ISI Interview Experience for Admission to MMath program

I appeared for the entrance exam of the Indian Statistical Institute for the MMath program in 2023. I had scored decent marks in the written exams (both objective and subjective) and hence, was called for the interview held at ISI Bangalore in late June 2023.

My interview was scheduled on June 28 and hence, I reached the campus a day earlier. The campus is about 50kms away from the airport and I had to take a cab to reach there. After arriving at the main gate, the guard guided me to the hostel. Shared accommodation was provided in the hostel free of cost for a day. Food was available in the hostel mess at a reasonable price.

For students belonging to the reserved categories, travel support was also provided through reimbursement of two-way sleeper class railway fare.

My interview was scheduled in the afternoon batch. After reporting at the venue at 2:00 pm, my documents were verified and I was asked to wait for my turn. The interviews typically lasted for around 50 minutes. I was called inside at 5:30 pm.

Once my name was called, I entered the classroom and was greeted by a panel of 7-8 professors. Since it was already evening by the time I was called, most of the profs looked tired. I was made to stand near the blackboard while the profs sat on the benches in front of me. They first asked me to introduce myself. After the introduction was over, they asked me my favorite area of mathematics, in which I felt comfortable answering the questions. I replied Algebra and Metric Spaces.

P1: Let (X,d) be a metric space. What can you say about the function [Tex]d'(x,y)=\frac{d(x,y)}{1+d(x,y)} \forall x,y \in X[/Tex]?

Me: It is also a metric on X, which is equivalent to the metric d.

P1: Prove it!

(I first proved that d’ is a metric on X and then showed it is equivalent to d by showing that every open ball in (X,d) is open in (X,d’) and vice versa.)

P2: Give me an element of [Tex]S_5[/Tex], the symmetric group on 5 elements.

Me: (1 2 3 4 5).

P2: How many conjugate elements does it have in the group?

Me: 4!=24.

P2: How?

Me: Two permutations are conjugates in [Tex]S_n[/Tex] if and only if they are similar and the number of permutations similar to ( 1 2 3 4 5) in [Tex]S_n[/Tex] is 24. Hence, the result.

P2: Similar?

Me: They have the same cycle structure when decomposed as the product of disjoint cycles.

P2: Okay Okay. Prove your claim.

(It took me some time to think and prove this. But after getting a hint or two, I proved the claim.)

P1: Okay. You may go now.

And with this, my interview was over.

Verdict:

Selected for the admission to the MMath program at ISI.