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I've just finished my undergraduate degree at an average uni in the UK. Clearly the content will not be as in depth or rigorous as some of the higher ranked universities. I intend (well, hope!) to continue my education through a PhD or a doctoral program (which include an MPhil degree) in some area of applied maths.

My question is, is there a standard toolbox of skills one would expect a maths graduate to have to seriously consider giving them a role. I am a little worried that despite doing well in my undergraduate, I could feel out of my depth in an interview, so would really like to get on top of any areas people would consider standard. For instance, I've never studied Laplace or Fourier Transforms.

Topics I have covered include: multivariable calculus; basic complex analysis; fluid dynamics; numerical analysis; basic groups; networks; nonlinear dynamical systems; basic statistics; programming in Maple; financial maths and some standard applications like Fourier series etc.

Sorry if this is a bit subjective, but I've tried to narrow it down as much as possible and I think the core advice will probably be the same. Many thanks for any suggestions.

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  • $\begingroup$ This is a perfect post. I am also starting graduate work and have the same skills....good luck to you and your studies! $\endgroup$ – Eleven-Eleven May 28 '14 at 23:07
  • $\begingroup$ @Eleven-Eleven Good luck to yourself too! $\endgroup$ – Mike Miller May 28 '14 at 23:08
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    $\begingroup$ You seem to have studied some kind of applied/financial mathematics as abstract, and non-so-abstract, stuff shines by its abscence: linear algebra, abstract algebra, Galois theory and fields extensions, number theory, topology and etc. $\endgroup$ – DonAntonio May 28 '14 at 23:36
  • $\begingroup$ @DonAntonio Also covered linear algebra, but the rest (apart from basic groups) I've not even touched upon. Best get crackin'! $\endgroup$ – Mike Miller May 29 '14 at 8:01
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As a current graduate student in the US, one suggestion I would give is BREADTH. I find breadth to be extremely important to a starting grad student. You will need to pass qualifiers in multiple subjects (analysis, topology, algebra, differential equations are the common ones). You seem to have good experience in applied maths and analysis. I think that especially if you want to do doctoral work, breadth will be the single most important "tool" you can obtain. This allows you to have a variety of advisers to choose from, as well as the ability to speak intelligently about "math" in general.

Grad schools accept you in part based on your potential, not just on your previous production. Breadth is something you can continue to develop as you go through grad school.

I did not study Fourier transforms until a starting grad course in analysis (although, my research and whatnot is entirely in algebra, so such a subject was not my focus as an undergrad).

Overall, do not worry about what you do not know. I had a really awful feeling about being an imposter my entire first semester as a grad student. I felt like everyone knew more than me. But now I am progressing along in the degree and finding that I know just as much as the next guy.

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  • $\begingroup$ Thank you, that is an excellent answer. $\endgroup$ – Mike Miller May 29 '14 at 8:01

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