Discrete Mathematical Structure
Teacher
MR. Sasi Bhusan Padhi
Category
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:
- 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:
- Discrete Mathematics with Graph Theory by Edgar G. Goodaire and Michael M. Parmenter
Session Plan
Session 1
Session 2
Session 4
Proportional Equivalence, Definitions of Tautology Contradiction and Contingency
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
Session 16
Session 18
Session 19 & 20
Project-3
Study on Universal Quantifiers and Existential Quantifiers
Session 21 & 22
Project-4
Study on Valid arguments in Logic
Session 25
Solving Recurrence Relations by using Generating Functions
https://www.youtube.com/watch?v=YB7qnuo-GRY
http://math.mit.edu/~goemans/18310S15/generating-function-notes.pdf
https://www.slideshare.net/preethicsekongu/generating-function-121065926
Session 27 & 28
Project-5
Study on different types of Recurrence relations
Session 29 & 30
Project-6
Study on Pigeon-Hole Principle
Session 32
Session 33
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 43
Relation and their properties and different types of relations
https://www.slideshare.net/umairsimjee/relations-50214662
https://www.youtube.com/watch?v=FI6j5QZNVx0
http://iiitdm.ac.in/old/Faculty_Teaching/Sadagopan/pdf/Discrete/Relations.pdf
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
Partially ordered set and Totally ordered set
https://www.youtube.com/watch?v=R36F8CWAi2k
Session 53
Maximal and minimal element, Supremum and infimum of a Poset
Session 54 & 55
Project-9
Study on partially ordered sets and Totally ordered sets
Session 56 & 57
Project-10
Study on Hasse Diagram
Session 61
Bounded and Distributive Lattices
https://www.youtube.com/watch?v=sQ-UovGxQl0
Session 62
Session 63 & 64
Project-11
Study on Lattices and Ordered Sets
Session 65 & 66
Project-12
Study on Boolean Algebra
Case Studies
Case Studies
Our Main Teachers
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 […]