What additional math course should I take?

Shackleford · 01-19-2008, 01:56 PM

Physics major with math minor. I need one 4000-level math course. Which should I pick?

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;4378: Advanced Linear Algebra
Cr. 3 per semester. (3-0). Prerequisites: MATH 2331 (formerly 2431) and a minimum of three semester hours of 3000-level mathematics. Matrices, eigen-values, and canonical forms.

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.

auscguy · 01-20-2008, 02:42 AM

I would take ODE or PDE. I think they are pretty useful

Shackleford · 01-20-2008, 02:44 AM

Would the MATH 4370: Mathematics of Financial Derivatives course be useful if I wanted to do some finance work after graduation while I'm working on a master's?

Brendank · 01-20-2008, 12:26 PM

If it were my choice, I'd take PDE or maybe ODE or Nonlinear Dynamics

Shackleford · 01-21-2008, 09:23 PM

Someone suggested Intro. to Real Analysis.

Shackleford · 01-16-2009, 07:08 PM

I need one more math course to have a math minor. Anymore suggestions?

Tboonepickens · 01-17-2009, 12:25 AM

if you are into proofs, intro to real analysis is the way to go!

if you arent,

stay away

Lacero · 01-17-2009, 09:14 AM

PDE's (ODE's if you haven't), Numerical Analysis, Signals or Stochastic Processes.

Shackleford · 01-17-2009, 04:42 PM

The math courses I'll have under my belt by then will be: Cal I-III, Linear Algebra, Diff. Eq., Introduction to Partial Differential Equations, and Vector Analysis.

mrego · 01-17-2009, 09:28 PM

Do you have any leanings in Physics (astro-, optics, electronics...)? A few of these are obviously financial, a few abstract math, the rest have more applications like probability or modeling. So good arguments can be made for most depending on your direction and past classes.

Shackleford · 01-17-2009, 10:50 PM

Hey, that's a good way to help me choose. Well, I intend on going to graduate school, and I'll probably focus my studies on thermal/solid state physics perhaps. I'd love to work on high-energy physics research/development/whatever. I'll probably be taking an introduction to astrophysics course, though. Still, Relativity and QM interest me as well. Does that help?