Summer Workshop in Applied Mathematics (SWAM)

Dedicated to our former colleague Prof A S Vasudeva Murthy who was very appreciative of this programme and encouraged us significantly.

This summer school is targeted at people who use sophisticated mathematics in applications. For example, researchers, scientists, and engineers in industry, academia, or research labs. The summer school has been designed with this audience in mind and the four topics that have been chosen have broad relevance and significant contemporary applications.

Mode of instruction

Due to the ongoing coronavirus pandemic, all the lectures will be online. There would be two lectures of 1½ hours each day. Each of the four topics would be explored in a set of 10 lectures.

Duration of the summer school

July 12 - August 6, 2021 (No lectures on Saturdays and Sundays)

Who can apply?

Anyone interested in learning these topics can apply. However, our selection process will give strong preference to researchers, scientists, engineers or students who use the topics mentioned below in their industrial applications or research.

Application deadline and selection

The application deadline has passed. The list of selected applicants is available at the end of this webpage.

Cost and resources

This summer school is free. However, you should have a reliable high-speed internet connection along with a laptop/desktop.

Topic	Week #	Lecture Timing	Instructor
Linear Algebra	1 & 2	5:00 pm - 6:30 pm	Sivaguru R
Matrix Analysis	1 & 2	7:00 pm - 8:30 pm	Venky Krishnan
Statistics and Machine Learning	3 & 4	7:00 pm - 8:30 pm	Sreekar Vadalamani
Numerical Methods and Algorithms	3 & 4	5:00 pm - 6:30 pm	Vishal Vasan

Overview of topics

The topics we plan to cover during these four weeks are mentioned below. Please note that problem solving and programming are integral parts of this summer school. Exercises and homework problems will be given over the course of this programme and participants are expected to solve them. Python language would be used for programming.

Linear Algebra	Matrix Analysis
Essentials of Linear Algebra (vector spaces, subspaces, linear transformations, linear independence, bases) Graphs and Networks Method of Least Squares, Orthogonality and Fast Fourier Transform Eigenvalues, Eigenvectors, Cayley-Hamilton Theorem, Minimal Polynomials Diagonalizability, Rational and Jordan Canonical Forms, and Applications to solving linear system of ODEs Positive definite matrices, Singular Value Decomposition (SVD), and Finite Element Method	Matrix norms Projectors QR Factorisation, Least Squares Conditioning and Stability Gaussian Elimination Eigenvalue problems, Rayleigh Quotient, and Inverse Iteration QR Algorithm for Eigenvalue problems Computing the SVD
Statistics and Machine Learning	Numerical Methods and Algorithms
Probability distributions Linear regression, logistic regression; model selection Classification: logistic, knn, linear and quadratic discriminant analysis Dimensional reductionality: PCA, factor analysis, CCA Clustering: k-means, spectral clustering, etc. Sampling methods; MCMC	Ill-conditioned linear inverse problems and Tikhonov regularisation Convex/sparse minimisation Linear Programming

Organizers

Venky Krishnan (Centre for Applicable Mathematics, TIFR)
Sivaguru (Centre for Applicable Mathematics, TIFR)
Sreekar Vadlamani (Centre for Applicable Mathematics, TIFR)
Vishal Vasan (International Centre for Theoretical Sciences, TIFR)

List of applicants selected for SWAM2021

If you have been selected, please check your email for more information.

Sl No.	Name
1	Abhinav Chinta
2	Alasakani Karthik
3	Aman Kumar
4	Anant Kumar
5	Anirudh Sathiya Narayanan
6	Anjali Beniwal
7	Ankit
8	Ankit Singh
9	Anmol Kumar
10	Arindam Basak
11	Arkajyoti Bhattacharjee
12	Ashwini S
13	Deepak Kumar Yadav
14	Dhiraj Gangaraju
15	Evana Islam Sarkar
16	Ekansh Verma
17	Ishita Mahapatra
18	Kottala Panduranga
19	Kiran Kumar Bandeli
20	Krishan Kumar Yadav
21	Kusal Kansara
22	Mohmad Ausif Padder
23	Md Imtiaz Ahmed Mollah
24	Md Sohidul Alam
25	Riya Ghosh
26	Ritika Kapoor
27	Ritika Singh
28	Sanjeev Kumar Tyagi
29	Swargam Santhosh
30	Shubham Kumar
31	Shuvranil Sanyal
32	Sourabh Pattanshetty
33	Souradip Chakraborty
34	Souvik Paul
35	Suman Prabha Yadav
36	Tausif Husain
37	Ujjwal Roy
38	Utkarsh Vardhan
39	Venkat Raman
40	Venkata Ravi Kishore Talluri
41	Vidya Ravi
42	Vipin V
43	Vishwa Prakash Jha
44	Yash Malhotra