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Currently I am a junior at UCLA. I have taken some math classes and they seem really interesting. However, I am not sure whether I should pursue a PhD in mathematics. So instead I'm thinking about getting a master degree. However there's very few information about master in mathematics online.

Question 1: How rare is it for people to go to industry first and then go back to academia (after 2 years, for example)? How should they deal with the recommendation letter part?

Question 2: Some of my friends have been taking honour classes since they were freshman. However I used to be a math/economics major so I've been taking regular courses. How would that impact my application? (suppose I'm NOT talking about master in computational finance or financial engineering. I took a class in option pricing and interest rate model, worst "math" class ever)

Question 3: Is there any "rule of thumb" of determining whether someone should pursue an advanced degree (master and PhD) in mathematics? I remember once one of my TA told me that "if you cannot get six A's, then probably this is not the right path for you". Now, my major GPA is 3.8. Got 3 A's in upper (analysis and linear algebra), bunch of A- (complex analysis, differential geometry, probability), and B+ for abstrac algebra.

Any advice/insight is greatly appreciated. Thank you very much.

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    Why do you want to pursue a Master's degree in mathematics?
    – Potato
    Commented May 5, 2015 at 8:39
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    I don't have any experience in honour courses, not to mention graduate courses or research. In fact, my goal has always been becoming an actuary after I graduate. And indeed I have passed couple of actuarial exams and have done two internships at two large companies. I wouldn't call them "bad experiences", I mean I get paid and the job itself isn't boring (well, sort of). But it's not really "math-related" as I expected. And I realized that probably no job would ever care about "when an open cover has a countable subcover", stuff like that...
    – 3x89g2
    Commented May 5, 2015 at 8:51
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    You discuss this with a trusted faculty member. You should ask that faculty member where they think you might have a chance at being admitted to a PhD program. A PhD in mathematics in probably not worth it unless you're going to a very good school, for a variety of reasons (number one being the terrible academic job market). If your application is not strong enough, then discuss Master's degree options.
    – Potato
    Commented May 5, 2015 at 8:52
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    Yes, a lack of independent work and honors/graduate coursework is going to be problematic. See my previous comment.
    – Potato
    Commented May 5, 2015 at 8:53
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    @Potato Thank you. I'll definitely do that. I've heard of stories that a math PhD ended up working as an actuary or going to investment banks. It seems to me that most PhD still end up in industry and doing things irrelevant to what they've been studying :(
    – 3x89g2
    Commented May 5, 2015 at 9:00

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Q1. Not rare at all; especially for Masters programs. They probably deal with it as everyone else: contact a professor that they did well in their class and that class relates to what they want to study afterwards and ask politely for a reference letter. There are some cases (eg. you are more than 5-6 years after your graduation) that you may not need an academic reference but these are edge cases and do not apply to your case.

Q2. Depends what you want to study. If you are thinking of doing something with conjunction with Mathematical Finance or Econometrics/Economics this might be viewed as a positive thing. For Ring Theory? Probably not so positive.

EDIT (based on your edit) As you clarify now you are not thinking of something associated with Finance and/or Applied Maths generally. If that is the case, most probably not having honours class will be detrimental. Having said that, if you apply for MSc it should not have a significant impact. After all you are apply for a MSc so you can do classes like that.

Q3. The only rule of thumb I can think of about pursing a PhD is liking your subject a lot. And even that is a rule of thumb. Sorry to say but your friend's advice about "six A's requirement" etc. is ungrounded advice. Sure enough if you are not good at something you should not have illusions of grandeur either though. :)

EDIT (based on the comments) According to the interesting discussion in the comments: Take into account that you risk not having a house mortgage at 27 as well as one day waking up and realizing nobody will pay you to do Approximation Theory. (Actually, I think you should consider this as extremely likely. Don't worry though, even if this happens chances are you 'll survive it.)

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    Thank you very much. Made some edit to the original post on question 2 :)
    – 3x89g2
    Commented May 5, 2015 at 8:34
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    Do you have any experience in a graduate mathematics program? I ask because this seems like misguided advice. For example, regarding question 1, letters that only say "Student X did well in my class" are worse than useless.
    – Potato
    Commented May 5, 2015 at 8:34
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    @Potato: Approximately; Statistics (and Physics). You are correct to note that "Student X did well in my class" is useless and I never said that. I believe though that having done well in a professor's class is essential if you are asking him to vouch for you in a reference. It goes without saying that it is not the whole story. How can you write though: "this person has great potential" but "in what I taught him and relates to what he want he wants to study was so and so"? Is there something else that you find misguided?
    – user8458
    Commented May 5, 2015 at 8:48
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    @Potato: Regarding Q3, reading your comment I think you are even more stringent on how much the OP should love his subject, you are talking about : "dead set on being an academic" as a rule of thumb. I do not think this is a good rule of thumb. I had great fun in grad school; read insightful papers, conversed with extremely intelligent people about them (felt a bit stupid afterwards), wrote a few papers myself, and then I went to industry. So what was the danger? That I don't have a house mortgage at 27 and that one day I wake up and realize nobody will pay me to do Approximation Theory?
    – user8458
    Commented May 5, 2015 at 9:38
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    I'm curious if someone has surveyed graduating PhDs going to industry about this. I know at least a few who regret it and bemoan the fact they spent 5 years learning abstract nonsense that has no relevance to their current lives. To be fair, they did also not enjoy the day to day life of graduate school. I suppose that's the key. If you find spending 8+ hours a day reading about math enjoyable, then perhaps going is not a terrible idea. I would describe that as obsession rather than love, though.
    – Potato
    Commented May 5, 2015 at 9:45

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