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LOGIC AND SETS

By Mr.MOHAMED NISHAD MANIPARAMBATH   |  
Learners enrolled: 74
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 : Upcoming
Course Type : Core
Language for course content : English
Duration : 15 weeks
Category :
  • Mathematics
Credit Points : 2
Level : Undergraduate
Start Date : 14 Jul 2025
End Date : 31 Oct 2025
Enrollment Ends : 31 Aug 2025
Exam Date :
NCrF Level   : 5.5

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
Day 3
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.

Instructor bio

Mr.MOHAMED NISHAD MANIPARAMBATH

Mr Mohamed Nishad Maniparambath (Course Coordinator) has 12 years of experience both in UG and PG level. He handled the topics Calculus, Differential Equations, Abstract Algebra, Logic, Numerical Analysis, Vector Calculus, Linear programming, Python and Latex in UG level, Algebra ,ODE, Multivariable Calculus and Geometry, Discrete Mathematics and Computer Oriented Numerical Analysis  in PG Level for the last 12 years.

Other Merits
• Delivered lectures for DTH programmes.
• Course Coordinator for two MOOC courses titled Differential Equations, Logic and Sets.
• Member, Board of Studies, Farook College.
• Member, Board of Studies, MASC College.
• Member, Board of Studies, SIAS.
• Criteria Head, NAAC steering committee, Farook College.
• Secretary, Staff Club, Farook College.
• Member, IQAC, Farook College.
• Former Member, Scholarship Committee, Farook College.
• Resource person at various colleges. 
• Published many research papers in international journal.
• Author of the  book titles Theta Function in the Lights of Ramanujan

Course certificate

  • Internal Assessment- Weekly assessments released in the course shall be considered for Internal Marks and will carry 30 percent for the Overall Result. Out of all weekly assignments, the best/top five scores will be considered for the final Internal Assessment marks.
  •  End-term Assessment - The final exam shall be conducted by NTA, and will carry 70 percent for the overall Result.
  •  All students who obtain 40% marks in the internal assessment and 40% marks in the end-term proctored exam separately will be eligible for the SWAYAM Credit Certificate.



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