# Math classes for a physics major

1. Jan 9, 2009

Hi, I'm a high school senior that's just been admitted to Caltech. They sent me their course catalog in the mail, and I've been looking over it this week. I want to major in physics, and someday study elementary particles, gravitation, and string theory. What math should I take?

Caltech requires five terms of math: Ma 1abc (Calculus of One and Several Variables and Linear Algebra), and Ma 2ab (Ordinary Differential Equations, Probability, and Statistics). Which other courses should I take? The physics department recommends Ma 5 and Ma 108, as well as ACM 95 and ACM 101. Which of these would have the most applications to physics and what I want to study?

(Everything listed in parentheses is a prerequisite.)

ACM 95 – Introductory Methods of Applied Mathematics
ACM 101 – Methods of Applied Mathematics I
ACM 106 – Introductory Methods of Computational Mathematics (ACM 95)
ACM 142 – Ordinary and Partial Differential Equations (Ma 108, Ma 109)
ACM 201 – Partial Differential Equations (ACM 101)
ACM 210 – Numerical Methods for PDEs (ACM 106)
Ma 5 – Introduction to Abstract Algebra
Ma 91 – Homological Algebra (Ma 5)
Ma 108 – Classical Analysis (Ma 2)
Ma 109 – Introduction to Geometry and Topology
Ma 110 – Analysis I (Ma 108)
Ma 111 – Analysis II (Ma 110)
Ma 120 – Abstract Algebra (Ma 5)
Ma 123 – Classification of Simple Lie Algebras (Ma 5)
Ma 130 – Algebraic Geometry (Ma 120, or Ma 5 plus additional reading)
Ma 131 – Algebraic Geometry of Curves (Ma 5, Ma 108, Ma 109)
Ma 135 – Arithmetic Geometry (Ma 130)
Ma 140 – Functional Analysis (Ma 110)
Ma 145 – Introduction to Unitary Group Representations
Ma 151 – Algebraic and Differential Topology (Ma 108)
Ma 157 – Riemannian Geometry (Ma 151)

These are the classes that interested me the most. I know that geometry and topology are important to physics, but I’m not sure which of these would be most useful – I barely started learning differential geometry this winter break for general relativity.

Any help? Oh, and course descriptions are on Caltech’s course catalog, which is at http://pr.caltech.edu/catalog/

2. Jan 10, 2009

### qntty

Obviously you'll want differential equations. For theoretical physics abstract algebra (+ lie algebra) has application.

3. Jan 10, 2009

### mal4mac

Decide what physics courses you want to take and ask the lecturers what the pre-requisites are, together with book & course recommendations.

4. Jan 10, 2009

### Staff: Mentor

By the time you arrive at Caltech (probably even before then), they will probably assign you a faculty member as academic advisor. Someone "on the scene" is best suited to tell you which math courses are useful for their physics courses, or for the research fields that they're in.

You don't have to plan your whole four years before you even get there!

5. Jan 11, 2009

### ice109

every single one of em on down from acm 142

you're lucky to have so many math classes available to you. avail yourself of them.