Free Basic Linear Algebra Course | IIT Bombay Prof. Inder K. Rana | 8-Week Guide
Course Details
| Exam Registration | 809 |
|---|---|
| Course Status | Ongoing |
| Course Type | Core |
| Language | English |
| Duration | 8 weeks |
| Categories | Mathematics |
| Credit Points | 2 |
| Level | Undergraduate |
| Start Date | 19 Jan 2026 |
| End Date | 13 Mar 2026 |
| Enrollment Ends | 02 Feb 2026 |
| Exam Registration Ends | 16 Feb 2026 |
| Exam Date | 29 Mar 2026 IST |
| NCrF Level | 4.5 — 8.0 |
Unlock the Power of Linear Algebra: Your Gateway to Engineering and Advanced Mathematics
Linear Algebra is not just a subject; it's the foundational language of modern engineering, data science, economics, and advanced mathematics. From the algorithms that power search engines and AI to the models used in quantum mechanics and computer graphics, a solid grasp of linear algebra is indispensable. If you're a B.Tech, B.Sc., or an aspiring mathematician looking to build an unshakable foundation, this detailed guide to a structured 8-week course, designed by an IIT Bombay legend, is your perfect starting point.
Course Overview: A Structured Path to Mastery
This comprehensive course is meticulously laid out over 8 weeks, transforming complex concepts into digestible, weekly modules. It is designed to take you from absolute fundamentals to confident application.
| Week | Core Topics Covered |
|---|---|
| Week 1 | Matrices, Matrix Operations, Row Echelon Form (REF) |
| Week 2 | Linear Systems, Gauss Elimination, Inverse of a Matrix |
| Week 3 | Vector Spaces (Rn), Subspaces, Linear Independence, Rank |
| Week 4 | Determinants, Relationship between Rank and Invertibility |
| Week 5 | Linear Transformations, The Fundamental Rank-Nullity Theorem |
| Week 6 | Inner Product Spaces, Orthogonality, Gram-Schmidt Process |
| Week 7 | Eigenvalues and Eigenvectors: Concept and Computation |
| Week 8 | Similarity, Diagonalization of Matrices, and Real-World Applications |
Learn from an IIT Bombay Legend: Prof. Inder K. Rana
The course is guided by the expertise of Prof. Inder K. Rana, an Emeritus Fellow at the Department of Mathematics, IIT Bombay. With 36 years of teaching experience at one of India's premier institutes, Prof. Rana has shaped the mathematical understanding of countless engineers and scientists. His accolades speak volumes:
- C. L. Chandna Mathematics Award (2000): For distinguished contributions to math research and teaching.
- IIT Bombay Excellence in Teaching Award (2004): Based on outstanding student evaluations.
- Aryabhata Award (2012): For exceptional contributions to mathematics education in India.
Prof. Rana is also a renowned author, with key texts like "From Geometry to Algebra: A Course in Linear Algebra" serving as the recommended book for this course. Learning from his structured approach ensures you gain not just procedural knowledge, but deep conceptual clarity.
Who Should Take This Course?
This course is perfectly tailored for:
- Undergraduate Students: B.Tech, B.Sc. (Mathematics, Physics, Statistics)
- Postgraduate Students: M.Sc. (Mathematics), MA (Economics, Statistics)
- Aspiring Data Scientists & Engineers: Building core competency for machine learning and algorithms.
- Competitive Exam Aspirants: Preparing for GATE, GRE, or other higher studies entrance exams.
Prerequisite: A basic understanding of school-level mathematics is sufficient to embark on this journey. The course builds everything from the ground up.
Why is Linear Algebra So Crucial?
Linear algebra provides the toolkit for handling multi-dimensional data and complex systems. Here’s what you’ll master:
- Matrices & Systems of Equations: Solve multiple equations simultaneously, a routine task in optimization and engineering design.
- Vector Spaces & Transformations: Understand the space where data lives and how it can be rotated, scaled, and manipulated—essential for computer graphics and robotics.
- Eigenvalues & Diagonalization: The core behind principal component analysis (PCA) in data science, stability analysis in control systems, and quantum mechanics.
- Inner Products & Orthogonality: Key for signal processing, error-correcting codes, and the Gram-Schmidt process used in numerical methods.
Course Outcomes & Industry Relevance
By the end of this 8-week journey, you will have a firm grasp of the theoretical underpinnings and practical problem-solving skills in linear algebra. This knowledge is directly applicable and highly valued in:
- Computer Science: Graphics, cryptography, search algorithms, machine learning.
- Engineering: Circuit analysis, structural design, control theory.
- Data Science & Economics: Multivariate statistics, econometric modeling.
- Higher Mathematics: Provides the foundation for functional analysis, differential equations, and more.
Embark on this structured learning path with one of India's most esteemed mathematics educators. Master the language of vectors and matrices, and unlock your potential in any technical field. Start your 8-week journey to mastering Basic Linear Algebra today.
Enroll Now →