Linear Algebra Course | 12-Week Undergraduate Program | Kerala School of Mathematics
Course Details
| Exam Registration | 451 |
|---|---|
| Course Status | Ongoing |
| Course Type | Core |
| Language | English |
| Duration | 12 weeks |
| Categories | Mathematics, Foundations of Mathematics, Algebra |
| 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 | 17 Apr 2026 IST |
| NCrF Level | 4.5 — 8.0 |
Master the Language of Modern Science: A Comprehensive Linear Algebra Course
Linear Algebra is far more than just a branch of mathematics; it is the essential language underpinning modern science, engineering, and data analysis. From the algorithms that power search engines and artificial intelligence to the models used in quantum mechanics and computer graphics, a firm grasp of linear algebra is indispensable. This 12-week undergraduate course, meticulously designed and taught by Prof. Pranav Haridas of the Kerala School of Mathematics, offers a deep and rigorous introduction to this foundational subject.
About the Instructor: Prof. Pranav Haridas
Leading this intellectual journey is Prof. Pranav Haridas, an Assistant Professor at the prestigious Kerala School of Mathematics. Prof. Haridas brings a wealth of expertise from his research in Complex Analysis, specifically quadrature domains in several complex variables, quasiconformal mappings, and Teichmüller spaces. He earned his doctorate from the Indian Institute of Science (IISc), Bangalore, ensuring that the course is built on a strong foundation of advanced mathematical thinking and clarity of instruction.
Who is This Course For?
This course is ideally suited for:
- Undergraduate students in Mathematics, Physics, Computer Science, and all Engineering disciplines.
- Anyone seeking a strong theoretical foundation in linear algebra, crucial for advanced studies in Theoretical Physics, Data Science, Machine Learning, and Computer Graphics.
- Professionals looking to solidify their understanding of core mathematical concepts used extensively in industry.
Industry Support: The concepts taught are directly applicable in almost all engineering and technology companies, particularly in fields like software development, robotics, finance, and cryptography.
Course Overview & Learning Objectives
This course moves systematically from basic concepts to powerful theoretical results. You will start by understanding the building blocks—vectors and spaces—and progress to mastering transformative operations like diagonalization and the Spectral Theorem. The goal is to develop both computational proficiency and deep conceptual understanding, viewing linear algebra as the study of linear transformations and their algebraic properties.
Detailed 12-Week Course Layout
| Week | Topics Covered |
|---|---|
| Week 1 | Vectors, vector spaces, span, linear independence, bases |
| Week 2 | Dimension, linear transformations |
| Week 3 | Null spaces, range, coordinate bases |
| Week 4 | Matrix multiplication, Invertibility, Isomorphisms |
| Week 5 | Coordinate change, products & quotients of vector spaces, duality |
| Week 6 | Review of row operations, rank, determinants |
| Week 7 | Eigenvalues, Eigenvectors |
| Week 8 | Diagonalization |
| Week 9 | Characteristic polynomials, inner products and norms |
| Week 10 | Orthogonal bases, orthogonalization (Gram-Schmidt), orthogonal complements |
| Week 11 | Adjoints, normal and self-adjoint operators |
| Week 12 | Spectral theorem for normal and self-adjoint operators |
Recommended Textbooks & Resources
To complement the lectures, Prof. Haridas recommends the following authoritative texts, catering to different learning styles:
- Linear Algebra by Stephen H. Friedberg, Arnold J. Insel, & Lawrence E. Spence (5th Ed.) – A comprehensive standard text.
- Linear Algebra by Kenneth Hoffman & Ray Kunze (2nd Ed.) – A classic, more theoretical approach.
- Linear Algebra Done Right by Sheldon Axler (2nd Ed.) – Renowned for its focus on linear transformations and conceptual clarity.
- Lecture Notes by Terence Tao – Offers insightful explanations from a leading mathematician.
Why Enroll in This Linear Algebra Course?
This course is your gateway to thinking in higher dimensions. By its conclusion, you will not only be able to solve complex problems involving matrices and vector spaces but also appreciate the elegant structures that make linear algebra a powerful tool across disciplines. Under the expert guidance of Prof. Pranav Haridas, you will gain the confidence and knowledge to apply these principles in academic research, competitive examinations, or cutting-edge industry applications. Build your mathematical future on a solid foundation—master Linear Algebra.
Enroll Now →