Logic and Sets

By Mr. Mohamed Nishad Maniparambath | Farook College, Kozhikode

Learners enrolled: 1082

The course is developed to enable the undergraduate students to get a comprehensive understanding of the logic and sets. This course provides an introduction to the basic concepts and results of mathematical logic and set theory. The course introduces some basic notions that will be needed as background for most of the mathematics and computer science courses. Also, the course will familiarize students with abstract mathematical thinking. We will present and explain how different mathematical theories can be modelled inside the set theoretic universe. The primary Learning Outcome for this course is Mathematical Reasoning, which is to understand and apply mathematical concepts and reasoning, and analyze and interpret various types of data. The Learning Outcome will be assessed through targeted questions on either the comprehensive final or an outside assignment. In an increasingly complex world, mathematical thinking, understanding, and skill are more important than ever. Students wishing to major in the sciences or engineering are required to understand logic and sets. It provides a solid foundation for further study in mathematics, the sciences, and engineering.

Summary

Course Status :	Ongoing
Course Type :	Core
Duration :	8 weeks
Category :	Mathematics
Credit Points :	2
Level :	Undergraduate
Start Date :	08 Jul 2024
End Date :	06 Sep 2024
Enrollment Ends :	31 Aug 2024
Exam Date :	15 Dec 2024 IST
EXAM SHIFT :	SHIFT 2

Note: This exam date is subject to change based on seat availability. You can check final exam date on your hall ticket.

Page Visits

Course layout

Weeks Weekly Lecture Topics (Module Titles)

1 Day 1 Module 1 : Introduction to Logic and Logical Propositions.

Day 2 Module 2 : Truth Table, Negation, Conjunction and Disjunction.

Day 3 Module 3 : Implications, Biconditional Propositions and Converse and
Contra Positive Propositions

Day 4

Day 5

2 Day 1 Module 4 : Inverse Propositions and Precedence of Logical Operators , Logical Equivalences

Day 2 Module 5 : Predicates and Quantifiers: Quantifiers, Binding Variables and Negations

Day 3 Module 6 : Introduction to Sets and Subsets

Day 4

Day 5

3 Day 1 Module 7 : Set Operations and The Laws of Set Theory

Day 2 Module 8 : Venn Diagrams

Day 3 Module 9 : Examples of Finite and Infinite Sets

Day 4

Day 5

4 Day 1 Module 10 : Finite Sets and Counting Principle

Day 2 Module 11 : Empty Set, Properties of Empty Set

Day 3 Module 12 : Standard Set Operations

Day 4

Day 5

5 Day 1 Module 13 : Classes of Sets

Day 2 Module 14 : Power Set of a Set.

Day 3 Module 15 : Difference and Symmetric Difference of Two Sets

Day 4

Day 5

6 Day 1 Module 16 : Set Identities

Day 2 Module 17 : Generalized Union and Intersections.

Day 3 Module 18 : Relation on Sets, Product Set Composition of Relations ,
Types of Relations

Day 4

Day 5

7 Day 1 Module 19 : Partitions of a Set

Day 2 Module 20 : Equivalence Relations 1

Day 3 Module 21 : Equivalence Relations 2

Day 4

Day 5

8 Day 1 Module 22 : Partial Ordering Relations and n –ary Relations

Day 2 Module 23:

Day 3 Module 24 :

Day 4

Day 5

Books and references

U. Daepp, P.Gorkin, Reading, Writing, and Proving. A Closer Look at Mathematics(Undergraduate Texts in Mathematics), Springer, Bucknell University, 2011
David Makinson, Sets Logic and Maths for Comuting, Springer 2008
R.P. Grimaldi, Discrete Mathematics and Combinatorial Mathematics, Pearson Education,1998.
P.R. Halmos, Naive Set Theory, Springer, 1974.
E. Kamke, Theory of Sets, Dover Publishers, 1950.
Seymour Lipschutz, Set Theory and Related Topics (Schaum's Outlines) , 1998.
J. Słupecki, L. Borkowski, Elements of Mathematical Logic and Set Theory, Pergamon Press, PWN- Polish Scientific Publishers, Warszawa, 1967.