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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/
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/