DISCRETE MATHEMATICAL STRUCTURES
Subject Code: 10CS34
I.A. Marks : 25
Hours/Week : 04
Exam Hours: 03
Total Hours : 52
Exam Marks: 100
PART – A
UNIT – 1 6 Hours
Set Theory: 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 7 Hours
Fundamentals of Logic: Basic Connectives and Truth Tables, Logic Equivalence – The Laws of Logic, Logical Implication – Rules of Inference
UNIT – 3 6 Hours
Fundamentals of Logic contd.: The Use of Quantifiers, Quantifiers, Definitions and the Proofs of Theorems
UNIT – 4 7 Hours
Properties of the Integers: Mathematical Induction, The Well Ordering Principle – Mathematical Induction, Recursive Definitions
PART – B
UNIT – 5 7 Hours
Relations and Functions: 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 7 Hours
Relations contd.: Properties of Relations, Computer Recognition – Zero-One Matrices and Directed Graphs, Partial Orders – Hasse Diagrams, Equivalence Relations and Partitions
UNIT – 7 6 Hours
Groups: 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 9
UNIT – 8 6 Hours
Group Codes: Decoding with Coset Leaders, Hamming Matrices Rings and Modular Arithmetic: The Ring Structure – Definition and Examples, Ring Properties and Substructures, The Integers Modulo n