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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

To apply, please click on the following link:

Apply Now

The deadline for submission is 5:00 pm, Sunday, July 4, 2021.  Please do not submit your application more than once. The selected applicants will be informed by email by Wednesday, July 7, 2021 and the list will be published on this webpage as well.


Cost and resources

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


TopicWeek #Lecture TimingInstructor
Linear Algebra 1 & 2 2:30 pm - 4:00 pm Sivaguru R
Matrix Analysis 1 & 2 11:00 am - 12:30 pm Venky Krishnan
Statistics and Machine Learning 3 & 4 4:00 pm - 5:30 pm Sreekar Vadalamani
Numerical Methods and Algorithms 3 & 4 11:00 am - 12:30 pm Vishal Vasan

 

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 AlgebraMatrix 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 LearningNumerical 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

 

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