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Courses What additional math course should I take?

  1. Jan 19, 2008 #1
    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.
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  3. Jan 19, 2008 #2


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    I took a course on Non-linear dynamics and chaos, and it is possibly my favorite course at university so far. PDES is also very useful.
  4. Jan 19, 2008 #3
    Take Introduction to Stochastic Processes. You will probably use the book by Ross. Its a very cool subject. Markov Processes are important in modeling real world situations (i.e probabilities of going into another state of some process).
  5. Jan 19, 2008 #4
    The Non-linear Dynamics and Chaos course sounds interesting.

    I am completely unfamiliar with Stochastic Processes.

    It would make sense, though, to take PDE, since I am already taking Intro. to Partial Diff. Eq.
  6. Jan 19, 2008 #5
    I concur with this sentiment. So much so that I am attempting to go to grad school in a field that uses a lot of this type of analysis.
  7. Jan 19, 2008 #6
    Another important question, down the road, I think I might like to do some kind of financial work part-time while I go to school for a master's. Would this class be helpful?

    MATH 4370: Mathematics of Financial Derivatives
  8. Jan 19, 2008 #7
    Personally i would chose from (depending on how many one can chose)

    Advanced Abstract Algebra
    Partial Differential Equations
    Differential Geometry
    Integral Equations
    Number Theory
  9. Jan 19, 2008 #8
    Which classes would be the best for graduate school preparation?
  10. Jan 19, 2008 #9
    Hehe you go to UH. Anyway, the professor who tends to teach Non-linear dynamics is rather cool and the class is fun. It's interesting, but it's mostly an introduction/

    If you want to prepare for graduate school, I would suggest Stochastic Processes or Differential Geometry. Although the PDE class seems tempting, it's mostly a theory on PDE. It isn't very useful in regard to your major. If you do go to UH you should have some "free electives" around senior year, so if you want, you could take PDE and non-linear dynamics during those times.

    Oh yea, I hear Numerical Analysis tends to be a useful skill.
    Last edited: Jan 19, 2008
  11. Jan 20, 2008 #10
    Why the Hehe? Actually, I don't go there yet. lol. The PDE consists of two classes. I've already picked my other electives and everything, so I might do the non-linear dynamics instead of PDE altogether.
  12. Jan 20, 2008 #11
    I would say a solid course in PDE (not just basic separation of variables) and a solid course in differential geometry (that got into riemannian geometry) would make grad school a lot easier for you.

    With PDE, I mean that if your intro course didn't go into the theory of Green's functions, convergence of fourier series, etc., it might be more useful than a course on stochastic processes, which is quite elementary when taught at the undergrad level (at least at the level of Ross' book, which was mentioned).
    Last edited: Jan 20, 2008
  13. Jan 20, 2008 #12
    what math have you taken?
    I'm sure most of those classes are hard, but Real Analysis is supposed to be one of the hardest classes to take. If you want the challenge i'd say take the analysis class, but it won't apply to very much for your physics major. I liked the class, took it because
    I have a dual physics maths degree.

    As far as what is most applicable, as others have said, choose from the PDE, Nonlinear Dynamics, the financial one since that's one of your interests, and the numerical analysis
  14. Jan 20, 2008 #13
    As of right now, I have Partial Differential Equations in there. That's all. I just mentioned finance because I want an "easy" job while I'm graduate school. I don't really know if a finance job would be "easy." I just assume it'd be a little easier than an engineering job or other technical job I would qualify for with a Physics BS.
  15. Jan 20, 2008 #14
    if I were you I would take real analysis or topology. After finishing them this semester, all of mathematics come together... seriously, in physics, one deals with integrals, derivatives...etc all the time but do most of the people really know what exactly that they are doing??? real analysis will tell you exactly what things are. Seriously, Real Analysis is what separates math people from normal people. It basically open up your eyes and after you finish the course, you will no longer fear really abstract mathematics. Also, ask around and see if the professors teaching the courses are any good. If not, you might be better off learning analysis yourself.

    Honestly, after finishing more than half of rudin's analysis book, and some of munkre's topology book, difficult things like tensors in general relativity become manageable. Be warned, however, analysis and topology are no easy matters. PDE is an insignificant piece of dust compare to them.
    Last edited: Jan 20, 2008
  16. Jan 20, 2008 #15
    Hmm. I really would like an in-depth mathematics understanding like that. This course is only an Introduction to Real Analysis. I'm still a ways off from this. Maybe next year or so.

    So, you recommend Introduction to Real Analysis over the two PDE courses?
  17. Jan 20, 2008 #16
    it depends on your personal motivation.... I took PDE this semester and felt that I could've learnt the material on my own; well, I had to take a PDE course as a physics major so no complaint there. Your PDE course might be better depending on the professor.

    To be honest, yes, analysis would not be as important as some others in terms of calculations in real life. But as a personal thing--to understand calculus once and for all, real analysis is a must.

    Anyway, as I can tell, hardcore physics majors take real analysis. Even though some of my professors are against it, the top kids take analysis. But do know that it will be a struggle. If you are worried about your grades dropping... think about it first.

    Also, does your school require you to take PDE? if so, then take it. Otherwise, if you are motivated enough, learn it over the summer after analysis. Anyway, I cannot imagine learning PDE without knowing what exactly partial derivatives do... it's a shame, really...learning PDE before even knowing what volume integrals are (all the divergence, curl, stokes theorem).

    I think I'll add an overview of the material covered in first semester analysis (yours might be a bit different):
    basically, the course starts with general things like set theories, countability, and then it goes over the real number system--in a theoretical sense--as a completion of the rational number.

    then, one learns about metric space, open sets, closed sets, limit points, compactness... topology stuff.

    after the fundamentals, the real fun begin, personally, I found the fundamental stuffs the most difficult part of the course, partly because I haven't seen such notations and rigorous definitions before.

    sequences, series, limits.

    then continuity, limits of functions, derivatives, Riemann integrals, then sequences of functions, sets of functions (Ascoli theorem). If you work hard on the exercises, you will go over some theories about fourier series, differential equations and other goodies.

    and that's about the first semester.
    Last edited: Jan 20, 2008
  18. Jan 20, 2008 #17
    As a physics major, I am required to take Introduction to Partial Differential Equations. As an elective/math minor, I'm taking Introduction to Complex Analysis. Will that be just as hard as Introduction to Real Analysis?
    Last edited: Jan 20, 2008
  19. Jan 20, 2008 #18
    Since you are required to take PDE, then take it.

    As for Complex Analysis, I haven't taken that course (and I don't think I will take it) so no comment personally. But I doubt it will be as hard as real analysis.

    Actually, it depends on what you mean by Complex Analysis. If you mean the kind where they go over Cauchy theorem, contour integrals.. then no, it would be as hard as analysis. Or if you are talking about Complex analysis as real analysis done using complex numbers, then heck yes... though I doubt it refers to the latter.
    Last edited: Jan 20, 2008
  20. Jan 20, 2008 #19
    I am required to take Introduction to Partial Differential Equations. That's an entirely different class than the TWO PDE mentioned here.
  21. Jan 20, 2008 #20
    It depends on what your PDE course is. Baby Rudin is pedantic compared to Evans' PDE book.
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