## 14 Jul Interview Experience at CMI (MSc in Applications of Mathematics)

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This is my interview experience at CMI for MSc in Applications of Mathematics. The syllabus for MSc in Applications of Mathematics includes single variable calculus, linear algebra, theory of equations, combinatorics and some other topics from class 12^{th} syllabus.

There were two classrooms for the interview process. In one classroom all the students were waiting, and in the other classroom, the interviews were going on. There were two professors taking the interview. For each interview the average time was 30 – 40 minutes. In the interview, the professors had a copy of the application form I filled while applying and my written exam.

They saw my profile in the application form, and were little surprised to know that I had done BE.

**Interviewer:** Oh, BE?

**Me:** Yes sir, I did BE in electrical engineering from Delhi College of Engineering. After that I joined Mahindra Two Wheelers, R&D, in Pune as Electrical designer.

**Interviewer:** I see, what was your work profile?

**Me:** My role was to design electrical systems like starting system, charging system etc. for two wheelers, particularly scooter. Say for example, while designing charging system, we have to ensure that the power generated by magneto should be more that the total power consumption of all loads of the vehicle. Other than that I have also worked on various technology projects.

**Interviewer:** Okay, did you use any specific statistical or numerical methods in your work.

**Me:** Not much sir, it was based more on experiments and tests.

(They were not much interested in what I did in my company until and unless it involved mathematics.)

**Interviewer:** Then how come all of a sudden you decided to pursue mathematics.

**Me:** Sir, it was not sudden, I was interested in mathematics from class 12 but I started preparing seriously last year only.

**Interviewer:** Okay Neha, have you studied analysis? I mean, calculus.

**Me:** Yes sir.

**Interviewer:** sequences, series?

**Me:** Yes

**Interviewer:** What do you mean by convergence of a sequence?

I explained by using the $$epsilon – delta$$ definition.

**Interviewer:** Prove that if the sequence of continuous functions converges uniformly to a function then that function is also continuous.

The same question came in written exam. I didn’t do it correctly in the written. I did the proof correctly in the interview. The interviewers asked some questions about small details in the proof e.g. I used the word limit function, they asked me the definition of it. I used the symbol $$f_n(x)$$, they asked me which $$n$$ is this.

**Interviewer:** what is a series?

I gave the definition. I used the word partial sum. They asked me what partial sum is. Whichever new word I used, I was asked to define it.

**Interviewer:** Is the series $$frac{1}{n^2}$$ convergent?

**Me:** Yes

**Interviewer:** How?

I started proving it using integral test.

**Interviewer:** How are you doing it?

**Me:** Sir, I am using integral test to prove it.

**Interviewer:** What is integral test? Why will it work?

I told that sum of series is bounded by integral of $$frac{1}{x^2}$$ and I plotted the graph of $$frac{1}{x^2}$$ for positive $$x$$. They were asking me how you can say that it is bounded. The mistake I had made was that I plotted the graph from zero when the sequence started from 1 (it was going towards infinity near zero so area was not bounded). I realized it soon and plotted it from 1.

**Interviewer:** Have you studied linear algebra?

**Me:** Yes

**Interviewer:** What is a positive definite matrix?

(I had not studied positive definite matrix part properly so I was hoping them not to ask from this but I guess it is their favourite part. There was a question on this in written exam also.)

**Me:** A matrix with positive eigenvalues.

**Interviewer:** Is this the definition of positive definite matrix?

**Me:** Suppose we have an $$ntimes n$$ matrix $$A$$, and a vector $$x$$ of size $$n$$, then $$x^TAx$$ should be positive.

**Interviewer:** For which $$x$$?

**Me:** For all $$x$$.

**Interviewer:** Are you sure. Is it true when $$x$$ is null vector?

I got little confused. I started solving $$x^TAx$$ for $$2times 2$$ matrix.

**Interviewer:** Don’t solve, just think.

**Me:** It will be zero for null $$x$$.

**Interviewer:** So, it should be positive for all $$x$$ not equal to $$0$$.

**Me:** Yes

**Interviewer:** Using this definition can you prove that eigenvalues of a positive definite matrix are positive.

I proved it by multiplying $$x^T$$ to the equation $$Ax=lambda x$$.

**Interviewer:** What is the rank of a matrix?

**Me:** It is the number of independent rows or columns.

**Interviewer:** What do you mean by independence?

**Me:** If I have vectors, $$x_1, x_2, ldots, x_n$$ and scalars $$a_1, a_2, ldots, a_n$$, then the only solution to the equation $$a_1x_1+a_2x_2+cdots+a_nx_n=0$$ is $$a_1=a_2=cdots=a_n=0$$.

**Interviewers:** Thank you Neha. Results will be announced tomorrow.

**Me:** Thank you sir.

Based on my experience, these are the suggestions for those preparing:-

Read and understand all the definitions and theorems. You should be able to define all the terms. Understand and practice the proofs of theorems. Practice past year papers for written exam. I used the books mentioned on CMI website. In addition, I also did assignments and referred notes of linear algebra and calculus with theory course from MIT OCW. The assignments also have solutions. MIT courses will be particularly helpful for students coming from different background and who have not studied these topics in classroom. Other than this, for all my doubts and queries I referred math.stackexchange.com. I always got excellent solutions there.

So, though the number of students getting selected every year is less, but if your concepts are clear, you will definitely get a seat. So, be confident.

**Disclaimer:** The conversation written above is based on what I remember from the interview. They are not the exact words of me or the interviewers.

## priya

Posted at 23:46h, 26 DecemberHi neha

I’m also thinking of applying for msc applied in cmi. It would be really helpful if I can talk to you , so if possible please share your email id. Also how are you doing now that you have started studying there.

## Neha

Posted at 20:14h, 12 JanuaryHi priya, you can send your queries on (neha at cmi dot ac dot in)

## priya

Posted at 20:36h, 25 JanuaryThanks Neha

## Sambhavi

Posted at 15:31h, 28 FebruaryHi Neha,

Happened to read your interview experience at CMI. I’ve sent you an email with queries as well. Would be glad if you could reply.

## alisha

Posted at 12:36h, 24 MarchHi,Neha

I have applied to Msc in application of mathematics this year,I also went through previous year papers too,so just wanted to know how many questions should be attempted correct for Part A and B both so as to get a interview call.

## Sue

Posted at 12:25h, 09 AugustThank you so much, Neha. That was very helpful.

## Karan Shah

Posted at 09:55h, 25 NovemberMs. Neha,

Where can I contact you? Is the CMI e-mail still active?