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# discrete mathematical structures

VTU
Subject code
18CS36
Semester
3rd Sem

## 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