TIFR CAM Exam Experience

I was a student of the Institute of Science, Banaras Hindu University enrolled in the program of the Bachelor of Sciences (Math Honors) in the session 2020-23. I wanted to go for higher studies in mathematics but since the current state of Indian Universities in the field of pure sciences is deplorable (even the topmost ones, my case, for instance). Therefore I appeared for several entrance exams for admission to the premier research institutes of the country, one of them being TIFR(https://www.tifr.res.in/).

The TIFR GS exams in mathematics (and other sciences) are generally held in the first week of December and the forms are out in October. The exams are usually conducted in CBT (computer-based) mode. The question mainly consists of beginning graduate-level analysis and algebra. It is a good idea to be well acquainted with Baby Rudin for analysis and Herstein/ Dummit Foote for algebra for sailing through both the written exams and the interview.

After clearing the written exam, I along with my friend appeared for the TIFR CAM(https://www.math.tifrbng.res.in/) interviews. Our interviews were held in April 4th, 2023 in the morning session. We reached Bangalore the day before our interviews, and after a two-day-long journey by train from Varanasi, we were dead tired. Anyway, I booked a hotel room in the Yehalanka area, from where our center was a walking distance away. After doing traditional South Indian vendors in the streets of Bangalore, we checked in the center, where after some formalities we were let in. The TIFR CAM is a big building with a faculty quarter, student rooms, library, and classroom all in one single building. Anyways, there were two panels for the interview, I was the first to be interviewed and my interview panel was headed by Agnid Banerjee.

After some brief introductions, I was asked to go to the board. The first question I was asked was to state the Bolzano Weierstrass theorem and use it to prove that a continuous function in [0,1] is bounded. After getting a lot of hints from the panel, I was somehow able to prove the theorem, it took about 30 minutes to prove which ideally should be solved in less than 5 minutes. Anyway, the next question I was asked was to prove that Gl(n,r) is a non-compact topological group, which I had no clue about whatsoever. The interview panel tried to give me hints, but I politely accepted that I could not prove the statement, and then they asked me to leave. I was heartbroken because I knew I would not be able to clear the interview. My friend who had accompanied me also had a similar interview experience to me. Both of us explored the city, visited places, and returned to our university after a week-long trip.

After two to three weeks of the interview, the final results were out. Both of us were not selected. Anyways, fast forward to now, I am an integrated Ph.D. in IISER Mohali and my friend is studying mathematics and computing form NIT Warangal. We are both happy and when we look at those times there is no remorse because we learnt that failure is the stepping stone of success.