsct.org

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Lecture Notes

UNIT 1:

Propositional Logic

Propositional equivalences

Predicates and Quantifiers

Nested Quantifiers

Rules of inference

Introduction to proofs

Rules of inference

Proof methods and strategy

UNIT 2:

Inclusion and exclusion principle and its applications.

Mathematical induction

Strong induction and well ordering

The basics of counting â€“ The pigeon hole principle

Strong induction and well ordering

Permutations and combinations

Recurrence relations

Solving linear recurrence relations

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

Homomorphismâ€™s

Normal subgroup and cosets

Lagrangeâ€™s theorem

UNIT 5:

Boolean algebra

Partial ordering â€“ Posets

Lattices as posets

Properties of lattices

Lattices as algebraic systems

Sub lattices

Direct product and homomorphism

Some special lattices

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