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Hello, I've come to seek opinions on what mathematics I should study to become a good theorectical physicist.

Some background on myself: I started out my university career (I'm a 2nd year student) interested in both physics and computer science. During my 1st semester I began to become interested in mathematics, and have since fostered a growing love for the subject. However taking 3 majors would be ridiculous, so I decieded on a math minor and to supplement that with independent study. To that end I've begun taking out mathematics books from my university library (with intentions of studying a single topic a semester, kinda like an extra course). The mathematics I'm planning to start with will be mathematics relavent to theoretcial physics, but time permitting I'd also like to study some pure mathematics as well. To that end I've devised a list of math subjects I would like to become familar with:

At the rate of one topic a semester (including summer) this will take me up to the completion of my undergraduate degree. My hope is to have a comprehensive mathematical background for graduate school

Does anybody have any suggestions on what other topics I should cover, or what order I should study them in? Has anyone attempted anything like this before and if so how did it work out? Have I bitten off more than I can chew? I have a feeling I should devote some time to studying PDE's more comprehensively but am unsure what topic I should drop, if anything.

Edit: Oh yeah I guess I should mention that my university offers 2 courses in mathematical physics that I entend to take when I meet the prerequisites.

...Oddly there isn't a Mathematical Physics I

Some background on myself: I started out my university career (I'm a 2nd year student) interested in both physics and computer science. During my 1st semester I began to become interested in mathematics, and have since fostered a growing love for the subject. However taking 3 majors would be ridiculous, so I decieded on a math minor and to supplement that with independent study. To that end I've begun taking out mathematics books from my university library (with intentions of studying a single topic a semester, kinda like an extra course). The mathematics I'm planning to start with will be mathematics relavent to theoretcial physics, but time permitting I'd also like to study some pure mathematics as well. To that end I've devised a list of math subjects I would like to become familar with:

**Math topics I wish to cover independently (Chronologically Ordered)**- Linear Algebra (currently studying)
- Non-Euclidian Geometry
- Differential Geometry
- Tenser Calculus
- Real Analysis
- Complex Analysis
- Group Theory
- Manifolds
- Algebraic Topology

At the rate of one topic a semester (including summer) this will take me up to the completion of my undergraduate degree. My hope is to have a comprehensive mathematical background for graduate school

**Topics covered through mathematics minor**- 3 courses in Calculus (Done)
- Linear Algebra (Done, although it wasn't comprehensive enough for me, thus I'm studying it independently)
- Basic statistics (In progress)
- Vector Calculus
- Discrete Math
- Ordinary Differential Equations (Done)

Does anybody have any suggestions on what other topics I should cover, or what order I should study them in? Has anyone attempted anything like this before and if so how did it work out? Have I bitten off more than I can chew? I have a feeling I should devote some time to studying PDE's more comprehensively but am unsure what topic I should drop, if anything.

Edit: Oh yeah I guess I should mention that my university offers 2 courses in mathematical physics that I entend to take when I meet the prerequisites.

**Mathematical Physics II**: examines the functions of a complex variable; residue calculus. Introduction to Cartesian tensor analysis. Matrix eigenvalues and eigenvectors. Diagonalization of tensors. Matrix formulation of quantum mechanics. Quantum mechanical spin. Vector differential operators in curvilinear coordinate systems. Partial differential equations of Mathematical Physics and boundary value problems; derivation of the classical equations, separation of variables; Helmholtz equation in spherical polar coordinates.**Mathematical Physics III:**covers further topics on partial differential equations of Mathematical Physics and boundary value problems; Sturm-Liouville theory, Fourier series, generalized Fourier series, introduction to the theory of distributions, Dirac delta function, Green's functions, Bessel functions, ' functions, Legendre functions, spherical harmonics....Oddly there isn't a Mathematical Physics I

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