Courses taken

Forum for the GRE subject test in mathematics.
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anything
Posts: 1
Joined: Mon Mar 02, 2020 5:11 pm

Courses taken

Post by anything » Sun Jun 06, 2021 6:17 am

Hey,

I am applying for Pure math PhD for fall 2022. I was just wondering if any of you guys can share the math courses you all have taken. I was a bit concerned about what are the courses that usually people seem to have done to show for PhD applications.

Jmr324
Posts: 47
Joined: Thu May 16, 2019 11:57 pm

Re: Courses taken

Post by Jmr324 » Sun Jun 06, 2021 12:48 pm

Here are the math (and cs theory) courses I have taken including what I am taking this Fall semester:
calculus1-3
diff eq
intro to proof writing class
linear algebra 1&2 (one is computational and two is proof-based using Friedberg et al)
analysis 1&2
abstract-algebra 1&2
graph-theory
combinatorics
graduate-level graph theory 1&2
theory of computation
graduate-level algorithms class
graduate-level computational complexity
graduate-level analysis
also some independent studies

PajamaSam
Posts: 8
Joined: Sun Dec 27, 2020 8:51 pm

Re: Courses taken

Post by PajamaSam » Sun Jun 06, 2021 2:08 pm

My undergrad courses were:

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Calc. 1-3
Differential Equations
Multivariable Calc. 1-2
Linear Algebra 1-2 (Undergraduate)
Intro. Proofs
Elementary Real Analysis 1-2 (Undergraduate)
Complex Analysis 1-2 (Mixed Grad/Undergrad)
Fourier Analysis 1-2 (Mixed Grad/Undergrad)
Intro. Real Analysis 1-3 (Mixed Grad/Undergrad)
Intro. Topology 1-2 (Mixed Grad/Undergrad)
Intro. to Manifolds (Mixed Grad/Undergrad)
Intro. Differential Geometry (Mixed Grad/Undergrad)
Abstract Linear Algebra (Mixed Grad/Undergrad)
Intro. Abstract Algebra 1-3 (Mixed Grad/Undergrad)
Abstract Algebra 1-2 (Graduate)

---

For reference, I got into a couple schools for Fall 2021, one of which was one of my higher choices (and I'm going there.)

A word of advice: if you wish to apply for pure math - take pure math courses! I think I was rejected by some places because I was missing some important elements of coursework at the time of applying (topology, graduate algebra) since I didn't take those courses until this year (my senior year). It's just a fact that applied math courses (undergrad complex analysis, fourier analysis, physics related courses) are NOT valued very much by committees (when applying for pure math.) Of course this is not true everywhere: some places it is a huge plus to have a wide range of courses and applied math and physics and stuff. But in general, I've received feedback letting me know that it really doesn't help much. But if you are interested in them of course you should take those. Essentially, all I'm saying is make sure youre focusing on pure math and taking a lot of it.

Good luck!

emmynoether126
Posts: 9
Joined: Mon Jan 04, 2021 1:54 pm

Re: Courses taken

Post by emmynoether126 » Sun Jun 06, 2021 10:01 pm

Here are the math and stat courses I have taken.

Intro Level:
Calc 1-3, Discrete Math, Linear Algebra, Differential Equations, Intro Geometry, Technology for Math (aimed at math education majors)

Pure:
Real Analysis 1-2, Modern Algebra 1-2 (only 1 reflected at time of applying), Topology, Number Theory, Senior Seminar, Linear Algebra (graduate)

Applied:
Applications of Math, Partial Differential Equations, Complex Analysis (computational and some proofs, no applications), Numerical Analysis (graduate)

Statistics:
Stat 1-2, Probability, Mathematical Statistics (like Probability 2), Regression, Statistical Learning

Notes:
For reference, I got into 2 of the 5 schools I applied to, one of which was my top choice :D (in the 30s on US News rankings). My school allows undergrads a max of 2 grad classes. I took all the undergrad math courses except for 2 aimed at math education majors. My independent studies are not specifically mentioned on my transcript.

I agree with PajamaSam that if your goal is pure math, take pure math courses. Some schools have stricter coursework requirements than others, so you may want to look into those. Generally speaking, your coursework is not the only aspect of your application. If you feel you are lacking in some aspect of coursework (e.g. not enough relevant courses), you may want to address this in your statement of purpose or explain how you will nonetheless be prepared for grad courses (perhaps through research or some other means).

aeiou12345
Posts: 12
Joined: Sat Mar 06, 2021 1:31 pm

Re: Courses taken

Post by aeiou12345 » Mon Jun 07, 2021 2:43 pm

Not applying to pure math programs (my passion is OR, hence the large number of applied math courses), but thought I’d chime in with my undergrad courses so far (I will be applying to grad programs this fall):
Linear Algebra
Discrete Math
Multivariable Calc
Probability
Linear Optimization
Analysis 1/2 (full course)
Scientific Computing
Abstract Algebra 1/2 (full course)
Graduate Analysis 1/2
Graduate Topology
Number Theory
Advanced Topics in Applied Mathematics - Numerical Methods in Linear Algebra
Math Modeling/Simulation
Differential Equations
Graduate Complex Analysis



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