Mathematics-I
Subject Overview
Mathematics-I gives B.Sc IT students the discrete-math foundation for computer science — set theory and relations, the algebra of logic and mathematical induction, graph theory, and recursion/recurrence relations and the binomial theorem. A 6-credit core theory paper with direct applications to programming, digital logic and computer graphics.
Unit-wise Syllabus
4 units — click WhatsApp below to get the full notes for each
Unit 1: Set theory and relations
Elements and methods of describing a set, types of sets, set operations (union, intersection, difference), Venn diagrams, associative/distributive/De Morgan's laws, duality, partitioning of a set, relation definitions and types, graphs of relations, domain/range/inverse/composite relations, matrix representation of a relation
Unit 2: Algebra of logic and mathematical induction
Propositions and logic operations, truth tables, arguments and validity, propositions generated by a set, equivalence and implication laws of logic, mathematical systems, quantifiers, principle of mathematical induction
Unit 3: Graph theory
Simple and multi-graphs, directed and undirected graphs, Eulerian and Hamiltonian graphs, graph connectivity, graph traversals, graph optimization, graph coloring, trees and spanning trees
Unit 4: Recursion, recurrence relations and the binomial theorem
Recursion and its applications, recurrence relations and common recurrence relations, binomial theorem of positive index, general term, middle terms, particular terms, terms from the end