Venue: TBA
Class Timings: TBA
First Meeting: TBA
Course Description: Linear-algebraic concepts underlie many theoretical ideas across mathematics. The utility of these concepts is not theoretical alone but also arises from the fact that these concepts motivate the development of highly efficient algorithms. Taking motivation from classical approximation theory and modern data science, in this course we will see how numerical algorithms and theoretical concepts go hand-in-hand to solve practical problems. A brief outline of the course is given below.
- Motivating examples: data, approximations and projections
- Floating point representation, conditioning, computational stability
- Matrix factorizations and iterative algorithms: QR, LU, Cholesky, Schur, eigenvalue
- The singular value decomposition
- Under- & over-determined systems of equations
- Advanced topics: FFT, image processing, inverse problems, optimization, randomized algorithms
Course Outcome: After completing this course, the student will:
- Possess tools and skills to develop computational solutions to practical problems as well as to understand computational complexities
- Understand various linear algebra concepts widely used in statistics, machine learning and approximation theory.
- Formulate well-defined problems using these concepts
- Develop oral and written communication skills relevant for mathematical discourse
Prerequisites: Proficiency in Python/Julia/MATLAB, linear algebra, introductory probability and statistics. Analysis concepts will be developed as needed hence undergraduate real analysis will be useful, but not necessary.
Textbooks:
- Teacher: Vishal Vasan