Best math classes for a physics major?

In summary: Intermediate analysis is required for a math major, but "intro" analysis is not, which is why it's optional.
  • #1
ZeroZero2
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Best math classes for a physics major??

So I'm double majoring in physics and math, what are some beneficial math classes?

REQUIRED FOR A MATH MAJOR:
- Calculus I
- Calculus II
- Calculus III
- Linear Algebra
- Abstract Algebra
- Differential Equations
- Intermediate Analysis
- Vector Analysis (I could replace with either Complex Analysis or Advanced Multivariable Calculus, but Vector Analysis is required for a Physics major)
- Survey of Undergraduate Mathematics

ELECTIVES:
I need to take:
- Partial Differential Equations I & II (required for a Physics major)

So I need three more math classes, here are most of my options:

- Advanced Multivariable Calculus
- Discrete Mathematics
- Complex Analysis
- Intro to Higher Geometry
- Intro to Stochastic Processes
- Intro to Real Analysis I & II
- Graph Theory
- Advanced Abstract Algebra
- Topology
- Nonlinear Dynamics and Chaos
- Differential Geometry
- Mathematics of Signal Representation
- Integral Equations
- Theory of Ordinary Differential Equations
- Numeral Analysis
- Advanced Linear Algebra I & II
- Number Theory
- Mathematical Statistics I & II

I could also take a seminar or a "special topics" class

Any suggestions??

-
 
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  • #2


My personal choices would be:
Differential Geometry
Complex Analysis
Linear Algebra

If I were to take any more, I'd probably do numerical analysis and Integral equations. I'm still an undergraduate though, so I don't have any personal insight on what will help in grad school.
 
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  • #3


How is "intermediate" analysis mandatory but "intro" analysis optional? You need to know the basics of linear algebra really well, but I can't tell if the introductory course is enough, because I don't know what it covers. If you intend to work with mathematical physics in the future, you're probably going to have to study real and complex analysis, differential geometry, integration theory, topology, functional analysis and the theory of representations of Lie groups and Lie algebras.
 
  • #4


Fredrik said:
How is "intermediate" analysis mandatory but "intro" analysis optional? You need to know the basics of linear algebra really well, but I can't tell if the introductory course is enough, because I don't know what it covers. If you intend to work with mathematical physics in the future, you're probably going to have to study real and complex analysis, differential geometry, integration theory, topology, functional analysis and the theory of representations of Lie groups and Lie algebras.

Thanks!

The course description for Intermediate Analysis is "Properties of real number system, properties of continuous functions, and sequences of functions" and the only prereq is Calculus 3.

On the other hand, the description for Intro to Real Analysis is "Properties of continuous functions, partial differentiation, line integrals, improper integrals, infinite series, and Stieltjes integrals" and it's prereq is Advanced Multivariable Calculus (and a prerequisite for AMCalculus is Intermediate Analysis...)

The intro Linear Algebra course description is: "Solutions of systems of linear equations, matrices, vector spaces, linear transformations, similarity eigenvalues and eigenvectors."

and Advance Linear Algebra is: "Linear systems of equations, matrices, determinants, vector spaces and linear transformations, eigenvalues and eigenvectors.
Similarity of matrices, diagonalization, Hermitian and positive definite matrices, normal matrices, and canonical forms, with applications."
 
  • #5


Fredrik said:
How is "intermediate" analysis mandatory but "intro" analysis optional?
It is "intro to real analysis" which is definitely a higher level course than "intermediate analysis". When they just say analysis they basically mean calculus but when they say real analysis they mean something like Rudin.
 

1. What are the recommended math classes for a physics major?

The most commonly recommended math classes for a physics major are Calculus I, II, III, and Linear Algebra. These classes provide a strong foundation in mathematical concepts and techniques that are essential for understanding and solving complex physics problems.

2. Do I need to take all of the recommended math classes?

While it is highly recommended to take all of the recommended math classes, it ultimately depends on the requirements of your specific physics program. Some programs may have additional math requirements, so it is important to check with your advisor or program guidelines.

3. Can I substitute other math classes for the recommended ones?

It is possible to substitute certain math classes for the recommended ones, but it is important to ensure that the substitute class covers the same material and is accepted by your program. It is best to consult with your advisor before making any substitutions.

4. Are there any other math classes that may be beneficial for a physics major?

In addition to the recommended math classes, other classes that may be beneficial for a physics major include Differential Equations, Complex Analysis, and Partial Differential Equations. These classes can provide a deeper understanding of mathematical concepts and their applications in physics.

5. Is it necessary to have a strong math background to major in physics?

While a strong math background is highly beneficial for a physics major, it is not necessarily a requirement. Many physics programs offer introductory math courses for students who may not have a strong math background but are interested in pursuing physics. However, it is important to have a willingness to learn and develop mathematical skills in order to succeed in a physics major.

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