I am an undergrad junior at a top 60 institution (big state school in the United States) majoring in Pure Math. Course selection for Spring 2020 is coming around, and I want to know which courses to take for the strongest graduate school applications.

I'm currently planning on going into either combinatorics, graph theory, or theoretical CS. I have done internships in Software Engineering and Data Science (Machine Learning). My GPA is a 3.75 and the courses I have taken/am planning on taken are the following:

  • Calculus I - III
  • Linear Algebra I and II
  • Differential Equations
  • Advanced Calculus I (Real Analysis)
  • Mathematical Statistics
  • Discrete Math I and II (II is graph theory)
  • Numerical Analysis I and II
  • Abstract Algebra I and II
  • Programming I, II, Data Structures, Computer Architecture,Theory of Computation, Analysis of Algorithms
  • Topology I
  • Complex Analysis

Classes I might take if they look better for graduate school:

  • Advanced Calc II
  • Number Theory
  • Mathematical Logic

Along with these courses, I have some interdisciplinary research in neuroscience under my belt, but I plan on doing research with a math professor next semester.

Will my chances of getting into a good graduate school (top 60) be affected heavily if I don't have a full year of Real Analysis? Also, would I be well suited for a PhD in computer science (TCS)?

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    This is not really an appropriate question for academia.stackexchange, since it depends so much on the particular details of your transcript and your interests. – Brian Borchers Sep 30 '19 at 15:31
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    You might want to mention the country in question. – Tommi Sep 30 '19 at 17:13
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    Related: academia.stackexchange.com/q/45476/101 – Mark Meckes Sep 30 '19 at 19:50
  • In which country do you want to study? – user114568 Sep 30 '19 at 20:15
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    "Advanced calculus" usually means something different from a standard undergraduate real analysis course. – Elizabeth Henning Sep 30 '19 at 20:41

It's hard to say. Your background sounds strong. Your interests are more to the applied side of pure or the pure side of applied. Really, a bit more towards applied than pure from my impression (e.g. CS interest).

I don't think you could go wrong taking another stats class (applied or theoretical, time series, whatever) or an operations research class. (Not on your list, but a guess.)

If you restrict to choosing from the list, consider number theory. Kind of useless but a lot of fun. Don't grind something you don't like just to look good. I would pass on the second semester of theoretical calculus.

  • Thanks for the reply! Yeah I dont think I would enjoy taking analysis 2. Regarding my interests, I enjoy doing the applied stuff in industry (since I gotta make that money lol), but I love learning about pure in school. – SciFiFish Sep 30 '19 at 16:20
  • I think you're in a good spot. There's demand for the pure side of applied, which seems like what interests you. Hotelling or Hamming type of stuff. And you'll find MORE academic options (than pure pure), and you preserve flexibility to go into industry also. – guest Sep 30 '19 at 16:58

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