# Courses Suggestions for Fall math elective courses?

1. Jun 19, 2012

### deskswirl

I am a senior physics major and I have several electives (up to 2) to fill with math courses this Fall. I have previously taken:

Calculus 1-3 (Stewart)
Ordinary Differential Equations (Edwards and Penny)
Partial Differential Equations (Haberman)
Matrix Algebra
Parallel Processing

I am also required to take Mathematical Methods for Physicists and Engineers ( Matthews and Walker) in the Spring.

From the list below please tell me your likes or dislikes of the courses (if you have taken them) and how they contributed to your further studies (I am planning on graduate school in physics). Thanks for your time!

Possible Courses:

Probability and Statistics I - probability axioms and properties; conditional probability and independence; counting techniques; and discrete, continues, univariate, and multivariate random variables

Linear Algebra - theory of real vector spaces and linear transformations. Topics include vector spaces, inner product, norm, distance, subspaces, spanning sets, linear dependence and independence, bases, dimension, linear systems, coordinates, linear transformations, kernel, image, isomorphisms, inverse linear transformations, matrix representations of linear transformations, similarity, direct sums, and canonical forms.

Point Set Topology - open and closed sets, interior, closure, boundary, neighborhoods, continuous functions, separation and subspaces. Additional topics will be selected from compactness, connectedness and continua. (This has a prerequisite of Advanced Analysis but I spoke to the professor and he said not to worry about it. )

Numerical Analysis - Topics will be selected from error analysis, solving algebraic equations, interpolation, numerical differentiation and integration, methods for solving systems of equations, approximation theory, and initial value problems of ordinary differential equations.

Discrete Mathematics - Techniques and tools of reasoning, decision making and combinational problem solving. Topics include sets and logic, combinations, probability, relations and functions, Boolean properties and graph theory.

Note:
I will also be taking:
Intermediate Mechanics (Fowles & Cassidy)
Intermediate EM (Griffiths)
Medical Physics I
and possibly Statistical Thermodynamics (Callen ?)

2. Jun 20, 2012

### electroweak

If you do not already know linear algebra, you should take the course. It is useful for a lot of physics, most notably quantum mechanics where it is absolutely indispensable.

Point-set topology is a good place to start if you plan on getting into certain types of theory like string theory, but most physicists don't need to think about topology. Same and to a greater extent with discrete math.

Numerical analysis sounds like a good course to take if you plan on getting into experimental or (especially) computational physics. But this isn't what I do, so I'll let someone else make a recommendation here.

Basic probability and statistics can't hurt since these ideas are somewhat fundamental to science.

3. Jun 20, 2012

### micromass

Staff Emeritus
You say you're wanting to go to grad school in physics. Can you be somewhat more specific?? What kind of physics are you considering. The answer will depend on that.
For example, if you're going into quantum mechanics, then you absolutely need to take linear algebra. If you're interested in general relativity, then topology might be helpful. Etc.

4. Jun 20, 2012

### chiro

My recommendation would be 1) Linear algebra and 2) Either probability/statistics or numerical analysis. I think both in 2) are really valuable for physics, but as electroweak pointed out, you should really take linear algebra if you haven't done already.

5. Jun 20, 2012

### deskswirl

My experience with linear algebra is that I think I know what an operator is and that it corresponds to taking a measurement or change of state (vaguely, I have take a intro Quantum mechanics course last fall) so not very deep at all. So I will take that course.

I am leaning toward something related to quantum mechanics, experimental or computational (molecular/atomic/nuclear or possibly medical physics).

Thanks for the replies!

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