discrete mathematical structures
| VTU | |
|---|---|
|
Subject code |
18CS36 |
|
Semester |
3rd Sem |
DISCRETE MATHEMATICAL STRUCTURES
(18CS36)
SYLLABUS
Module-1
Fundamentals of Logic: Basic Connectives and Truth Tables, Logic Equivalence – The Laws of Logic, Logical Implication – Rules of Inference. Fundamentals of Logic contd.: The Use of Quantifiers, Quantifiers, Definitions and the Proofs of Theorems.
Textbook 1: Chapter2
RBT: L1, L2, L3
Module-2
Properties of the Integers: The Well Ordering Principle – Mathematical Induction,
Fundamental Principles of Counting: The Rules of Sum and Product, Permutations,
Combinations – The Binomial Theorem, Combinations with Repetition.
Textbook 1: Chapter4 – 4.1, Chapter1
RBT: L1, L2, L3
Module-3
Relations and Functions: Cartesian Products and Relations, Functions – Plain and One-to-One, Onto Functions. The Pigeon-hole Principle, Function Composition and Inverse
Functions.
Relations: Properties of Relations, Computer Recognition – Zero-One Matrices and Directed
Graphs, Partial Orders – Hasse Diagrams, Equivalence Relations and Partitions.
Textbook 1: Chapter5, Chapter7 – 7.1 to 7.4
RBT: L1, L2, L3
Module-4
The Principle of Inclusion and Exclusion: The Principle of Inclusion and Exclusion,
Generalizations of the Principle, Derangements – Nothing is in its Right Place, Rook
Polynomials.
Recurrence Relations: First Order Linear Recurrence Relation, The Second Order Linear
Homogeneous Recurrence Relation with Constant Coefficients.
Textbook 1: Chapter8 – 8.1 to 8.4, Chapter10 – 10.1, 10.2
RBT: L1, L2, L3
Module-5
Introduction to Graph Theory: Definitions and Examples, Subgraphs, Complements, and
Graph Isomorphism,
Trees: Definitions, Properties, and Examples, Routed Trees, Trees and Sorting, Weighted
Trees and Prefix Codes
Textbook 1: Chapter11 – 11.1 to 11.2 Chapter12 – 12.1 to 12.4
RBT: L1, L2, L3
textbook recommended by vtu
reference books recommended by vtu
- Basavaraj S Anami and Venakanna S Madalli: Discrete Mathematics – A Concept based
approach, Universities Press - Kenneth H. Rosen: Discrete Mathematics and its Applications, 6th Edition, McGraw Hill
- Jayant Ganguly: A Treatise on Discrete Mathematical Structures, Sanguine-Pearson
- D.S. Malik and M.K. Sen: Discrete Mathematical Structures: Theory and Applications, Thomson.
- Thomas Koshy: Discrete Mathematics with Applications, Elsevier