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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, im a transfer student so my schedule isnt 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 ive 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?