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Courses What applied math courses should i take?

  1. Mar 4, 2009 #1
    i only need 3 more for the B.S. degree. I know for sure I have to take Intro to Stats B, so I need to pick 2 more classes from: Numerical Analysis A, Combinatorics, Optimization, Abstract Algebra (I dropped the honors version), Topology, Fourier Analysis, Real Analysis B

    i'm scared to take real analysis B since i havent taken real analysis A since a year ago, so i forgot alot of the stuff. but, i am good at proofs

    i cant take numerical analysis A as it has a time conflict with a required class for my physics major (I'm double major). Also, is it worth it to complete the degree asap? I can technically finish next quarter, spring (we use trimester system), but I'm not set to complete the physics major untit next winter

    i also plan on taking fluid dynamics from the mechanical eng department, since I havent taken any engineering classes yet. also, since i plan on doing Computational fluid dynamics for grad school since it has a nice balance of physics, theory and math modeling, and job applications.
     
  2. jcsd
  3. Mar 5, 2009 #2
    no math majors here?
     
  4. Mar 5, 2009 #3
    I'm merely an undergraduate, hence I can't really give you good advice. I'm just going to state subjects that I think are interesting or very applicable. I really enjoyed topology when I took it, so I would recommend it, although I'm not too sure how applicable it is. Every physics professor I've spoken to always highly recommends taking a numerical analysis class. I also believe that Fourier analysis is extremely useful, as it's widely applicable in physics and engineering, or so I've heard.
     
  5. Mar 5, 2009 #4

    All those subjects are important and interesting, so it is hard to say without knowing more about what your goals are.

    Analysis, Topology and Abstract Algebra are very important if you are looking to go further in math, or want to get a rigorous understanding of why the math you do in physics actually works. I'm also of the opinion that these classes stretch your brain and make you a better problem solver in any field, though many people will probably take issue with that opinion.

    Numerical analysis and Fourier analysis are key for physics, engineering and many other applications - basically anywhere that you actually want to compute an answer and not just talk about existence and uniqueness. Fourier analysis has pure math applications as well.

    I don't know very much about optimization, other than the fact that it seems like a pretty cool topic from the outside, and has many applications.

    Combinatorics is probably the least immediately useful subject you listed - unless you want to do more combinatorics or some areas of computer science. I only know a little combinatorics so I may be completely wrong, but to me (so far) it seems like the field is still all about finding little tricks, where every problem is its own little puzzle to play around with, and there is less deep overarching theory.
     
  6. Mar 5, 2009 #5
    Only two more?
    The physics and applied maths lecturers say it's better to take more applied maths courses than more maths courses if you want to do physics, since you will be picking up new mathematics on your own in your physics career. I suppose they think it's harder to teac yourself in Applied Maths. Of course you need some mathematics as an undergrad, so you have a base to work from later on.
    I would not do topology without a thorough understanding of real analysis, and probably abstract algebra too.
    Most importantly, ask one of your physics profs. Their advice is probably best.
     
  7. Mar 6, 2009 #6
    i'm looking into math modeling or mechanical engineering for my career goals

    i'm not going into physics at all, unless computational fluid dynamics counts

    i'm leaning towards computational fluid dynamics the most for right now

    i dont want to do theoretical physics or pure math

    out of those classes, i'm mostly thinking between abstract algebra A, real analysis B, fourier analysis, or optimization

    i can always take numerical analysis A during grad school.
    OR i can just take 1 of those electives, and wait until fall to take numerical analysis A
     
  8. Mar 6, 2009 #7
    You didn't list it, but if you are interested in math modeling give some consideration to a PDE course.

    There are usually different levels of PDE courses, ranging from the standard physics intro-to-pde courses that focus on physical meaning for linear PDE like the heat equation laplace equation wave equation etc, all the way to extremely abstract mathematical theory involving higher order nonlinear pde, sobolev spaces and the like, which would probably require functional analysis. Start slow, to say the least - PDE is a hard subject.

    Also, for mechanical engineering and math modeling, numerical analysis and numerical linear algebra are very very important. If you get it at the graduate level, thats certainly fine. In fact its probably required for many (most?) applied math and mathy-engineering graduate programs. Just make sure you get it at some point.
     
    Last edited: Mar 6, 2009
  9. Mar 6, 2009 #8
    i've already taken PDEs
    the theory was uninteresting(maximal principle, etc)
    the applications were fun(solving heat eq, etc)
     
  10. Mar 6, 2009 #9
    You could take Functional Analysis to possibly learn the theory behind the PDEs techniques. It might help though if you posted course descriptions.
     
  11. Mar 6, 2009 #10
    i just said i dont like the PDE theory. i like USING PDEs, hence why i've been thinking about mechancial engineering for grad school

    heres the course descrptions
    110A. Algebra (4)
    Lecture, three hours; discussion, one hour. Requisite: course 115A. Not open for credit to students with credit for course 117. Ring of integers, integral domains, fields, polynomial domains, unique factorization

    -this class isnt offered during next quarter

    117. Algebra for Applications (4)
    Lecture, three hours; discussion, one hour. Requisite: course 115A. Not open for credit to students with credit for course 110A. Integers, congruences; fields, applications of finite fields; polynomials; permutations, introduction to groups.

    131B. Analysis (4)
    Lecture, three hours; discussion, one hour. Requisites: courses 33B, 115A, 131A. Derivatives, Riemann integral, sequences and series of functions, power series, Fourier series.

    133. Introduction to Fourier Analysis (4)
    Lecture, three hours; discussion, one hour. Requisites: courses 33A, 33B, 131A. Fourier series, Fourier transform in one and several variables, finite Fourier transform. Applications, in particular, to solving differential equations. Fourier inversion formula, Plancherel theorem, convergence of Fourier series, convolution. P/NP or letter grading.

    164. Optimization (4)
    Lecture, three hours; discussion, one hour. Requisite: course 115A. Not open for credit to students with credit for Electrical Engineering 136. Fundamentals of optimization. Linear programming: basic solutions, simplex method, duality theory. Unconstrained optimization, Newton's method for minimization. Nonlinear programming, optimality conditions for constrained problems. Additional topics from linear and nonlinear programming. P/NP or letter grading.

    heres a class i forgot about, that may be useful for me?

    171. Stochastic Processes (4)
    Lecture, three hours; discussion, one hour. Requisite: course 170A or Statistics 100A. Discrete Markov chains, continuous-time Markov chains, renewal theory. P/NP or letter grading.
     
  12. Mar 8, 2009 #11
    no applied math majors here huh?
     
  13. Mar 8, 2009 #12
    For my money, take Fourier Analysis if you're going into anything where you'll touch physics with a fifteen-foot pole.
     
  14. Mar 8, 2009 #13

    cristo

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    Stop bumping your thread like this: someone will give you their advice in their own time.

    It's hard to advise you as to which courses to take if we don't know the classes that you've already taken. Furthermore, it would help if you gave your (or your school's) definition of applied maths: the majority of the courses you list in your OP I would class as pure maths.
     
  15. Mar 9, 2009 #14
    i've already taken:
    linear algebra (proofbased)
    complex analysis for applications
    ordinary differential equations (upperdiv - covered laplace transforms, PDEs, existence and uniquenessm etc)
    Real analysis A
    PDEs
    Probability theory A
    Systems of linear and nonlinear DEs
    Mathematical modeling
     
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