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I am currently a junior in a completely unknown liberal arts college/mathematics department. So far, I have take two courses in Abstract Algebra and group theory, one in linear algebra, currently taking Real Analysis. Next semester, I will most probably be taking Complex Analysis,Rings and Fields theory, Introductory Topology and Introductory Number Theory at a nearby larger school. Besides these, of course, I have calculus sequence, probability and statistics, graph theory and Combinatorics under the belt.

So far, I find Algebra extremely fascinating (I will be taking my third course in Abstract Algebra next semester) and its application to number theory (I have self-learned a little about Galois Extensions but not significantly much). Ideally, I would like to go to a nice enough program where I can learn and do Algebra and Number Theory. However, I do not have any idea as to how hard it is to get into a school with such programs. I searched over the internet and could only find like topmost school that offer Number Theory. I do not think my profile is competitive enough to get into any of such programs. I have not done any summer research yet, except one that I did at my home institution (which bordered more on engineering than mathematics). I have gotten a scholarship at my home institution, which is like the largest one here, but it is not something huge as seen by an outsider. My teachers are not working mathematicians at all. They completed their PhD some 20 years ago, and stopped doing any mathematics except teaching. So I don't know how much their recommendations will count. I do not have anything Earth-shattering to show for in my profile either.

How likely would it be for me to get into a program where I can have an option of doing Number Theory and/or Algebra? I would also appreciate if you could tell me about such programs (except ones that are already listed in US NEWS AND WORLD REPORT). Any other general advice would be highly appreciated too. Thank you in advance.

HumbleStudent
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  • Outside study always helps, and I would imagine it becomes necessary when your school can't offer you what you need. – Matt Samuel Oct 03 '15 at 07:06
  • @HumbleStudent If you don't mind, would you be able to provide any information regarding your question now, as you appear to be still doing Number Theory as per your recent MSE posts? I too find myself in a similar situation as you. – user600016 Jan 19 '22 at 14:00

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If you've already taken a couple courses in Abstract Algebra, try reading dummit and foote and do the hard problems. As far as number theory books go, I'm not sure since I have not taken any Number Theory at my University.

I used to look at the syllabi and homeworks for classes at top schools and also found them very difficult. Even at those schools, only the top math majors make it through Analysis and Topology so don't be discouraged. If possible try getting an independent study.

Yunus Syed
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  • Most of the mathematics classes I have taken are in independent studies. I stopped taking classes in class settings, because all they did was frustrate me with their triviality and slow pace. I took all of my algebra, linear algebra and Combinatorics in directed studies. I am currently taking Analysis in directed studies too. This is the reason I have been able to cover most of Linear Algebra in just one semester, with good bit of theory in Vector Spaces. – HumbleStudent Oct 03 '15 at 06:31
  • What book are you using for analysis? I feel your frustration. Sitting in analysis, algebra and linear are really boring since I already studied them prior to entering the university. Luckily, my topology class is at the same level as the top schools so I been enjoying my time in that class. – Yunus Syed Oct 03 '15 at 06:32
  • I am using both Abbot's and Bartle's book with the teacher, and then doing problems from baby Rudin. – HumbleStudent Oct 03 '15 at 06:34
  • I studied straight from Rudin when i studied analysis. Its a much better book for learning how to read math. – Yunus Syed Oct 03 '15 at 06:35
  • I am taking it with a senior, and she won't be comfortable with Rudin. Hence, I do Rudin on my own. Plus, being in a very strict LAC like mine, where we have to take 20 courses outside Mathematics, it becomes difficult to compete in world of Mathematics. – HumbleStudent Oct 03 '15 at 06:39
  • What year are you? – Yunus Syed Oct 04 '15 at 13:48
  • ^^First sentence --> JUNIOR – HumbleStudent Oct 04 '15 at 16:12
  • Oh woops didn't see that. If you were a sophomore I would suggest transferring. – Yunus Syed Oct 04 '15 at 16:14