📘 DM

DISCRETE MATHEMATICS

Access study materials and notes for this subject

DM Unit 1: Mathematical logic

PDF Document

PreviewDownload

DM Unit 2: Set Theory

PDF Document

PreviewDownload

DM Unit 3: Algebraic Structures

PDF Document

PreviewDownload

DM Unit 4: Elementary Combinatorics

PDF Document

PreviewDownload

DM Unit 5: Graph Theory

PDF Document

PreviewDownload

Syllabus Overview

UNIT - 1 Mathematical logic

Mathematical logic

  • Introduction
  • Statements and Notation
  • Connectives
  • Normal Forms
  • Theory of Inference for the Statement Calculus
  • The Predicate Calculus
  • Inference Theory of the Predicate Calculus

UNIT - 2 Set theory

Set theory

  • Introduction
  • Basic Concepts of Set Theory
  • Representation of Discrete Structures
  • Relations and Ordering
  • Functions

UNIT - 3 Algebraic Structures

Algebraic Structures

  • Introduction
  • Algebraic Systems
  • Semigroups and Monoids
  • Lattices as Partially Ordered Sets
  • Boolean Algebra

UNIT - 4 Elementary Combinatorics

Elementary Combinatorics

  • Basics of Counting
  • Combinations and Permutations
  • Enumeration of Combinations and Permutations
  • Enumerating Combinations and Permutations with Repetitions
  • Enumerating Permutation with Constrained Repetitions
  • Binomial Coefficient
  • The Binomial and Multinomial Theorems
  • The Principle of Exclusion

UNIT - 5 Graph Theory

Graph Theory

  • Basic Concepts
  • Isomorphism and Subgraphs
  • Trees and their Properties
  • Spanning Trees
  • Directed Trees
  • Binary Trees
  • Planar Graphs
  • Euler’s Formula
  • Multi-graphs and Euler Circuits
  • Hamiltonian Graphs
  • Chromatic Numbers
  • The Four-Color Problem
DISCRETE MATHEMATICS Notes