Courses Which math course should I take (as a physics major)?

[babylonsashes]

I am entering my third year as a physics major, I have space for around 2 math courses this term and I plan on taking 2 from these courses:

- Introduction to Analysis II
- Functional Analysis
- Introduction to the Calculus of Variations
- Algebra I

I am pretty sure I will take Analysis II. I'm confused about the others though. A graduating undergrad student recommended Calculus of Variations but I was leaning towards functional analysis. Which courses would be the most useful from a theoretical physics standpoint?

 

[berkeman]

Welcome to PF.

- Algebra I

Is that a typo or incomplete course title?

 

[fresh_42]

I am entering my third year as a physics major, I have space for around 2 math courses this term and I plan on taking 2 from these courses:

- Introduction to Analysis II
- Functional Analysis
- Introduction to the Calculus of Variations
- Algebra I

I am pretty sure I will take Analysis II. I'm confused about the others though. A graduating undergrad student recommended Calculus of Variations but I was leaning towards functional analysis. Which courses would be the most useful from a theoretical physics standpoint?

The first 3 are all reasonable and you will need them sooner or later if you have contact with QM. However, Ana 2 can be viewed as a precondition for functional analysis and variation of calculus.

 

[babylonsashes]

Welcome to PF. Is that a typo or incomplete course title?

Thank you!

It's the complete title. The "I" is a roman 1. Like the first course in abstract algebra.

 

[babylonsashes]

The first 3 are all reasonable and you will need them sooner or later if you have contact with QM. However, Ana 2 can be viewed as a precondition for functional analysis and variation of calculus.

Hmm, I think I will end up taking Analysis 2 and Calculus of Variations then. It has pre req of Analysis I and Intro to Differential Equations. Functional Analysis needs Analysis 2 but I was thinking that I would get it waived.

Thank you

 

[fresh_42]

Functional Analysis needs Analysis 2 but I was thinking that I would get it waived.

Here is a brief walkthrough of the fundamentals of functional analysis. No substitution for a book or a course, but a collection of the basic definitions and theorems (2 parts):
https://www.physicsforums.com/insights/hilbert-spaces-relatives/

 

[romsofia]

From an ideal theoretical standpoint, Analysis II (if it's just reals...) is "useless" compared to functional analysis and calculus of variations.

However, you said it's a pre-req for functional, so looks like you should take it. Def try to take functional analysis before you graduate if you can. You will be have more routes available to you in graduate school (some mathematical physicists like to hide in the theoretical world!)