Gaurav Bhatnagar

Gaurav Bhatnagar is a mathematician who communicates the beauty of mathematics, engineers rich mathematical experiences for his students, and subjects them to a never-ending stream of bad jokes.

Summer 2024 – Ashoka Math Apprenticeship Programme

The Ashoka Math Apprenticeship Programme was started in Summer 2023 as an adjunct to the Lodha Genius Programme (LGP)), open to all interested TAs. The programme included an intense course in elementary number theory. In addition, many students wrote an expository article on a topic they are interested in, which they have not studied yet. The design of this programme is modelled on parts of Chicago’s Math REU.

In the summer of 2025, we expect to expand the program to include students from outside Ashoka.

Discover Elementary Number Theory

This problem solving course in elementary number theory was conducted by Gaurav Bhatnagar (Ashoka), Ojas Kumar (CMI) and Sagar Shrivastava (TIFR). The Lodha Genius Programme students who attended Amitabha Tripathi’s “A Problem Solving Seminar” also attended the course. Here is the course description:

This is a discovery approach to elementary number theory. Doing some easy problems every day you will discover ideas of elementary number theory and proofs, including theorems on prime numbers, congruences, and great theorems discovered by Fermat, Euler, Gauss and others, and you will also get an insight on how these giants did mathematics.

The topics covered include Gauss’ Lemma and the quadratic reciprocity theorem, continued fractions and the arithmetic of Gaussian integers.

About the instructors

Gaurav Bhatnagar is at Ashoka University. He is a Ph.D. in Mathematics from the Ohio State University. His interests are in the areas of mathematics influenced by Ramanujan, such as basic hypergeometric series.

Ojas Kumar is pursuing his master’s degree in Mathematics from the Chennai Mathematical Institute.

Sagar Shrivastava is a Ph.D. in Mathematics from the School of Mathematics, Tata Institute of Mathematics. His research interests are in Representation Theory and Algebraic Combinatorics.

The course consisted of 20 problem sets, closely following a few chapters in Hardy and Wright. In the design of the course, I wanted to capture the sense of what I remember from the Ross program, which I attended in 1990 at Ohio State University as a graduate student. I don’t have the material Ross created, but I do remember that at the end of 8 weeks of that program, I had become familiar with most of Hardy and Wright. I had taken the course after my graduate Algebra sequence; still, I found it useful to understand the motivations behind much of what I learnt in Algebra. Our course was only for 4 weeks.

Here is a link to download the lecture notes. Here is a link to my (handwritten) solutions. See the solutions only after trying the problems yourself.

Math articles (2024)

These are student papers explaining ideas which the students themselves are learning. Please use the cited references to gain a complete understanding of the material. The intended audience is undergraduate students interested in mathematics and its applications.

Mentors

The following acted as mentors to the students. They helped students to choose topics, assigned reading, and gave detailed feedback and comments on the paper.

  • Neelam (Utah)
  • Saujanya Bharadwaj (Ashoka University)
  • Tejasi Bhatnagar (Wisconsin, Madison)
  • Avneet Kaur (Macquarie University, Sydney)
  • Ojas Kumar (CMI)
  • Piyush Naresh (Ashoka University and Imperial College, London)
  • Manodeep Raha (TIFR)
  • Manjil Saikia (Ahmedabad University)
  • Souradeep Sengupta (Ashoka University)
  • Sagar Shrivastava (TIFR and Ashoka University)