Courses

The tentative list of courses will be added shortly.

Game theory

Instructor: Umang Bhaskar, TIFR.

Course description

The course will be a mathematical introduction to the theory of games. We’ll look at different kinds of ‘real life’ games, including voting in elections and selling items via auction. We’ll also look at the role algorithms play in games, and how wrong incentives can lead to suboptimal outcomes in these games.

Prerequisites

Basic linear algebra, probability, discrete math. The following topics will be particularly useful: vectors, matrices, and basic operations on these, matrix rank, basic probability distributions, random variables and expectation. Knowledge of graphs, including matchings and flows, may also be useful but is not required.

Error Correcting Codes

Instructor: Ramprasad Saptharishi, TIFR.

Course description

The problem of storing and transmitting data effectively in the presence of noise is a fundamental problem of interest at the intersection of computer science, engineering and mathematics. Ideally, we would like communication and storage schemes that allow us to efficiently recover the original information even if a part of the data is corrupted, for instance, if your DVD has some scratches, or if some of the packets are dropped while being transmitted over the internet.

Error correcting codes are mathematical objects designed to solve precisely these problems. The foundations of the theory of error correcting codes (or simply coding theory) emerged from the beautiful and profound works of Shannon and Hamming in the 1940’s. This course will be a gentle introduction to this world of error correcting codes. We will discuss what these objects are, why they are of interest, and talk about some examples of codes and their properties.

Prerequisites

Basic linear algebra, discrete probability and undergraduate algorithms.

Compressed sensing, or how math of sparsity can inform ML

Instructor: Jatin Batra, TIFR.

Course description

We live in an era of big data and big compute resources for ML. To fully use these resources, we must leverage math to enable computation to exploit structure in the natural world. In this short course, we will use linear algebra to play with the setup of compressed sensing. We will learn how leveraging sparsity enabled a host of compressed sensing applications such as the seemingly miraculous low dose CT and MRI, and how these principles can help advance data science.

(Post Quantum) Cryptography

Instructor: Venkata Koppula, IIT Delhi.

Course description

We all use cryptography on a daily basis for secure communication. In this course, we will discuss one of the fundamental cryptographic primitives - public key encryption. We will start with the formal definitions of public key encryption, and see some traditional public key encryption schemes.

Traditional public key encryption schemes can be broken using a quantum computer, and therefore we need new encryption schemes that are quantum-resilient. Such encryption schemes are called post-quantum encryption schemes, and we will discuss one of the leading candidates for post-quantum encryption schemes.

Finally, we will discuss how to go beyond public key encryption.

Prerequisites

linear algebra, discrete probability, modular arithmetic.No cryptography background will be assumed for this course.