MCS-013: Discrete Mathematics

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Syllabus

BLOCK 1: Elementary Logic

Unit 1 : Prepositional Calculus

Propositions, Logical Connectives, Disjunction, Conjunction, Negation, Conditional Connectives, Precedence Rule, Logical Equivalence, Logical Quantifiers

Unit 2 : Methods of Proof

What is a Proof?, Different Methods of Proof, Direct Proof, Indirect Proofs, Counter Examples, Principle of Induction

Unit 3 : Boolean Algebra and Circuits

Boolean Algebras, Logic Circuits, Boolean Functions

BLOCK 2: Basic Combinatorics

Unit 1 : Sets, Relations and Functions

Introducing Sets, Operations on Sets, Basic Operations, Properties Common to Logic and Sets Relations, Cartesian Product, Relations and their types, Properties of Relations, Functions, Types of Functions, Operations on Functions

Unit 2 : Combinatorics - An Introduction

Multiplication and Addition Principles, Permutations, Permutations of Objects not Necessarily Distinct, Circular Permutations, Combinations, Binomial Coefficients, Combinatorial Probability

Unit 3 : Some More Counting Principles

Pigeonhole Principle, Inclusion-Exclusion Principle, Applications of Inclusion, Exclusion, Application to Surjective Functions, Application to Probability, Application to Derangements 26

Unit 4 : Partitions and Distributions

Integer Partitions, Distributions, Distinguishable Objects into Distinguishable Containers, Distinguishable Objects into Indistinguishable Containers, Indistinguishable Objects into Distinguishable Containers, Indistinguishable Objects into Indistinguishable Containers.