Course

Unit 1

Logic, Mathematical Reasoning and Counting: Logic, Prepositional Equivalence, Predicate and Quantifiers, Theorem Proving. Recursive Definitions, Recursive Algorithms, Basics of Counting, Pigeonhole Principle, Permutation and Combinations.

Unit 2

Number theory: Divisibility- Primality Testing. GCD- Properties of the Greatest Common Divisor- Euler’s Theorem. – Euclid’s Algorithm-Extended Euclid’s Algorithm. The Fundamental Theorem of Arithmetic. The Prime Number Theorem. Modular Arithmetic- Congruence – Arithmetic with a Prime Modulus- Multiplicative Inverses- Fermat’s Little Theorem- Chinese Remainder Theorem.

Unit 3

Graph Theory: Introduction to Graphs, Graph Operations, Graph and Matrices, Graph Isomorphism, Connectivity. Graph centralities: Degree and distance-based centralities. Clustering and Eigenvalue centralities. Case studies on data networks.

Unit 4

Review of basic probability and distributions.

Statistics – Bayesian statistical inference, point estimators, parameter estimators, test of hypotheses, tests of significance.

Unit 5

Introduction to optimization: classical optimization, Optimality criteria – Necessary and sufficient conditions for existence of extreme point.

Direct search methods: unidirectional search, evolutionary search method, simplex search method, Introduction, Conditions for local minimization. One dimensional Search methods: Golden search method, Fibonacci method, Newton’s Method, Secant Method.

Course Description 

This course introduces the mathematical concepts essential for computer applications. It covers logical reasoning using propositional and predicate logic, recursive problem modeling, basic combinatorics, number theory, and graph theory. The course also emphasizes the application of statistical and optimization techniques for analyzing data and solving real-world computational problems. 

Course Objectives 

• To apply logical reasoning and recursion in computational problem solving. 

• To use combinatorics and number theory concepts in discrete and numerical systems. 

• To analyze graphs and apply basic statistical and optimization techniques to real-world data. 

Course Outcomes 

CO-PO Mapping 

• Kenneth H Rosen, ‘Discrete Mathematics and its Applications, Seventh Edition, McGraw-Hill publications, 2007.
• Ronald E. Walpole, Raymond H. Myers, Sharon L. Myers and Keying Ye, Probability and Statistics for Engineers and Scientists, 8th Edition, Pearson Education Asia, 2007.
• Edwin K.P. Chong, Stanislaw H. Zak, “An Introduction to Optimization”, 2nd edition, Wiley, 2013.