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Homework Help: Algebra or PDEs?

  1. Jun 28, 2006 #1
    Hi all,

    I'm facing a bit of a dilemma regarding subject choices for the second semester of second year univeristy and I was wondering if anyone could lend some of their advice. First a bit of context. I'm enrolled in a BSc (Advanced) degree at The University of Sydney, Australia with a real passion for physics so this will definitely be my major (followed by honours year and PhD in some aspect of plasma physics). Although I've already started to specialise with the research I'm doing for the plasma physics group, I have always found the most interesting part of physics to be the deep underlying theories (eg special and general relativity) and in particular, their connection with sophisticated mathematics. I should stress, however, that I'm no maths wiz: the only reason I liked linear algebra was that I saw connections with almost every concept and special relativity. Although I finding mathematics by itself devoid of meaning, I gain great satisfaction applying it to some physical problem (the more advanced and abstract the maths the better :). At heart, maybe I want to be a theoretician, but I appreciate the need for applications which is why I'm changing tack next year to work in industry on first-wall (blanket) materials for use in the ITER project.

    So, as for my subject choices, each semester we are required to do 4 subjects worth 6 credit points each, totalling 24 credits per semester. The prerequisite for third year physics is a 6 credit course which focuses on quantum physics and electromagnetic properties of materials. I also want to do 6 credit points of French for both interest and for my future ITER aspirations. That leaves 12. I think it's a good idea to do the ``other'' physics course which is a course in astrophysics, special relativity and experimental physics, although quite honestly relativity is the only part of this course which interests me and I'm not even sure how much I'd learn which I haven't already taught myself from my copy of Taylor and Wheeler. Now, filling up that 6 credit hole with maths is the tricky part. There are two courses of interest, one is on abstract algebra and the other on partial differential equations. Here are the outlines

    Algebra (Advanced)

    This unit provides an introduction to modern abstract algebra, via linear algebra
    and group theory. It starts with a revision of linear algebra concepts from
    junior mathematics and MATH2961, and proceeds with a detailed investigation
    of inner product spaces over the real and complex fields. Applications
    here include least squares lines and curves of best fit, and approximation of
    continuous functions by finite Fourier series. Further topics in linear algebra
    covered in this unit include dual space, quotient spaces and (if time permits)
    possibly tensor products. The second part of the unit is concerned with introductory
    group theory, motivated by examples of matrix groups and permutation
    groups. Topics include actions of groups on sets, including linear
    actions on vector spaces. Subgroups, homomorphisms and quotient groups
    are investigated, and the First Isomorphism Theorem is proved.

    Introduction to Partial Differential Equations (Advanced)

    This unit of study is essentially an advanced version of MATH2065, the emphasis
    being on solutions of differential equations in applied mathematics.
    The theory of ordinary differential equations is developed for second order
    linear equations, including series solutions, special functions and Laplace transforms.
    Some use is made of computer programs such as Mathematica. Methods
    for PDEs (partial differential equations) and boundary-value problems
    include separation of variables, Fourier series and Fourier transforms.

    From the applied physics perspective the choice is obvious, since I've already run into the problem of solving partial differential equations in Poisson's equation in my work on plasma physics. On the other hand, I suspect that Algebra could be more beneficial in terms of understanding abstract theories like general relativity and so on.

    Ideally, I would do both, but this would mean sacrificing the relativity subject which is probably not a good idea since it is ``strongly recommended for those majoring in physics''. The question is then, which of these subjects would be the easiest to self-learn? If I can answer this question then I guess the hardest subject would be the one to study at uni.

    What do you think?


  2. jcsd
  3. Jun 28, 2006 #2
    I just realised that I posted to the complete wrong section. Apologies mods.
  4. Jun 28, 2006 #3


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    Based on your own view of math, I would recommend the PDE course.
  5. Jun 28, 2006 #4

    Meir Achuz

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    The PDE course is the more important one for what you will probably be doing in physics. Actually the best course would be a grad course in
    "mathematical physics". You should be ready for that level, and it would be more relevant to physics than a pure math course. Concentrate on your four courses and don't try to self learn either algbra or pde.
  6. Jun 28, 2006 #5
    Clearly you should take the PDE course.
    And if it is possible a course introducing you in differential geometry, that will give you a good basis in your study of general relativity.

    Dont do relativity in a too abstract way.
    Do physics first.
    If possible read Einstein text in general relativity, after having an introduction to Rieman geometry.

    Remember think physics first.

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