Lecture Notes || SNS Courseware

Subject Details

Dept : CST

Sem : 3

Regul : 23

Faculty : Ms.Shila. D

phone : NIL

E-mail : kishoreshila@gmail.com

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Lecture Notes

UNIT 1:

Consistency of premised and Indirect method of proof

Proposition & Connectives

Tautology & Logical Equivalence

Normal Forms

Inference theory of Statement Calculus & Rules of Inference

Problems based on inference theory of Statement Calculus

Predicate & Quantifiers

Problems on Predicate Calculus

Proof methods and strategy.

Tutorial 1

Tutorial 2

Tutorial 3

UNIT 2:

Mathematical induction

Problems on Mathematical induction, Strong induction and well ordering

The basics of counting

The pigeonhole principle

Permutations and combinations

Recurrence relations

Solution of Linear Recurrence relations

Generating functions

Inclusion and exclusion principle and its applications.

Tutorial 4

Tutorial 5

Tutorial 6

UNIT 3:

Graphs and graph models

Graph terminology and special types of graphs

Handshaking Theorem

Matrix representation of Graphs

Isomorphic Graphs

Connectivity

Euler & Hamiltonian Paths

Theorems on Euler & Hamiltonian Paths

Circuits and Isomorphism

UNIT 4:

Algebraic systems

Semi groups and monoids

Groups

Subgroups

Homomorphism

Normal Subgroups

Cosets

Lagrangeâ€™s theorem

Def and eg of Rings and fields

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