IGNOU MCA First Semester MCS-013 Syllabus

IGNOU MCA First Semester MCS-013 Syllabus
Discrete Mathematics

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 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 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 Unit 3: Some More Counting Principles

 

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