Discrete Mathematical Structure

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MR. Sasi Bhusan Padhi

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Core Courses

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Course Name : Discrete Mathematical Structure

Code(Credit) : CUTM1522(3-1-2)

Course Objectives

  • To understand mathematical reasoning in order to read, comprehend and construct mathematical arguments as well as to solve problems, occurred in the development of programming languages.
  • To work with different types of Sets, Lattices and Boolean Algebra.

Learning Outcomes

Upon successful completion of this course, students will be able to :

 

  • Evaluate elementary mathematical arguments and identify fallacious reasoning.
  • Apply the logical structure of proofs and work symbolically with connectives and quantifiers to produce logically valid, correct and clear arguments.
  • Reformulate statements from common language to formal logic. Apply truth tables and the rules of propositional and predicate calculus.

Course Syllabus

Module-I    ( T-5 hrs-P-4 hrs-P-4 hrs )

 

Introduction to Logic, Logical connectives, Converse, Inverse, Contrapositive, Proportional Equivalences, Propositional Calculus, Translating English sentences to Logical expressions.

 

Practice-1  : Finding the truth values of compound propositions using Python

Practice-2  :  Writing  conditional statements in Python

 

Project-1  :  Study on equivalent statements in Logic

Project-2  :  Study on Propositional Calculus

 

 

Module-II   ( T-5 hrs-P-0 hrs-P-4 hrs )

 

Predicates, Quantifiers, Bound and free variables, Rules of inference, Derivation of Valid conclusion, Nested Quantifiers.

 

Project-3  :  Study on Universal Quantifiers and Existential Quantifiers

Project-4  :  Study on Valid arguments in Logic

 

 

Module-III    ( T-4 hrs-P-0 hrs-P-4 hrs )

 

Recurrence Relation and it's solution by using Generating function, Pigeon-Hole Principle.

 

 

Project-5  :  Study on different types of Recurrence relations

Project-6  :  Study on Pigeon-Hole Principle

 

 

Module-IV    ( T-4 hrs-P-6 hrs-P-2 hrs )                                                                                                     

 

The basics of counting, Generalized Permutations, Combinations and their Applications.

 

Practice-3  :  Finding Factorial of a number using Python

Practice-4  :  Finding out the value of P(n,r) using Python

Practice-5  :  Finding out the value of C(n,r) using Python

 

Project-7  :  Study on permutations and combinations

 

 

Module-V    ( T-4 hrs-P-2 hrs-P-2 hrs )

 

Relations and their operations and properties, Equivalence relation, Representation of a relation, Closure of a relation.

 

Practice-6  :  Finding Composition of Relations using Python

Project-8  :  Study on different types of Relations

 

 

Module-VI   ( T-3 hrs-P-0 hrs-P-4 hrs )                                                                                                       

 

Partial order relation, Partially ordered set and totally ordered set, Hasse diagram, Maximal and minimal elements, Greatest and least elements, Supremum and infimum of a Poset.

 

Project-9  :  Study on partially ordered sets and Totally ordered sets

Project-10  :  Study on Hasse Diagram

 

 

Module-VII    ( T-5 hrs-P-0 hrs-P-4 hrs )

 

Lattice and it's algebraic structure, Properties of a Lattice, De-Morgan's Law, Bounded and Distributive Lattices, Boolean Algebra, Boolean Function.

 

Project-11  :  Study on Lattices and Ordered Sets

Project-12  :  Study on Boolean Algebra

 

 

 

Text Book:

  1. Kenneth H. Rosen, Discrete Mathematics and Applications, Tata Mc-Graw Hill Publications,

Chapters: 1(1.1 To 1.5), 5(5.1, 5.2, 5.5), 6(6.1, 6.2, 6.4), 7, 10(10.1, 10.2).

 

Reference Book:

  1. Discrete Mathematics with Graph Theory by Edgar G. Goodaire and Michael M. Parmenter

 

 

Session 2

Session 4

Proportional Equivalence, Definitions of Tautology Contradiction and Contingency

https://www.youtube.com/watch?v=yo7aULLUz_0

https://slideplayer.com/slide/8280241/

Session 5

Session 6 & 7

Practice-1

Finding the truth values of compound propositions using Python

Session 8 & 9

Practice-2

Writing  conditional statements in Python

Session 10 & 11

Project-1

Study on equivalent statements in Logic

Session 12 & 13

Project-2

Study on Propositional Calculus

Session 14

Predicates and Quantifiers definitions Universal and Existential Quantifiers

https://www.youtube.com/watch?v=jSYqo5XIeVk

https://slideplayer.com/slide/760301/

Session 15

Session 16

Session 17

Derivation of valid conclusion

https://www.youtube.com/watch?v=pO7X-EheJBU

Session 19 & 20

Project-3

Study on Universal Quantifiers and Existential Quantifiers

Session 21 & 22

Project-4

Study on Valid arguments in Logic

Session 27 & 28

Project-5

Study on different types of Recurrence relations

Session 29 & 30

Project-6

Study on Pigeon-Hole Principle

Session 34

Session 35 & 36

Practice-3

Finding Factorial of a number using Python

Session 37 & 38

Practice-4

Finding out the value of P(n,r) using Python

Session 39 & 40

Practice-5

Finding out the value of C(n,r) using Python

Session 41 & 42

Project-7

Study on permutations and combinations

Session 44

Session 45

Representation of a relation

https://www.youtube.com/watch?v=rTo_AO59KlE

Session 46

Session 47 & 48

Practice-6

Finding Composition of Relations using Python

Session 49 & 50

Project-8

Study on different types of Relations

Session 51

Session 53

Maximal and minimal element, Supremum and infimum of a Poset

https://www.youtube.com/watch?v=b5sDjo9tfE8

Session 54 & 55

Project-9

Study on partially ordered sets and Totally ordered sets

Session 56 & 57

Project-10

Study on Hasse Diagram

Session 60

Session 63 & 64

Project-11

Study on Lattices and Ordered Sets

Session 65 & 66

Project-12

Study on Boolean Algebra

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    MR. Sasi Bhusan Padhi

    Asst. Prof. Department of Mathematics
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    MR. Sasi Bhusan Padhi works as an Assistant Professor, Department of Mathematics, Centurion University of Technology and Management. He has received M.Sc degree in Mathematics from Berhampur University in the year 2001 with Gold Medal. He has 17 years of teaching experience in different Graduate and Post Graduate colleges. Now he is doing research in […]