Mcs-013 Syllabus

Syllabus

Block 1: Elementary Logic

Unit 1: Prepositional Calculus
• Propositions
• Logical Connectives
o Disjunction
o Conjunction
o Negation
o Conditional Connectives
o Precedence Rule
• Logical Equivalence
• Logical Quantifiers

Unit 2: Methods of Proof
• What is a Proof?
• Different Methods of Proof
o Direct Proof
o Indirect Proofs
o 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
o Basic Operations
o Properties Common to Logic and Sets
• Relations
o Cartesian Product
o Relations and their types
o Properties of Relations
• Functions
o Types of Functions
o Operations on Functions

Unit 2: Combinatorics – An Introduction
• Multiplication and Addition Principles
• Permutations
o Permutations of Objects not Necessarily Distinct
o Circular Permutations
• Combinations
• Binomial Coefficients
• Combinatorial Probability

Unit 3: Some More Counting Principles
• Pigeonhole Principle
• Inclusion-Exclusion Principle
• Applications of Inclusion – Exclusion
o Application to Surjective
Functions
o Application to Probability
o Application to Derangements

Unit 4: Partitions and Distributions
• Integer Partitions
• Distributions
o Distinguishable Objects into Distinguishable Containers
o Distinguishable Objects into Indistinguishable Containers
o Indistinguishable Objects into Distinguishable Containers
o Indistinguishable Objects into Indistinguishable Containers

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