Set Theory & Mathematical Logic Course | IIT Kanpur | Prof. Amit Kuber
Course Details
| Exam Registration | 45 |
|---|---|
| Course Status | Ongoing |
| Course Type | Core |
| Language | English |
| Duration | 12 weeks |
| Categories | Mathematics |
| Credit Points | 3 |
| Level | Undergraduate |
| Start Date | 19 Jan 2026 |
| End Date | 10 Apr 2026 |
| Enrollment Ends | 02 Feb 2026 |
| Exam Registration Ends | 20 Feb 2026 |
| Exam Date | 19 Apr 2026 IST |
| NCrF Level | 4.5 — 8.0 |
Set Theory and Mathematical Logic: A 12-Week Journey into the Foundations of Mathematics
Have you ever wondered what lies at the very bedrock of mathematics? How concepts like infinity are rigorously defined, or how mathematical truth itself is formalized? A new 12-week course, Set Theory and Mathematical Logic, offered by Prof. Amit Kuber of IIT Kanpur, is designed to answer these profound questions. This undergraduate-level course serves as a gateway to understanding the logical frameworks that underpin all of modern mathematics.
About the Course and Instructor
This course provides a comprehensive introduction to two pillars of foundational mathematics: set theory and mathematical logic. It explores how mathematical theories are structured as formal logical systems, bridging the gap between intuitive concepts and their precise symbolic representations.
The course is led by Prof. Amit Kuber, a faculty member in the Department of Mathematics and Statistics at IIT Kanpur. Prof. Kuber holds a Ph.D. in Mathematical Logic from the University of Manchester (2014), and his research expertise spans representation theory, model theory, and category theory. His deep understanding ensures the course is both rigorous and insightful.
Who Should Take This Course?
Intended Audience: This course is perfectly suited for undergraduate students in mathematics, computer science, or philosophy. Interested postgraduate students seeking a solid foundation are also welcome.
Prerequisites: A student who has completed their 12th-grade examinations should possess the necessary background to enroll and succeed. A curious and analytical mind is the most important asset.
Detailed 12-Week Course Layout
The course is meticulously structured over 12 weeks, building from fundamental concepts to advanced theorems.
Weeks 1-3: The World of Sets and Infinity
The journey begins with the axioms of Zermelo-Fraenkel set theory, confronting puzzles like Russell's Paradox. You'll master the glossary of set operations and functions before diving into the heart of infinity.
- Week 1: ZF axioms, Russell's Paradox, functions, and Cantor's groundbreaking theorem on power sets.
- Week 2: Equivalence relations, the pivotal Axiom of Choice (AC), and the Cantor-Schroeder-Bernstein theorem.
- Week 3: Construction of standard number systems (N, Z, Q, R) and applications of set-theoretic principles.
Weeks 4-6: Order, Choice, and Boolean Algebras
This module explores structured sets and the equivalence of fundamental axioms.
- Week 4: Ordinal & cardinal numbers, illuminating different sizes of infinity.
- Week 5: Partially ordered sets, lattices, and the powerful Zorn's Lemma, shown to be equivalent to the Axiom of Choice.
- Week 6: Introduction to Boolean algebras—the bridge between set theory, logic, and order theory—culminating in Stone's Representation Theorem.
Weeks 7-9: Propositional Logic and Proof
Shifting to logic, you'll learn to distinguish syntax (form) from semantics (meaning).
- Week 7: Syntax and semantics of propositional logic, and the Lindenbaum-Tarski algebra.
- Week 8: Normal forms, adequate connectives, and the setup of formal proof systems.
- Week 9: The crucial Soundness and Completeness Theorems, and the Compactness Theorem.
Weeks 10-12: Predicate Logic and Advanced Topics
The course concludes with the richer system of predicate logic and its profound consequences.
- Week 10: Syntax and semantics of predicate logic, structures, and homomorphisms.
- Week 11: Theories, models, ultraproducts, and a construction of the hyperreal numbers.
- Week 12: Key theorems like Löwenheim-Skolem, and an introduction to Gödel's earth-shattering Incompleteness Theorems.
Recommended Textbooks
The following texts provide excellent support for the course material:
| Book Title | Author(s) | Focus Area |
|---|---|---|
| Elements of Set Theory | H.B. Enderton | Set Theory Foundation |
| Naive Set Theory | P. R. Halmos | Intuitive Set Theory |
| A Course on Mathematical Logic | S.M. Srivastava | Comprehensive Logic |
| Mathematical Logic | I. Chiswell & W. Hodges | Modern Logic Approach |
| First Order Mathematical Logic | A. Margaris | Predicate Logic |
Embarking on this course is more than an academic pursuit; it's an exploration of the very language and structure of mathematical thought. Under the guidance of Prof. Kuber, you will gain the tools to understand not just *how* mathematics works, but *why* it works, from the finite to the infinite.
Enroll Now →