Discrete mathematics, sometimes called finite mathematics, is the study of mathematical structure that are fundamentally discrete, in the sense of not supporting notion of continuity. A study of discrete sets has become more and more necessary because of many application of computer science and various areas of engineering. In computer science, discrete mathematics are useful to study or express objects or problems in computer algorithm and programming languages. For instance, to improve the efficiency of a computer programs, we need to study its logical structure, which involves a finite number of 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. Therefore, a study of these areas would complement and improve the understanding of courses based on algorithm and problem solving. This Course is designed to give basic concepts of Propositions, Predicates, Boolean Algebra, Logic Circuit, Sets, Relations, Functions, Combinatorics, Partitions and Distributions.
Propositions Logical Connectives o Disjunction o Conjunction o Negation o Conditional Connectives o Precedence Rule Logical Equivalence Logical QuantifiersUnit 2: Methods of Proof
What is a Proof? Different Methods of Proof Properties Common to Logic and Sets Relations Cartesian Product Relations and their types o Properties of Relations Functions Types of Functions Operations on Functions o Direct Proof o Indirect Proofs o Counter Examples Principle of InductionUnit 3 : Boolean Algebra and Circuits
Boolean Algebras Logic Circuits Boolean Functions
Introducing Sets Operations on Sets o Basic OperationsUnit 2 : Combinatorics – An Introduction
Multiplication and Addition Principles Permutations Permutations of Objects not Necessarily Distinct Circular Permutations Combinations Binomial Coefficients Combinatorial ProbabilityUnit 3 : Some More Counting Principles
Pigeonhole Principle Inclusion-Exclusion Principle Applications of Inclusion – Exclusion Application to Surjective Functions Application to Probability Application to DerangementsUnit 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 I ndistinguishable Container
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