Advice for a chem major becoming more interested in physics

[Pauli'sPennies]

subjects like Solid state chemistry, QFT, QCD, general relativity, particle physics, etc look interesting to me and i really would like to master them at some point.

so far i have taken basic physics, calculus i-iii, introductory courses to ODE and PDE, pchem, and 2 introductory modern physics courses. the first modern physics course, which i signed up for on a whim, was really what introduced these subjects to me.

i am nearing the completion of a BS in chemistry (just a couple of labs and inorganic 2 to go, I am a transfer student so my schedule isn't like everyone elses) and need to take a 4000 level math course if i want a minor in math.

what courses do i need to take to prepare for graduate level courses in these subjects? would i be able to study these as a graduate student if i pursued a PhD in physical chemistry? also, what is a 4000 level math course that i could learn with the very limited preparation I've had? i never took linear algebra but have been able to get by without it where it was listed as a prerequisite


Here is a listing of 4000 level math courses offered by my school:

MATH 4315: Graph Theory with Applications
Cr. 3. (3-0). Prerequisite: MATH 3330 or MATH 3336. Introduction to basic concepts, results, methods, and applications of graph theory.

MATH 4320: Introduction to Stochastic Processes
Cr. 3. (3-0). Prerequisite: MATH 3338. Generating functions, discrete and continuous versions of Poisson and Markov processes, branching and renewal processes, introduction to stochastic calculus and diffusion.

4331;4332: Introduction to Real Analysis
Cr. 3 per semester. (3-0). Prerequisite: MATH 3334 or consent of instructor. Properties of continuous functions, partial differentiation, line integrals, improper integrals, infinite series, and Stieltjes integrals.

MATH 4333: Advanced Abstract Algebra
Cr. 3. (3-0). Prerequisites: MATH 3330 and consent of instructor. Direct products, Sylow theory, ideals, extensions of rings, factorization of ring elements, modules, and Galois theory.

MATH 4335;4336: Partial Differential Equations
Cr. 3 per semester. (3-0). Prerequisite: MATH 3331. Existence and uniqueness for Cauchy and Dirichlet problems; classification of equations; potential-theoretic methods; other topics at the discretion of the instructor.

MATH 4337: Topology
Cr. 3. (3-0). Prerequisite: MATH 3333 or MATH 3334 or consent of instructor. Metric spaces, completeness, general topological spaces, continuity, compactness, connectedness.

MATH 4340: Nonlinear Dynamics and Chaos
Cr. 3. (3-0). Prerequisite: MATH 3331 or consent of instructor. Dynamical systems associated with one-dimensional maps of the interval and the circle; elementary bifurcation theory; modeling of real phenomena.

MATH 4350;4351: Differential Geometry
Cr. 3 per semester. (3-0). Prerequisites: MATH 2433 and MATH 2331 (formerly 2431) or equivalent. Frenet frames, metric tensors, Christoffel symbols, Gaussian curvature, differential forms, moving frames, Euler characteristics, the Gauss-Bonnet theorem and the Euler-Poincare index theorem.

MATH 4355: Mathematics of Signal Representation
Cr. 3. (3-0). Prerequisites: MATH 2433 and either MATH 2331 (formerly 2431) or MATH 3321. Fourier series of real-valued functions, the integral Fourier transform, time-invariant linear systems, band-limited and time-limited signals, filtering and its connection with Fourier inversion, Shannon's sampling theorem, discrete and fast Fourier transforms, relationship with signal processing.

MATH 4360: Integral Equations
Cr. 3. (3-0). Prerequisites: MATH 3331 and MATH 3334. Relation to differential equations; Fredholm, Hilbert-Schmidt, and Volterra type equations; special devices and approximation methods.

MATH 4362: Theory of Ordinary Differential Equations
Cr. 3. (3-0). Prerequisites: MATH 3331 and MATH 3334. Existence, uniqueness, and continuity of solutions of single equations and systems of equations; other topics at the discretion of the instructor.

MATH 4364;4365: Numerical Analysis
Cr. 3 per semester. (3-0). Prerequisites: MATH 2331 (formerly 2431), MATH 3331; COSC 1301 or COSC 2101 or equivalent; or consent of instructor. Topics selected from numerical linear algebra, approximation of functions, numerical integration and differentiation, interpolation, approximate solutions of ordinary and partial differential equations, Fourier methods, optimization.

MATH 4370: Mathematics of Financial Derivatives
Cr. 3. (3-0). Prerequisites: MATH 2433 and either MATH 3338 or MATH 3341. Stochastic processes for modeling the dynamics of returns of financial instruments and commodities. Use of Ito's calculus and Black-Scholes Model to value contingent claims and real options in capital budgeting.

MATH 4377: Advanced Linear Algebra I
Cr. 3. (3-0). Prerequisites: MATH 2331 and a minimum of three semester hours of 3000-level mathematics. Linear systems of equations, matrices, determinants, vector spaces and linear transformations, eigenvalues and eigenvectors.

4378: Advanced Linear Algebra II
Cr. 3. (3-0). Prerequisite: MATH 4377. Similarity of matrices, diagonalization, hermitian and positive definite matrices, normal matrices, and canonical forms, with applications.

MATH 4380: A Mathematical Introduction to Options
Cr. 3. (3-0). Prerequisites: MATH 2433 and MATH 3338. Arbitrage-free pricing, stock price dynamics, call-put parity, Black-Scholes formula, hedging, pricing of European and American options.

MATH 4383: Number Theory
Cr. 3. (3-0). Prerequisite: MATH 3330 or consent of instructor. Perfect numbers, quadratic reciprocity, quadratic residues, algebraic numbers, and continued fractions.

MATH 4385;4386: Mathematical Statistics
Cr. 3 per semester. (3-0). Prerequisite: MATH 3339 or equivalent. Linear models-estimation, testing and application to designs of experiments, nonparametric statistical models.

MATH 4389: Survey of Undergraduate Mathematics
Cr. 3. (3-0). Prerequisites: MATH 3330, 3331, 3333, and three hours of 4000-level Mathematics. A review of some of the most important topics in the undergraduate mathematics curriculum.

some courses will list as a prerequisite for example MATH 3334: Advanced Multivariable Calculus which in turn has as a prerequisite MATH 3333: Intermediate Analysis, neither of which have i taken.

is it foolish to expect to be able to take a 4000 course without more of a foundation in math?

 

[Howers]

With a name like yours I don't think anyone will take you seriously here...


Anyway, linear algebra is an absolute must. Without it, studying modern physics will be like learning calc without knowing algebra. Then, focus on complex and real analysis. Real analysis isn't really needed, but it will open the door to differential geometry which is. Differential geometry you could probably pick up on your own, and will help you understand relativity. And you will definitely need vector calc.

As for physics, you should learn 2 terms of electrogmagnetism. Advanced classical mechanics too. Chemists usually do a good job of teaching you thermo/stat mech, so you are set in that department. I can't say the same about quantum mechanics. It varies from school to school, and if you got through it without linear algebra I have a feeling what your quantum course was like. So look into some quantum mechanics books, unless you are doing your advanced one now. This I believe would be the bare minimum.

And yes, doing advanced math without linear algebra (and other pre-reqs) will slaughter you. Especially since you didn't yet taste what rigorous math is. Expect your gpa to drop by 1-2 points.

 

[Mene]

First of all, congratulations on your interest in physics and your progress in your chemistry degree! It's great to see someone with a strong passion for science and a desire to learn more. As a scientist myself, I can understand your excitement about delving into new subjects and mastering them.

To answer your question, I would say that it is not foolish to expect to be able to take a 4000 level math course with your current foundation. However, it may require some extra effort on your part to catch up on the prerequisite material. It is important to have a strong foundation in math in order to understand and excel in physics, especially in subjects like solid state chemistry, QFT, QCD, general relativity, and particle physics. These areas of physics require a deep understanding of mathematical concepts and techniques.

Based on the courses listed, I would recommend taking MATH 3333: Intermediate Analysis and MATH 3334: Advanced Multivariable Calculus before attempting any of the other 4000 level math courses. These courses will provide you with the necessary foundation for the other courses listed. It may also be helpful to review your calculus and linear algebra skills, as they are essential for understanding many topics in physics.

In terms of pursuing a PhD in physical chemistry, it is definitely possible to study the subjects you mentioned as a graduate student. However, it may require some additional coursework and self-study to catch up on the necessary math skills. It would also be helpful to speak with your academic advisor or a professor in the physics department about specific courses or areas of math that would be most beneficial for your research interests.

Overall, my advice would be to start with the prerequisites and then gradually work your way up to the more advanced courses. Don't be discouraged if it takes some extra time and effort to get to where you want to be. Remember, the journey to mastery is just as important as the destination. Good luck in your studies!