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Rising Math/Physics double major sophomore here. Math background: Calc I-III, Diff Eq and Elem Linear Algebra. Right now I'm leaning more towards Math or Theoretical Physics as something I'd like to do in graduate school but I want to focus more on the math for now. I was wondering which classes I should take this upcoming year if I want to do an REU in Math the following summer? Here are the some of the classes which my school is offering next semester (fall), and I think would be relevant to the REU:

Complex Variables (offered only by the applied math department in the fall)

Advanced Calculus and Applied Mathematics

Introduction to Real Analysis (conflicts with Advanced Calc, confused about which to take out of these two, Advanced Calc is part of the physics major while Analysis is obviously a very important one for a math major)

Advanced Linear Algebra (almost certain about taking this)

Intro to Differential Geometry

General Topology (conflicts with a physics course required for the physics major).

Here's most likely what they'll be offering in the spring:

Complex Variables (in the regular math department)

Partial Differential Equations and Applied Mathematics

Introduction to Abstract Algebra

Number Theory

Intro to Geometry

Intro to Differential Geometry

Advanced Multivariate Calculus (maybe offered)

So out of these, which math classes should I be taking over the next two semesters which will give me a good chance to get admitted into an REU assuming all else goes well (I get good recs and grades are okay too)? Also note that along with the math, I'm gonna be taking 2-3 physics classes each semester too which might include labs as well. That might come in the way of me taking a good amount of math classes because of conflicts.

As of right now I don't know much about REUs so if someone could shed some light on how difficult it is to get one as a sophomore and which classes would be beneficial, that would be great.

Complex Variables (offered only by the applied math department in the fall)

Advanced Calculus and Applied Mathematics

Introduction to Real Analysis (conflicts with Advanced Calc, confused about which to take out of these two, Advanced Calc is part of the physics major while Analysis is obviously a very important one for a math major)

Advanced Linear Algebra (almost certain about taking this)

Intro to Differential Geometry

General Topology (conflicts with a physics course required for the physics major).

Here's most likely what they'll be offering in the spring:

Complex Variables (in the regular math department)

Partial Differential Equations and Applied Mathematics

Introduction to Abstract Algebra

Number Theory

Intro to Geometry

Intro to Differential Geometry

Advanced Multivariate Calculus (maybe offered)

So out of these, which math classes should I be taking over the next two semesters which will give me a good chance to get admitted into an REU assuming all else goes well (I get good recs and grades are okay too)? Also note that along with the math, I'm gonna be taking 2-3 physics classes each semester too which might include labs as well. That might come in the way of me taking a good amount of math classes because of conflicts.

As of right now I don't know much about REUs so if someone could shed some light on how difficult it is to get one as a sophomore and which classes would be beneficial, that would be great.

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