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.
Courses taken
Re: Courses taken
Here are the math (and cs theory) courses I have taken including what I am taking this Fall semester:
calculus13
diff eq
intro to proof writing class
linear algebra 1&2 (one is computational and two is proofbased using Friedberg et al)
analysis 1&2
abstractalgebra 1&2
graphtheory
combinatorics
graduatelevel graph theory 1&2
theory of computation
graduatelevel algorithms class
graduatelevel computational complexity
graduatelevel analysis
also some independent studies
calculus13
diff eq
intro to proof writing class
linear algebra 1&2 (one is computational and two is proofbased using Friedberg et al)
analysis 1&2
abstractalgebra 1&2
graphtheory
combinatorics
graduatelevel graph theory 1&2
theory of computation
graduatelevel algorithms class
graduatelevel computational complexity
graduatelevel analysis
also some independent studies
Re: Courses taken
My undergrad courses were:

Calc. 13
Differential Equations
Multivariable Calc. 12
Linear Algebra 12 (Undergraduate)
Intro. Proofs
Elementary Real Analysis 12 (Undergraduate)
Complex Analysis 12 (Mixed Grad/Undergrad)
Fourier Analysis 12 (Mixed Grad/Undergrad)
Intro. Real Analysis 13 (Mixed Grad/Undergrad)
Intro. Topology 12 (Mixed Grad/Undergrad)
Intro. to Manifolds (Mixed Grad/Undergrad)
Intro. Differential Geometry (Mixed Grad/Undergrad)
Abstract Linear Algebra (Mixed Grad/Undergrad)
Intro. Abstract Algebra 13 (Mixed Grad/Undergrad)
Abstract Algebra 12 (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!

Calc. 13
Differential Equations
Multivariable Calc. 12
Linear Algebra 12 (Undergraduate)
Intro. Proofs
Elementary Real Analysis 12 (Undergraduate)
Complex Analysis 12 (Mixed Grad/Undergrad)
Fourier Analysis 12 (Mixed Grad/Undergrad)
Intro. Real Analysis 13 (Mixed Grad/Undergrad)
Intro. Topology 12 (Mixed Grad/Undergrad)
Intro. to Manifolds (Mixed Grad/Undergrad)
Intro. Differential Geometry (Mixed Grad/Undergrad)
Abstract Linear Algebra (Mixed Grad/Undergrad)
Intro. Abstract Algebra 13 (Mixed Grad/Undergrad)
Abstract Algebra 12 (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!

 Posts: 9
 Joined: Mon Jan 04, 2021 1:54 pm
Re: Courses taken
Here are the math and stat courses I have taken.
Intro Level:
Calc 13, Discrete Math, Linear Algebra, Differential Equations, Intro Geometry, Technology for Math (aimed at math education majors)
Pure:
Real Analysis 12, Modern Algebra 12 (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 12, 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 (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).
Intro Level:
Calc 13, Discrete Math, Linear Algebra, Differential Equations, Intro Geometry, Technology for Math (aimed at math education majors)
Pure:
Real Analysis 12, Modern Algebra 12 (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 12, 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 (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).

 Posts: 12
 Joined: Sat Mar 06, 2021 1:31 pm
Re: Courses taken
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
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