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.

Who wants to be a Ramanujan?

Apparently, everyone. My teaching approach is all about developing the creativity in children and young adults. This page has links to resources I have made, that help you recognize the Ramanujan in you.

The picture above was taken on Dec 22, 2024, when we celebrated Ramanujan’s birthday in Ashoka University, with a bunch of very bright high school students attending the Lodha Genius Programme.

Middle and High School Level

I have written three books at the middle and high school level. These are all problem oriented, and will help you learn to develop your own creativity in mathematics. Begin early and get tuned to how mathematics is done.

  • Get Smart! Maths Concepts (Penguin (2008).
  • Maths Puzzles for Smart Kids (with Tejasi Bhatnagar) (Hachette, 2023).
  • Experience Mathematics (Hem Aunty Publications, 2024).

More information and links to buy/download are here. See also my page for High School Students.

High school/Undergraduate level

  • Ramanujan was interested in number theory. Ojas Kumar (CMI), Sagar Shrivastava (TIFR and Ashoka) and I made a course: Twenty Problem Sets to learn Elementary Number Theory from Hardy and Wright. This was targeted at the high school students in LGP and first year math students. The problem sets and my (handwritten) solutions are available for download. This much of elementary number theory is what everyone who is in mathematics should know. You can learn it in about an hour a day in less than a month.
  • The problems in my first year calculus course at Ashoka University contain a large amount of classical mathematics, and emphasize sequences, series and such — the kind of mathematics that Ramanujan liked. The lecture notes are available: Calculus (Last updated: Jan 2025). Do the problems if you want to understand what creativity in mathematics means. Also do these problems if you think Calculus is easy, and learn that life is deep and meaningful!
  • My lectures in Combinatorics introduce many problem solving tricks. The title is An introduction to manipulatorics. The lecture notes are not available yet, but you can watch the lectures on youtube. Here is the link to the playlist. This was targeted at mathematics and computer science students. The promise of this course is that it will make you smarter!
  • I gave an introduction to Special Functions to my Ph.D. students. The lecture notes are available. Click here to download: Special Functions by Example.
  • Shaun Cooper and I are editing and annotating Dick Askey’s course notes of his famous course on Special Functions. This is work in progress.
What They Say about my teaching

Ramanujan Explained

My lectures on RamanujanExplained.org explain the mathematics of Ramanujan and are at a level suitable for mathematics undergraduates. Lecture notes are available on the website, along with the links to the lectures on youtube. The lectures are arranged by technique, so that you can learn the techniques to understand Ramanujan’s mathematics. There are plenty of exercises too.

For more resources, do look at my page for undergraduate students.

Research scholars and mathematicians in other areas: Topics in Special Functions and Number Theory

Atul Dixit (IIT, Gandhinagar), Krishnan Rajkumar (JNU) and I co-organise an online seminar on Topics in Special Functions in Number Theory which meets online approximately once every two weeks. The talks are by active researcher, and feature the Who’s Who of the Ramanujan world — including Bruce Berndt (UIUC) and George Andrews (Penn State) — the authors of Ramanujan’s Notebooks and Ramanujan’s Lost Notebook. Every year begins with a Ramanujan Special given by a distinguished mathematician. If you wish to attend the Seminar or speak in it, please write to the organisers at sfandnt@gmail dot com. To get familiar with some of the recent work of mathematicians who work in this area, browse the talks on the website sfnt.org. All talks are available online, so you can use this site as a starting point to enter the area. You can access the playlist from here.

For some more resources on Ramanujan, including some expository notes, look at my Research page.