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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?

Thanks

James

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# Homework Help: Algebra or PDEs?

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