Course Module
of
Discrete Structure
[12 Week Course]
Course Starting from 10th
September 2022
[1 Day Demo Classes]
Days: Monday/Tuesday/Wednesday Time: 8.00PM
Discrete Structure
By Dr Sonendra Gupta | Author of 22 Books on Mathematics
Objective of Course: This course introduces the applications of discrete mathematics
in the field of computer science. It covers sets, logic, proving techniques, Combinatorics,
functions,
Relations, Graph theory and algebraic structures. These
basic concepts of sets, logic functions, and graph theory apply to Boolean algebra, logic networks while the advanced concepts of functions and algebraic
structures are applied to finite state machines and coding theory.
Ø To
introduce the idea of applying Set theory, function, and Relation in the field
of Engineering.
Ø To
introduce the fallouts of algebraic structures in the field of Computer
applications.
Ø To
develop the tool of Graph theory for learning advanced computational
mathematics.
Course
Layout
Chapter-1 Set Theory and Relation
v
Set theory
v
Countable and Uncountable sets
v
Venn Diagrams
v
Relations and Properties
v
Equivalence relation
v
Partial ordering relation
v
Function and Type of functions
v
Inverse Function
v
Job-Scheduling Problems function
v
Mathematical induction
v
Pigeonhole Principal
v MCQ Test
Chapter-2 Algebraic Structures
v
Algebraic Structures
v
Group theory
Ø
Quasi Group
Ø
Semi Group
Ø
Monoid Group
Ø
Abelian and Non-Abelian Group
v
Properties of Group
v
Subgroup
v
Cyclic Group
v
Coset, Right and Left Coset
v
Permutation Group
v
Homomorphism and isomorphism of Groups
v
Rings and Fields
v MCQ Test
Chapter-3 Algebra of Logic and Boolean algebra
v
Propositional Logic
v
logical operation, Truth Table
v
Tautologies, Contradictions
v
Algebra of Proposition
v
logical implications and Logical equivalence
v
Predicates
v
Universal and existential quantifiers
v
Boolean Algebra
v
Properties of Boolean Algebra
v MCQ Test
Chapter-4 Graph Theory
v
Introduction and basic terminology of graphs
v
Planer graphs, Multigraphs, and weighted graph
v
Paths, Cycles and connectivity
v
Eulerian paths and circuits
v
Hamiltonian paths and circuits
v
Graph coloring, chromatic number
v
Isomorphism and Homomorphism of graphs
v
Shortest path in weighted by Dijkstre’s Algorithm
v
Minimum Spanning Tree by Prism Algorithm
v
Minimum Spanning Tree by Kruskals Algorithm
v MCQ Test
Chapter-5 Relation, Poset and Lattices
v
Relations and Properties
v
Equivalence relation
v Partial ordering relation
v Partial Order Set (Poset)
v Hass Diagram of Partially ordered
set
v Well-ordered set
v Lattice
v properties of Lattices
v Bounded Lattice and complemented lattices.
v MCQ Test
Chapter-6 Combinatorics
v
Introduction of Permutation
v
Introduction of Combination
v
Binomial Theorem and Multinomial Coefficients
v MCQ Test
Chapter-7 Recurrence Relation and Generating Function
v
Discrete Numeric Function
Ø
Sum of Numeric Function
Ø
Multiplication of Numeric Function by Constant
Ø
Product of Numeric Function
Ø
Forward and Backward Numeric Function
v
Convolution of Numeric Function
v
Generating Function
Ø
Sum of GF
Ø
Multiplication of GG by Constant
Ø
Product of GF
v
Operations on Generating Function
v
Recurrence Relation
v
Homogeneous Recurrence Relation (Linear Recurrence Relation)
v
Non-Homogeneous Recurrence Relation (Non-Linear Recurrence Relation)
v
Particular Solution of Recurrence Relations
v MCQ Test
How to Enroll in the Course…
2. All the information filled correctly
3. 2-Days Demo Classes
4. Final Registration by Google Form [Link Given on Same Time]
5. 4-Hours Weekly classes
Online Platform…
Google
Meet [Download Google Meet from Google play store]
Follow
the following steps:
Study Material
Full Study Material and some
Recorded video Lectures are provided.
Fees Structure
Overall
Charges 5000/- in Indian Currency
1st
Installment 2000/- at final
Registration
2nd
Installment 3000/- after 10
Days of Final Registration
Online Payment Mode [Ask from Sir/Madam]:
1. Google Pay by QR Scan
2. Paytm by QR Scan
Online Assistant:
WhatsApp/Call: +91-9893455006
Dr. Sonendra Gupta
Dr. Sonendra Gupta, HOD (Department of Mathematics) in Oriental College of Technology, Bhopal (MP). He received Ph.D., M.Phil(Maths), M.Sc.(Computer Science) and
M.Sc.(Maths) degree. He has 20 years of teaching experience.
He is equipped with an extraordinary caliber
and appreciable academic potency. He has always been a topper throughout his
educational career. He secured the Seventeenth position in Bhopal merit, in the intermediate examination in 1995.
He ranked as a topper in the university 1997 in
B.Sc. II year. He has authored 20 popular books of Mathematics titled “Advanced Mathematics”, “Engineering
Mathematics-I”, “Engineering Mathematics-II”, Engineering Mathematics-III, Differential
equation part-II, Vector Analysis and
Geometry, Business Mathematics, Abstract
Algebra, Numerical Analysis, etc.
for numerous universities, viz. RGPV Bhopal, U.P. Technical University,
Barkatullaha University, Bhopal, and Chhattisgarh University.
