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IGNOU BCA- II Second sem SYLLABUS-----------IGNOU JAIPUR
MCS-013: Discrete Mathematics
BLOCK 1: Elementary Logic
Unit 1 : Prepositional Calculus
Propositions, Logical Connectives, Disjunction, Conjunction, Negation, Conditional Connectives, Precedence Rule, Logical Equivalence, Logical Quantifiers.
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.
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.
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, Functions, Operations on 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, 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.
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.
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.
Pigeonhole Principle, Inclusion-Exclusion Principle, Applications of Inclusion Exclusion,Application to Surjective Functions, Application to Probability,Application to Derangements.
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.
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