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I got into an interesting situation and I would love if you could help me with an advice, opinion or something. I have an offer for an MSc study (one year) in applied mathematics (with a scholarship) at a renowned university. The only problem is that I love pure mathematics far more than applied. In fact I can honestly say that I hate numerical mathematics. In future, after finishing MSc study I wish to continue with a PhD (in pure mathematics).

So, my question is how detrimental (if at all) would it be if I was to go for that MSc in applied mathematics (thus "losing" a year I could have spent studying something in pure) in trying to go to a PhD in pure mathematics a year later? I have heard of transitions from physics to pure mathematics but so far I don't know for somebody who did such a transition (from applied mathematics that includes numerical mathematics to a PhD in pure mathematics).

P.S. I also have an offer for an MSc in pure mathematics, but with a far weaker scholarship, at a not so "famous" university, and some additional problems with visa and stuff.

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I would suggest that you do what you like the most. Having to do something which you don't like for a long time will get you in trouble with yourself. –  Jonas Teuwen Jul 9 '11 at 16:26
Please stop upvoting the only opinion that has been expressed in some detail (mine), and produce a range of answers to guide this student. –  André Nicolas Jul 9 '11 at 17:01
Fair warning regarding asking for advice on important life decisions from strangers who don't know you: meta.mathoverflow.net/discussion/688/… –  Qiaochu Yuan Jul 9 '11 at 19:02
I don't know if it is from the pessimistic overtones, pragmatism, rationality or something else but currently I am leaning towards going at that applied maths programme. I don't see it as killing my "dreams", but rather as a means towards fulfilling them. One year spent at something that I am not completely inclined to but what could help me greatly further on seems like a good wager. But, it could as well be that I should go for what I (currently!) love and reject the rationale behind going at that applied programme. Having a choice sometimes makes things hard... –  aljosa Jul 9 '11 at 20:44
I'm with Jonas Teuwen on this: be true to yourself; that can be a point in your favor when you apply for PhD programs (in that, you can mention that your commitment to and passion for pure math was so strong that you accepted a less tempting offer at the MSc level, despite a much more lucrative offer in applied math. I'm not saying that doing the applied math program will hurt, but why not use the next year pursuing what you are more interested in, while applying to PhD programs in pure math? –  amWhy Jul 9 '11 at 22:41
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closed as off topic by amWhy, Jonas Teuwen, Chandru, Qiaochu Yuan Jul 9 '11 at 23:05

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1 Answer

My opinion:

All of mathematics is beautiful. A problem is a problem is a problem.

In particular, Applied Mathematics is beautiful. And, occasionally, it even has applications.

Do be careful about letting irrational prejudices get in the way. Also be careful about going into a marginal (from the hiring point of view) branch of mathematics for which you have a temporary infatuation.

If you think that the "hate" you mention is destined to be a permanent state of mind, then the MSc in Applied Mathematics will be painful. But the damage will not be permanent, and if you turn ultimately to what you call pure mathematics, you will be surprised about the degree to which your experiences in Applied Mathematics have informed your research work.

Is there an alternative of going directly to a PhD program, with a decent scholarship?

Added: And congratulations on having the problem. I am sure that many would envy your quandary.

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+1 for all mathematics is beautiful. As a current undergrad, I don't like the idea of people specializing or avoiding certain parts of mathematics in the graduate area (e.g: I study applied/pure math only). Why leave any of it out? –  ae0709 Jul 9 '11 at 16:32
Thanks for the answers:) Unfortunately, there is no opportunity to go for a PhD directly, these MSc opportunities are for courses starting in october 2011. Yes, I believ i will never like numerics, but I suppose that I could survive one year with it... So, the opinion is that if I was to go for that one year course, it wouldnt lower my chances on going for a PhD in a good university starting in winter 2012? –  aljosa Jul 9 '11 at 16:41
You should seek a range of opinions, particularly at your university, where they will know more details and where you have established relationships. About numerics, kind of messy, right? Well, real research in any field is kind of messy. In your pure maths courses, all the rough edges have been smoothed down. –  André Nicolas Jul 9 '11 at 16:58
I don't understand why you'll only be doing numerical analysis... there are plenty of other parts of applied –  ae0709 Jul 9 '11 at 16:59
@Eric: Hmm.. keep going until you die then. I'm not sure if I'll live for finitely many years, so I can't relate just yet. –  ae0709 Jul 10 '11 at 1:10
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