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Subject Syllabus

CB-101 - Discrete Mathematics

CSBS · Semester 1

Course Modules

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Introduction of Boolean algebra Truth table Basic logic gate Basic postulates of Boolean algebra Principle of duality Canonical form Karnaugh map

Set Relation Group Ring Field

Basic counting Balls and bins problems Generating functions Recurrence relations Proof techniques Principle of mathematical induction Pigeonhole principle

Graphs and digraphs Complement, isomorphism, connectedness and reachability Adjacency matrix Eulerian paths and circuits in graphs and digraphs Hamiltonian paths and circuits in graphs and tournaments Trees Planar graphs, Euler's formula, dual of a planar graph Independence number and clique number Chromatic number Statement of Four-color theorem

Propositional calculus - propositions and connectives, syntax Semantics - truth assignments and truth tables, validity and satisfiability, tautology Adequate set of connectives Equivalence and normal forms Compactness and resolution Formal reducibility - natural deduction system and axiom system Soundness and completeness