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

In summary, the conversation discusses a physics major's plan to take two math courses, including Introduction to Analysis II, Functional Analysis, Introduction to the Calculus of Variations, and Algebra I. The student is unsure which courses would be most useful from a theoretical physics standpoint and seeks advice from a graduating undergrad student. It is recommended that the student take Analysis II and Calculus of Variations, with the possibility of getting Functional Analysis waived. The conversation also includes a brief explanation of functional analysis and its importance for mathematical physics.
  • #1
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?
 
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  • #2
Welcome to PF. :smile:

babylonsashes said:
- Algebra I
Is that a typo or incomplete course title?
 
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  • #3
babylonsashes said:
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.
 
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  • #4
berkeman said:
Welcome to PF. :smile: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.
 
  • #5
fresh_42 said:
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
 
  • #6
babylonsashes said:
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/
 
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  • #7
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!)
 
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What math courses are required for a physics major?

Typically, a physics major will be required to take courses in calculus, linear algebra, and differential equations. Some programs may also require courses in multivariable calculus and/or complex analysis.

What is the difference between calculus and linear algebra?

Calculus is a branch of mathematics that deals with the study of change and is essential for understanding many physical phenomena. Linear algebra, on the other hand, is a branch of mathematics that deals with the study of vector spaces and linear transformations, which are crucial in solving systems of equations and understanding properties of matrices.

Should I take multivariable calculus or differential equations?

Both courses are important for a physics major, but it ultimately depends on your specific interests and career goals. Multivariable calculus is essential for understanding vector calculus and fields, while differential equations are used to model physical systems and phenomena.

What math course should I take first as a physics major?

Most physics programs will require you to take calculus as your first math course. It provides the foundation for many other mathematical concepts and is essential for understanding the principles of physics.

Are there any other math courses that would be beneficial for a physics major?

Yes, courses in statistics and probability can be useful for analyzing and interpreting data in physics experiments. Additionally, courses in computational methods and numerical analysis can be helpful for solving complex equations and performing simulations in physics research.

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