Unit- I Objective: To acquaint students with notation, terminology and concepts of set theory and to develop problem solving and theorem proving skills. Sets and operations on Sets, Relations, Functions, Methods of Proof, Problem Solving Strategies, Fundamentals of Logic, Logical Inferences, Methods of Proof of an Imlication, First Order Predicate Logic, Quantified Propositions, Mathematical Induction. Unit-II Objective: To develop counting techniques without direct enumeration which will be used in Measuring the complexity. Combinotorics: Basics of Counting, Combinations and Permutation – without repetitions, with Unlimited repetitions, with Constrained repetitions, Binomial Coefficients, Binomial and Multinomial Theorems, Principles of Inclusion and Exclusion.
Unit-III Objective: To introduce probability concepts useful for decision theory. Elementary Probability: Introduction, sample space and events, Axioms of probability, Finite Probability Spaces, Finite Equiprobable spaces, Infinite Sample spaces, Conditional Probability- Multiplication theorem, stochastic processes, Baye’s theorem, Independence. Unit – IV Objective: To introduce graph theoretical modeling of real time environment. Graphs: Basic Concepts, Isomorphism and Sub graphs, Trees and their Properties, Spanning Trees, Directed Trees, Binary Trees, Planar Graphs, Euler Circuits, Hamiltonian Graphs, Chromatic Number. Unit – V Objective: To familiarize the mathematical concepts useful in digital circuit design. Boolean Algebra: Introduction, Boolean Algebra, Boolean Functions, Switching Mechanisms, Minimization of Boolean functions, Applications to Digital computer Design, Finite State diagrams. Suggested Reading: 1. Joe L Mott, Abraham Kandel, Theodore P Baker: Discrete Mathematics for Computer Scientists and Mathematicians, Prentice Hall 2. Seymour Lipschutz – Theory and problems of Probability, Schaum’s Outline Series, McGrawHill
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