10CS34 Discrete Mathematical Structures syllabus for CS


Part A
Unit-1 Set Theory 6 hours

Sets and Subsets, Set Operations and the Laws of Set Theory,Counting and Venn Diagrams,
A First Word on Probability, Countable and Uncountable Sets

Unit-2 Fundamentals of Logic 7 hours

Basic Connectives and Truth Tables, Logic Equivalence – The Laws of Logic,
Logical Implication – Rules of Inference

Unit-3 Fundamentals of Logic contd 6 hours

The Use of Quantifiers, Quantifiers,Definitions and the Proofs of Theorems

Unit-4 Properties of the Integers 7 hours

Mathematical Induction, The Well Ordering Principle – Mathematical Induction, Recursive Definitions

Part B
Unit-5 Relations and Functions 7 hours

Cartesian Products and Relations, Functions –Plain and One-to-One,
Onto Functions – Stirling Numbers of the Second Kind, Special Functions, The Pigeon-hole
Principle, Function Composition and Inverse Functions

Unit-6 Relations contd 7 hours

Properties of Relations, Computer Recognition – Zero-One Matrices and Directed Graphs,
Partial Orders – Hasse Diagrams, Equivalence Relations and Partitions

Unit-7 Groups 6 hours

Definitions,Examples,and Elementary Properties,Homomorphisms, Isomorphisms, and Cyclic Groups,
Cosets, and Lagrange’s Theorem.
Coding Theory and Rings: Elements of Coding Theory, The Hamming Metric, The Parity Check, and
Generator Matrices

Unit-8 Group Codes 6 hours

Decoding with Coset Leaders, Hamming Matrices
Rings and Modular Arithmetic: The Ring Structure – Definition and Examples, Ring Properties
and Substructures, The Integers Modulo n

Last Updated: Tuesday, January 24, 2023