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Programs Can you do a PhD in maths with 2.1?

  1. Aug 22, 2011 #1
    I'm at a decent university(Manchester university) know I can get first. Got 70% in first year even through I failed a course because it was stupid matlab and refused to do it, if I did would have got 80%(read book about Grothendieck that strongly influenced me, which probably hurt my grades through). The problem is my second year grade is 63% because I was depressed as hell last year(family problems).

    I know I can get 80%> and if I choose the subjects I'm really good at could get 85%>. The problem is my social life goes down the drain, plus the subject I really want to be good at and study is category theory. I spent a lot of time reading books like conceptual mathematics, Serge Lang Algebra and other book on category theory. Feel be waste of time trying to read hard books if want to get high grades.

    The problem is I fear that I'm going to be judged on stuff like how well I can differentiate or how fast I can do algebra or worst how well I can memorize definitions.

    It's very painful as I feel like I'm not even learning stuff. But, with my grades even if I'm better at Maths then everyone else at my uni I'm going to get rejected.

    So yeah can get high grades. Just mean, stop learning stuff that isn't going to be on the exam, rote learn the definitions everyday, rote learn all the proofs and go over the example sheets n times a day. The sad thing is I doubt I will have greater understanding of Maths, which is all I really want.

    My social life is probably going to be non-existent now so got time to study. Just feel like should I grind to get 90%> or learn something that I actually care about and am interested in.

    The joke I don't even care about money as have very little social life and never want a gf. But, it would be distracted as hell if I had to get a normal job, which I would be forced to do. So doing 2 years of stuff that I consider pointless looks worth it to get high grades.
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  3. Aug 22, 2011 #2
  4. Aug 22, 2011 #3
    Why would you want to do a PhD if you don't even like basic topics such as calculus...? I think if you're to get a doctorates in math, you shouldn't have a problem with calculus and algebra... Even my dad still knows his calculus and he hasn't used it in ~15 years at his job (EE). But you're going for a PhD in math, people will be asking you questions about calculus, and how will you answer? That you just "Don't like calculus because it isn't important"?

    You also need to memorize solutions to succeed in DEs, period. You can't say you're the best at math in your uni if you don't try...
  5. Aug 22, 2011 #4


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    So you think you're going to be better than everyone else yet are scare to be judged in the absolute basics such as calculus?

    What are you even good at? Clearly not anything you've been tested on.

    A PhD is for someone who loves the field and doesn't gripe about having to learn things like Matlab.
  6. Aug 23, 2011 #5


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    Although Pengwuino is being a little harsh, I have to agree with his core message: To do maths, you have to enjoy it - not bits of it, ALL of it.

    Although Postgraduate Research is vastly to undergraduate study (and research for that matter), you are still going to have do things that you don't want to do. Moreover, if you want to do a PhD you will have to have a strong grounding in ALL areas of mathematics.

    I'll give you an example. I'm working towards a PhD in Applied Mathematics and I'm currently working on a solid mechanics problem. Yet, I spent all of yesterday formulating and proving existence and uniqueness lemmas for matrix equations.

    You can't simply refuse to learn what you don't find interesting. You can get away with it if you just want to get a degree, but not if you want to go on to further study.

    Although to answer your question directly: yes, you can do a PhD with a 2.1, although getting funding may be tough.
    Last edited: Aug 23, 2011
  7. Aug 23, 2011 #6
    Actually, Algebra and real Analysis is one of my best subjects. Through I hate metric spaces because you need to memorize about 30 metrics. Like last semester I only used calculus in one subject and that was called calculus of several variables.

    Last time I did DEs was about half a year ago. I'm not doing any applied any more through.

    I'm not scared to be judged on calculus. I'm scared I will judge on how well I can grind problems and memorize definitions. For example, metric spaces I needed to learn 30 metrics + about 15 definitions. Then I needed to memorize 10 proofs he gave me.

    Well, algebra, analysis and logic. If you overlooked metric spaces got like 80% on analysis subjects.

    To be fair, I have grown up a bit and would do matlab now. It's just I held strong bourbaki views which I still do. I don't really think Maths should be done by computers and thought it was a big waste of time trying to learn it. Like I don't like reading examples because Grothendieck would never think of an example.

    Well, I doubt I will be doing matlab or solving calculus question if studying categories(even then I don't suck at calculus got 85% last calculus unit I did a year ago). It's more of the memorization and grinding out problems. Like in a PhD I wouldn't need to memorize a boat load of definitions as I could look them up in books. I just feel like everything is memorizing definitions + grinding problem sheets above understanding what maths is.

    It's not that I don't find stuff interesting. More like I heavily disagree on how things are done.

    How tough will getting funding for a PhD with 75%. Just don't know what grade you need to get. I can get good references from lecturers.
  8. Aug 23, 2011 #7


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    You would be surprised. You're going to look a little silly in your supervisor meetings, or during a conference if you have to constantly refer to textbooks for standard definitions. There are things you will be expected to know and be able to recall from memory. Trust me, a PhD is frustrating enough without having to constantly look up definitions in texts.
    Well, prepared yourself for more of the same. What are you going to do if you disagree with your supervisor's way of doing things?
    Well, 75% is a first, but in general it is difficult to say and varies from year to year and place to place. There were two funded mathematics PhD studentships at my University last year, both went to people who got good firsts. I'm not sure if there are any funded places this year.
  9. Aug 23, 2011 #8


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    I will also add that I'm in no way trying dissuade you from doing a PhD. I think its great and if that's what you want to do - go for it.
  10. Aug 23, 2011 #9
    I suppose it was mostly arrogance. Like Maths should be logic and require no memorization in my mind. But, I suppose should have learnt all definitions. I'm planning to write down every definitions and go over them at three points of the day everyday. If I do that consistently I will know all definitions.

    I get on very well with nearly all my lecturers. I think because there is a big difference between passing Maths test and discussing Maths with someone.

    Was wondering how you get funding. I come from a very poor family so not like I got money to not work for three years.

    To be fair, in first year I rote learned a lot and made sure to go through the example sheets constantly, it wasn't fun but I did it. Then, on another forum people saying grades aren't everything and that should try to have fun. Then my grades slipped as I had more fun. So can get high grades, but would mean no fun.

    You make valid points. In a lot of ways I'm arrogant and inflexible, which I guess isn't good if want to do Maths. The Maths isn't hard it's just that I feel it's pointless and so hard to motivate myself to learn a ton of definitions. Like what I want to study I don't need to force myself to study it. Lang Algebra for example is mean't to be hard but I don't need to force myself to read it. However, learning 30 metric feels like I'm forcing myself and it's not that fun.
  11. Aug 23, 2011 #10
    I know what it feels like to be in this slumped. I've only recently gotten out of it. In my first year I had a 96%, was able to get a funded summer research position, and was on top of the world. But I let the arrogance get the better of me. I felt better than my peers, felt I didn't have to work. I stopped doing homework completely, stopped going to lectures, and didn't hand a single assignment in during my calculus course. It was exactly that attitude, and depressive state I was in, that got me my 72% in second year.

    This summer, going into third year, I've just tried my best to get my drive back, and want to do well. I'm fixing my GPA through retaking courses, course overloads, and summer courses to inflate my GPA and correct my wrong doings.

    The thing is, that I've found, is to just have a positive outlook on learning. I hate computations as much as your probably do (I did research in observational astrophysics, spending days just running scripts on data, and just hated it). And it was that hate that caused me to not want to do Calculus assignments. But I've realized that, though it may not be as enjoyable as proofs, its still fun as long as I put the effort in.

    Just throw yourself back into it. I know that's almost trivial, but its the best way. For example, I learned LaTeX so I could type everything out because my writing is abysmal, but I feel that this has helped me astoundingly. It has helped my reasoning, my laziness, and it has made me so much more proud of my work.

    Pessimism and nihilism eat away at you. They suck. You just have to throw yourself outside of your surroundings and struggle, and you'll realize that the productivity is just as much of a source of pleasure than what ever else you're doing instead of being productive. And it has lasting effects.

    Now I'm ranting, but I hope this helps you.
  12. Aug 23, 2011 #11


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    There is one thing that I want to point out, even though Penqwino and Hootenany have already touched on it.

    I think your (the OP) largest impediment to getting a PhD is your attitude to work you find tedious. Across all fields, if there is one thing PhD studies have in common, it's tedious grunt work that's only peripherally related to your research!

    I didn't like MATLAB as an undergrad either. Then, I got to grad school and realized that every figure I would need to make for papers/conferences/group meetings would need to be made it MATLAB. So, I sat down and learned it! (MATLAB has grown on me.) I joined my lab group because because I wanted to work in an optics lab and work with lasers. However, Our laser cooling pump broke down and needed to be replaced. So, I sat down and learned about pumps and water filtration systems (we had an algae problem in the water lines).

    My point is that part of doing a PhD is gaining the ability to independently learn whatever you need to learn for your research, whether it be directly related or on the periphery.
  13. Aug 23, 2011 #12


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    Are you serious?? You're having troubles that there are too much definitions in metric space theory?? And you want to go into category theory?? News flash: category theory is one big definition!!

    And what 30 metrics do you have to memorize?? I think you're complaining a bit too much here. What do you think you will do as a PhD? Never memorize anything and just read the books I like? Good luck with that.

    You don't get the importance of examples, do you? Examples tend to present the limitations of the theory. Ever wondered if the image of a category under a functor is a category?? Think about it for a long time. Only an example will give you the final answer though.

    Oh, good luck with that. A PhD students needs to know a boat load of definitions. How else can he do research?? Do you think that PhD students need to look up what a metric space is? Do you think they would do new stuff if they had to look up every little stupid thing?

    Seriously, memorize your things now. Now is your chance to do it, you'll regret it later if you didn't. I regret myself all the time that I didn't study more in my undergrad years, because I need to catch up all these things now.
  14. Aug 23, 2011 #13


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    To reiterate what others have said, going for a PhD requires that you know definitions. If you don't want to learn definitions and obtain a strong foundation in a particular field of mathematics, then getting a PhD (or a bachelor's degree in math, even) is not for you.

    Just out of my own curiousity, what math classes have you completed?
  15. Aug 23, 2011 #14
    Definitions are a tremendous part of mathematics; one analogy I liked is that mathematicians are sort of like wizards in that it is often the case the more obscure -yet relevant- esoterica they have memorized, the more powerful they become. When you know that trick or that proof or that theorem that no one else would have thought of, you can attack the problem in a way that no one else can.

    You need to be intimate with the details of the definitions of the objects you're working with; sure, you can look them up when you're thinking about a problem, but you won't make as much headway as the person who lives and breaths theorems and can attack the problem in many different ways. You have to sort of assimilate the theorems as a part of your stream of consciousness and really try to be intimate with them.
  16. Aug 23, 2011 #15
    To be fair, I'm just sort of mad I left everything to the end in metric spaces and geometry. Should have really been revising everything when I went along and hence like at the last month suddenly dawned on me I need to memorize all this.

    I suppose it's just laziness. Couldn't really be bothered to learn something that isn't even that hard. I'm not going to do it again through. Also, let my calculation skills get sloppier. Combination of distractions and laziness. Like did very little work and never fully attempted the problem sheets and looked at the answer to much.

    Yeah, I'm correcting it now. I think it's more of the wrong state of mind and being depressed. But, it's not that big of a problem as going over complex analysis now and my algebra is naturally good. Just scared I've screwed up my chances of getting PhD because of the second year.

    Algebra= up to basic ring theory like Kronecker theorems, Real and complex analysis, Pdes and vector calculus, Discrete Maths, Metric spaces, Some geometry, propositional logic.
  17. Aug 23, 2011 #16
    Hi, I'm currently coming to the end of a maths PhD in the UK so hopefully my experiences will be helpful. First of all, it's perfectly possible to get a place on a PhD course at a solid university doing maths, and get funding, with a 2.1. I know this because I did it, and while you may not be able to get your pick of prestigious institutions and world famous supervisors you will certainly not be alone in that. Most of us are not Terry Tao (who incidentally has some good advice http://terrytao.wordpress.com/career-advice/" [Broken]), but we get on with it and can make a decent contribution.

    Secondly, I must disagree with some of the other posters about the need for interest in calculus etc. If your interest is in a particular area of pure maths you don't really need to know about anything except that. Sure awesome advances can be made by people linking two or more seemingly disparate fields together, but those are special people, and for most of us a good understanding of our main (sub)area, and a working knowledge of the basics of its related subfields is good enough. If you really don't like an area it doesn't mean you're not suited to maths, though if you can't bring yourself to get a decent exam mark in it that may indicate problems with your ability to make yourself work, which will be important. For example, I hated number theory, my solution to this was to work in the border between order theory and logic, where we don't have any numbers. You can get by without remembering everything too. What you need to remember you'll remember because you use it all the time. Maths isn't really about remembering loads of details and facts (though this can be useful), it's about developing your intuition so that you get a feel for the kinds of things that should be true. Definitions are things you use to communicate ideas to other people, when you understand the ideas, their formal statements become less important. I'm simplifying here, and to some extent idealizing, but this is something worth thinking about.

    Finally, some advice about category theory. I'm far from an expert, though I know the basics, but category theory is hard. Not because of its technical difficulty as such, but because it takes a high level of mathematical sophistication to understand why things are being done, and prevent it from becoming an exercise in the purely formal manipulation of increasingly confusing definitions. I'm not saying you can't achieve that, but if category theory is your interest you're going to need a broad base in other subjects to get the most out of it.
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  18. Aug 23, 2011 #17
    See I don't know why they would fund 2.1 as 30% get a first. I don't care about supervisor or about prestige of the uni, through read that pure Maths is hardest to get funding for which scares me. Like in the internet age I can read top Mathematician blog and get a lot of papers of arxiv to read.

    I've been thinking that I should focus my study on logic+algebra+small bit topology for last two years of undergrad. Focusing on two subjects to me seems a lot easier. Is it impossible to work in multiple fields for normal mathematician? As John Conway has got impressive results in several fields.

    I think it's mostly random. Algebra and logic I don't need to force myself to do it. But, I don't know. Would you feel you would be a better Mathematician if you forced yourself to do number theory?

    As in a sense if chopping of my index finger would make me a better Mathematician I would do it. Also, if doing a lot of calculus/analysis work I would do it. Just feels pointless as it would be nothing like category theory.

    I've stopped learning it now to focus on work that would get me high grades. I suppose I worry about the most is mathematical sophistication. What you mean broad base? Thought you just needed algebra+logic+ abit of topology. I should know algebraic topology, algebraic geometry and stuff like model theory when I finish undergrad in two years.

    Anyway, thanks for your post. Feel less screwed.
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  19. Aug 24, 2011 #18
    Historically category theory was an outgrowth of algebraic topology, and as you're probably aware, Grothendiek applied notions from category theory/algebraic topology to algebraic geometry. Later on people like Lawvere started building it into an alternate "foundation" -used a bit loosely- without explicitly referring to set theory.

    "Categories for the working mathematician" draws on a lot of examples from algebra and algebraic topology, though other texts (like Awodey's introduction) don't. If you really want to be able to get a feel for it, you probably should attack it after taking algebraic topology. I made the mistake (or not, depending on your point of view) of trying to tackle it (via CWM) my sophomore year after having done well in my abstract algebra courses (text was Dummit and Foote, which is pretty easy going, good for self study). I didn't really get much out of it; I could clumsily manipulate the definitions and follow the proofs, but I had no feel for it and the examples were foreign to me.

    So really hit algebra hard, check out M. Artin's book and maybe study algebraic topology a good bit on your own between taking your topology and algebraic topology courses and that should make learning category theory that much smoother.

    ETA: out of curiosity, is it the foundational aspects of categories that interest you? Or the categorical logic/constructive maths side? Something else?
  20. Aug 24, 2011 #19
    Yeah, that's why I have been trying to learn topology so I can read Hatcher book plus plan to take Algebraic topology class this year. But, I don't like topology although the person who teaching topology in about a month said he hated topology when he first did it, now he differential topologist.

    Personally, I don't find categories for the working mathematician to be hard. I've read all of Birkoff and Maclanes Algebra book and don't really look at examples to learn stuff. If you ignore the examples in Categories for the working mathematician it's not that hard. Certainly, the first two chapters aren't that hard if you just ignore examples.

    Don't know if would be able to go onto algebraic topology that fast as find topology tricky. Hmm I would look into M. Artin's algebra. I can read Serge Langs Algebra even through it's very painful at times. Don't like group theory because of the heavy use of number theory, however most algebra books have group theory first and so it's painful to read.

    Heavy influence by a book about Bourbaki that mostly focused on Grothendieck. It was talking about how you don't need problem solving skills like being good at IMO and instead there is new way of doing Mathematics.

    I suppose I'm one of the gullible person that believes in bourbakism. Originally I wanted to go into Analytical number theory, but I don't know if my number theory is strong enough. In a sense you probably only need analysis(through my complex analysis is a lot weaker than my real analysis) to do Analytical number theory, but even then books on RH I've read are saying that Algebraic geometry is the way to approach RH. In a sense if I was going to work towards something in life it would be RH even through I doubt will ever prove it. So in a strong way I don't see how I could possible avoid category theory if I want to do Mathematics.
  21. Aug 24, 2011 #20
    Just to verify, this means that you have no trouble at all working the exercises, correct? I'm asking because I don't consider a text to be "not too hard" unless I can easily see how to start every exercise and don't have much trouble working them out.

    There are certainly parts with number theory and more concrete sections, and showing things like the rational root theorem and why you can't square a circle and stuff about the Galois group of the roots of a polynomial etc.

    Again, just being able to read through Lang and feel like you know it is not sufficient; are you actually able to get through the exercises?

    You don't need problem solving skills if you're a pure theorist, but doing mathematics without problem solving skills is like working with one hand behind your back. Of course, you had better have strong theorem proving skills either way.

    Probably not if you actually hate number theory, then again, elementary number theory really isn't that interesting; I did well in my course, but I really didn't care much for it (except for playing with geometric numbers, I remember once they were introduced I spent an afternoon deriving the formula in general for n-gonal numbers, that was kind of fun; lots of ways to generalize on top of that as well) find algebraic number theory much more interesting.

    My question is :how do you know you've actually got the raw skills needed to do this stuff? It sounds like you are making things difficult on yourself because of some silly romantic notion that you could do it the way Grothendiek did, when in reality there are fields medalists who could not have done mathematics the way Grothendiek did. Grothendiek was extremely unusual.
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