IGNOU MCS-013 Discrete Mathematics

Discrete Mathematics

Objectives Discrete mathematics, sometimes called finite mathematics, is the study of mathematical structure that are fundamentally discrete, in the sense of not support become more and more necessary because of many engineering. Regarding computer science concept from objects or problems in computer algorithm and p efficiency of a computer programs, we need to stud) steps each requiring a certain amount of time. Using the theory of combinatory and graph theory, major areas of discrete mathematics, we can do this. The improve the understanding of courses based on algorithm and problem solving. This course is designed to give basic concepts of _ sets, relations, functions, combinatorics, partitions and distributions. Syllabus Block 1: Elementary Logic Unit 1: Prepositional Calculus *Propositions *Logical Connectives 0 Disjunction 0 Conjunction 0 Negation 0 Conditional Connectives 0 Precedence Rule *Logical Equivalence *Logical Quantifiers Unit 2: Methods of Proof *What is a Proof? *Different Methods of Proof 0 Direct Proof 0 Indirect Proofs 0 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 0 Basic Operations 0 Properties Common to Logic and Sets *Relations 0 Cartesian Product 0 Relations and their types 0 Properties of Relations Functions 0 Types of Functions 0 Operations on Functions Unit 2: Combinatorics - An Introduction *Multiplication and Addition Principles Permutations * Permutations of Objects not Necessarily Distinct 0 Circular Permutations *Combinations *Binomial Coefficients *Combinatorial Probability * Pigeonhole Principle * Inclusion-Exclusion Principle * Applications of Inclusion - Exclusion 0 Application to Surjective Functions 0 Application to Probability 0 Application to Derangements Unit 4: Partitions and Distributions *Integer Partitions *Distributions 0 Distinguishable Objects into Distinguishable Containers 0 Distinguishable Objects into Indistinguishable Containers 0 Indistinguishable Objects into Distinguishable Containers 0 Indistinguishable Objects into 0 Indistinguishable Containers Unit 3: Some More Counting Principles S. No. Counselling2 Sessions Number of Sessions Comments 1. Theory Sessions 3 One Session on Block -1 Two sessions on Block-2 Sessions Session Block to be Topics to be covered Number Covered Theory 1 Block-l Propositional Calculus, Methods of Proof & Boolean Counselling (Units 1, 2 & Algebra and Circuits 3) 2 Block-2 Sets, Relations and Functions & Combinatorics – An (Units 1, 2) Introduction 3 Block-2 Some more Counting Principles, Partitions and (Units 3, 4) Distributions