**Edit: Disclaimer: These questions were asked during MY interview. I have posted them thinking that they may possibly be of use to anyone preparing for such exams. However, please don’t ask advice from me. I may not be good at advising and also, it is often disinteresting.**

Interviewers: Prof Nitin Nitsure (TIFR), Prof C S Rajan (TIFR), Prof Balwant Singh (IITB), Prof Shobha Madan (IITK). Most questions were asked by Prof Nitsure, including the last one. They asked me what I was interested in. I told Algebra; Nitsure sir observed that I had correctly attempted all but one question in the Algebra section of the written exam. I was asked to try that question then but I gave up.

is a morphism from to . Then what can you say about ?

(I interpreted the question in geometry to algebra, worked out coordinate ring homomorphisms but couldn’t reinterpret the result geometrically.)

State the inverse function theorem.

(I couldn’t answer that one and I personally think, one who doesn’t know InFT doesn’t deserve to get a PhD scholarship. There followed a discussion as to how poor I was at analysis, having scored only two points in the analysis section out of a possible ten. One section was optional, though. “Let us see if you know any Complex Analysis:” )

is a holomorphic function defined on the whole complex plane and whose image is the complement of the open ball of radius centered at the origin. Then what can you say about ?

(Constant map. Every complex analysis interview question is a variant of the Liouville theorem. )

What is the fundamental group of a *hawai chappal*?

(. They asked if I knew the proof. I hinted van Kampen. )

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March 29, 2010 at 19:58

ksdf asldfkji am visiting you blog many times. You are selected in M.Sc scholarship test, phd scholarship test ,tifr, csir etc what not in mathematics field. Your are an engineer but how you achieved this. I want to know the secret of your success. If possible please write an article in your blog, about the aptitude you have in creating such wonders. waiting for your article

best wishes for your future

March 29, 2010 at 20:01

ksdf asldfkjalso tell me how will read

March 29, 2010 at 21:18

abhishekparabIf you have a mission that you badly want to achieve, you will find the necessary resources around you. I am far from being a prodigy or a genius but there are so many people from whom we can take inspiration, Ramanujan and Sachin Tendulkar, to name a few.

March 31, 2010 at 15:35

ksdf asldfkjI am very much impressed by your simplicity. Thank you for your reply.

September 7, 2010 at 01:18

debashishhi i am happy to know your performance in the nbhm interview. actually i am also a recipient of nbhm scholarship 2009-10. its nice to know your experience. good night

December 28, 2010 at 21:46

kunalI am preparing for IIT-JAM ( mathematics ) and appearing in 2012. I would be really grateful to you if you could give me some tips on how to prepare properly because till now I have only studied whatever was in my college curriculum ( matrix algebra,vector calculus, differential equations and a little bit of abstract algebra )

December 29, 2010 at 23:47

abhishekparabI can’t give tips to prepare properly because I don’t know how one prepares properly. But perhaps you can try reading Rudin’s Principles of Mathematical Analysis, Herstein’s Topics in Algebra

thoroughly.December 31, 2010 at 16:07

KunalCould you tell me something about NBHM Scholarship ( M.Sc. ) and its preparation like the topics to be laid stress on and the level of mathematical maturity expected of the students ie. are we expected to solve problems of olympiad/putnam caliber?

January 30, 2011 at 20:31

Kunal SuriHow do we calculate the limit points of a given sequence

January 30, 2011 at 22:45

abhishekparabIn a Hausdorff space, the limit point is unique. To find a limit point, usually one guesses a point and proves that it is the limit point.

February 3, 2011 at 00:53

Kunal SuriWell thanks for the insight,but what i wanted to know is related to the euclidean space. I mean when we learn the definition of a limit point in real valued sequences, we see that the definition is more or less same as that of the limit of that sequence. This definitely means that the limit is a limit point but vice versa isn’t really true but a sequence can have more than one limit point. Now, my question is: if a sequence has a limit point other the limit, then can we find that point explicitly and if not, then can a particular interval containing that point be found. I would be grateful if you would tell me the method or atleast the source where i can find ( its not in Rudin or Apostol )

February 3, 2011 at 09:57

abhishekparabYour question is not well defined. By “can we find” do you mean compute the limit, or find if the limit exists.

A sequence can have many limit points. The sequence 1, -1, 1, -1, .. has both 1 and -1 as limit points but no limit. A limit of a real valued sequence is the unique real number (if it exists) whose every neighbourhood contains all but finitely many points of the sequence. The sequence 1, 2, 3, … has no limit and no limit point.

See Munkres’ Topology for details.

About your second question, I am not the right person to ask since I have (as yet) not done any substantial research.

February 3, 2011 at 00:56

Kunal SuriOne more question, to be able to do mathematical research is it necessary to have a mastery of the olympiad level mathematics i.e combinatorics, geometry, elementary number theory? I mean do we need to have mastery of these topics or should we just focus on the college-level mathematics i.e linear algebra, abstract algebra, real analysis, etc.

February 3, 2011 at 22:55

Kunal SuriI guess if we are given a sequence, then we can always prove if it has a limit point or not .When I say ” can we find”, I mean computing the limit point ( NOT THE LIMIT, which can be done ) and if not the limit point, then atleast the interval in which it lies.

March 2, 2013 at 03:56

Arijit DasThe level of questions are getting higher in the exams like TIFR,IIT JAM,NBHM etc year by year.

Can you please suggest me some books in Linear Algebra to qualify the above exams.

Thanks in advance.

August 27, 2013 at 11:16

Rohith SHi, I find your posts rather interesting and highly informative (I couldn’t find any other blog similar to this regarding NBHM). Could you tell me if I am eligible to apply for the MSc/MA scholarships if I did my BSc Mathematics course through distance mode (from IGNOU)? Thanks!

April 2, 2014 at 16:35

Raju Kumar SinghHi,

I am a BE graduate of 2010 batch. Very lately, I come to know that I have special passion for mathematics and want to continue my in this field. I have panned to take NHBM phd scholarship test for the 2015. I want to know the syllabus for the same and books required for its preparation.

Please provide me those information, I would be highly obliged to you.

Hoping your sooner response.

Thanks.

April 2, 2014 at 16:39

Raju Kumar SinghHi,

I am a BE graduate of 2010 batch. Very lately, I come to know that I have special passion for mathematics and want to continue my career in this field. I have planned to take NHBM phd scholarship test for the 2015. I want to know the syllabus for the same (someone says graduate level while other says master level) and books required for its preparation.

Please provide me those information, I would be highly obliged to you.

Hoping your sooner response.

Thanks.

July 2, 2014 at 20:49

amrit100000Hello sir, you are presently at purdue. could you post a journey to the purdue university. I mean those exact credentials of gre score, ielts score(if required), previous research experience required or any other factor that comes into play for getting an admission there? Please post from the context of mathematics student. Thank you 🙂

October 16, 2014 at 02:34

S. Revathisir. i do want to pursue my higher studies in mathematics. It ll be very useful when u give full informations regarding NBHM .

March 31, 2016 at 07:50

John SHello, I just want to know when does NBHM declare the final selected candidates list after the interviews. Thanks.