1
$\begingroup$

I am an undergraduate student at a university in Sweden who am studying my second semester of a three year undergraduate degree. I have always loved mathematics and had a few years between high school and university to realize that. I am therefore certain that I want to prep myself for advanced studies and try to go for a PhD after a master's degree. What I am wondering is - should I take the recommended programming courses and statistical courses or instead read advanced material such as galois theory or partial differential equations (both graduate level books)? I understand that both probability/statistics and programming can be very useful for mathematicians, but I am highly sceptical of how much of that information I will retain over the coming years of not having any follow-up courses in them and also if I simply cannot just learn them when I find out that I need them.

So I am reaching out to you, Stack Exchange community. Should I skip the probability/statistics and programming to do at a later date when/if I need it? Or should I bite the bullet and just take the courses?

We are talking about 5 courses that are: Numerical Analysis, probability 1, stochastic processes (or statistical analysis), programming 1 and programming 2. Together they make 5/4th of a semester. Comparatively, I could read 5 equal courses on a master's/grad introductory level (springer graduate texts).

Thank you in advance!

$\endgroup$

closed as off-topic by Stefan Mesken, Arnaud D., Cm7F7Bb, Gabriel Romon, user223391 Nov 18 '17 at 20:06

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "Seeking personal advice. Questions about choosing a course, academic program, career path, etc. are off-topic. Such questions should be directed to those employed by the institution in question, or other qualified individuals who know your specific circumstances." – Stefan Mesken, Arnaud D., Cm7F7Bb, Gabriel Romon, Community
If this question can be reworded to fit the rules in the help center, please edit the question.

  • 1
    $\begingroup$ This site is not intended for advice so theres a chance the question might be closed. That being said it is highly unlikely that if you have an aptitude for mathematics that any time spent on it will be "wasted" in any sense. It is rather the other way around, you should come into contact with advanced concepts as early in your development as possible. Your brain can do lots of "munching" on the material in the background. $\endgroup$ – mathreadler Nov 17 '17 at 11:36
  • $\begingroup$ @mathreadler oh I am sorry! I saw other threads similar to this one earlier and thought it was alright. Thank you very much for your input, it means a lot. $\endgroup$ – Alexander Lind Nov 17 '17 at 11:44
  • $\begingroup$ The more important is that you obtain your current studies successfully. After as second target is if in your university there exists an introductory course to research in mathematics, then take it. Finally the professors of the department of mathematics of your university are specialist in some fields, then you should to know what were the topics covered in some thesis and what are those fields and unsolved questions (that you prefer instead of others). Then you can take a decission of what books should read. Is a good idea topics with bridges to physics. And a book/video on creativity. $\endgroup$ – user243301 Dec 2 '17 at 21:15
0
$\begingroup$

Probability and statistics are subfields of mathematics. Obviously, if you are interested in that, you should take those courses (you can always cover more advances material later on and do a PhD in probability or statistics if you want).

If not, and if your university does not require that you take these courses, I don't think there is any mathematical requirement in probability, statistics or programming to understand Galois theory (to use your examples). However, depending on your background, other intermediate courses might be a good idea (group theory for Galois theory, and functional analysis before PDEs).

$\endgroup$
  • $\begingroup$ Thank you for a great answer! Would you say programming is not necessary for conducting research in modern areas of number theory/algebra/analysis? $\endgroup$ – Alexander Lind Nov 17 '17 at 11:26
  • 1
    $\begingroup$ It never hurts, but for example I never took a programming course (though I learned a bit by myself and occasionnally program a bit as part of my research). So no, it is not necessary $\endgroup$ – Glougloubarbaki Nov 17 '17 at 12:46
0
$\begingroup$

I'll disclose my bias as a probabilist, but: I think knowing some probability theory is useful for many other areas of math. Especially at the start, much of probability is just combinatorics and careful counting; these skills are useful in many other areas of mathematics. There were specific proof tactics that I became familiar with in my graduate probability study that later helped me when I had to take abstract algebra classes later. As you get into more advanced notions and measure theory, most of what you're doing is pretty transparently real analysis with a slightly modified perspective, and this may help impart useful intuition for analysis as well. Many other mathematical subjects can be "randomized" (e.g. random graphs, random simplicial complexes, random matrices) and it's useful to have some basic background on these before you start diving into them.

As a fun coda: after I survived those aforementioned algebra classes, I swore to myself that I would never again have to think carefully about abstract algebra. Just a few years later, I found myself wanting to write a paper about random walks that required me to recall a bunch of finite group theory that I'd forgotten. Math is more connected than you'd think!

Disclosure: I like statistics well enough, but it's hard for me to justify that subject in the same way. Programming is likely useful, though.

$\endgroup$
  • $\begingroup$ Someone on Reddit gave me the tip to skip the intro courses and read them on my own as the advanced mathematical courses will require more support from an instructor. What would you say about this strategy? $\endgroup$ – Alexander Lind Nov 18 '17 at 18:50
  • $\begingroup$ That could be fine. The utility of a class is definitely not universal; there are good instructors and bad, and there are people who can self-teach material effectively and people who can't. But I see no obvious red flags with that plan. $\endgroup$ – Aaron Montgomery Nov 18 '17 at 19:00
0
$\begingroup$

As a general principle, do what you love. Statistics is highly unlikely to be helpful in pursuing pure mathematical studies. However, knowing any amount of programming can only be helpful to you regardless of what you are studying. You don't need to take a programming course to get familiar with the basics, though. Go at your own pace with self study. I like combinatorics (the Art of Counting) a lot, and other parts of discrete mathematics. You may find it useful in your studies.

For your own information I strongly suggest reading at least parts of The Princeton Companion to Mathematics to get some overview of what Mathematics consists of. The importance of an area of study is what is important to you. Only you can be the judge of that. You can listen to and take advice, but only you can decide what you want to know and do. There is too much to learn so you have to be selective. You can still change your mind later if your needs develop on different lines.

$\endgroup$
  • $\begingroup$ The book stands on my shelf! Thank you, I felt that I should do what I am drawn towards but it is difficult to justify when I don't know the importance of what I am considering to skip. $\endgroup$ – Alexander Lind Nov 18 '17 at 12:00

Not the answer you're looking for? Browse other questions tagged or ask your own question.