Real Analysis I Course | IIT Palakkad | Prof. Jaikrishnan J
Course Details
| Exam Registration | 53 |
|---|---|
| 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 |
Real Analysis I: Building the Rigorous Foundation of Calculus
Welcome to Real Analysis I, a pivotal 12-week undergraduate course designed to take your understanding of calculus from intuitive computation to rigorous mathematical proof. Taught by Prof. Jaikrishnan J, an Assistant Professor specializing in Complex Analysis at IIT Palakkad, this course is your gateway to the logical backbone of higher mathematics.
Who Should Take This Course?
This course is primarily designed for Undergraduate students of Mathematics. However, its value extends far beyond. Students from Science or Engineering disciplines who seek a deeper, more formal understanding of the calculus tools they use will find immense benefit. It is also essential for anyone aspiring to pursue advanced fields like Theoretical Physics, Computational Complexity, Advanced Statistics, or Machine Learning research.
Prerequisites & Industry Relevance
The only formal prerequisite is a solid grasp of 12th Standard (High School) Mathematics, particularly calculus concepts. The course builds from this foundation, introducing the precision and proof-based approach of university-level mathematics.
The analytical thinking and rigorous problem-solving skills developed in Real Analysis are highly valued in top tech industries. This course provides foundational knowledge relevant to roles in:
- Google & DeepMind: For algorithm design, machine learning theory, and AI research.
- Microsoft Research: For work in theoretical computer science, cryptography, and data science.
Course Instructor: Prof. Jaikrishnan J
Learn from Prof. Jaikrishnan J, an expert in Complex Analysis from IIT Palakkad. His deep expertise ensures that the fundamental concepts of Real Analysis are taught with clarity and precision, preparing you for more advanced topics in analysis and beyond.
Detailed 12-Week Course Layout
The course is meticulously structured to guide you from basic logical foundations to powerful classical theorems.
Weeks 1-2: The Bedrock
We begin with the essential language of mathematics: Set Theory and Logic. This is followed by a deep dive into the properties of The Real Numbers as a Complete Ordered Field, establishing the very stage on which calculus is performed.
Weeks 3-4: Sequences and Series
You will explore the concepts of convergence and divergence with rigor, moving past intuition to formal definitions (like epsilon-N proofs) for Sequences and Series. This is the cornerstone of understanding infinite processes.
Weeks 5-7: A Taste of Topology
This module introduces key topological concepts on the real line:
- Week 5: Limits and Continuity of functions, defined precisely.
- Week 6: Compactness, a crucial property for proving important theorems (like the Extreme Value Theorem).
- Week 7: Connected and Perfect Sets, exploring the structure of the real number line.
Weeks 8-9: The Core of Calculus
We revisit the pillars of calculus with a rigorous lens:
- Week 8: Differentiation, proving theorems like the Mean Value Theorem.
- Week 9: The Riemann Integral and the profound Fundamental Theorem of Calculus, linking differentiation and integration.
Weeks 10-12: Advanced Topics & Applications
The course culminates with powerful concepts that have wide applications:
- Week 10: Uniform Convergence of sequences of functions and Power Series.
- Week 11: Constructing The Elementary Functions (like exponential, logarithmic) rigorously from analysis.
- Week 12: Improper Integrals and the celebrated Weierstrass Approximation Theorem.
Recommended Textbooks
To support your learning, the course aligns with several acclaimed textbooks. You are encouraged to refer to one or more of the following:
| Book Title | Author | Style & Note |
|---|---|---|
| Analysis I and II | Terence Tao | Extremely clear and insightful, great for building intuition alongside rigor. |
| Mathematical Analysis | Tom Apostol | A classic, comprehensive text with a broad scope. |
| Understanding Analysis | Stephen Abbott | Highly accessible and student-friendly, perfect for a first encounter with the subject. |
Conclusion
Real Analysis I is more than just a mathematics course; it is a training ground for logical thought and precise argumentation. By understanding the "why" behind the calculus rules, you empower yourself to tackle complex problems in pure mathematics, applied sciences, and cutting-edge technology. Enroll today to begin building your rigorous mathematical foundation.
Enroll Now →