Modern Algebra

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Modern Algebra

Postby naseermk » Tue Jan 20, 2009 10:24 pm

So, I am planning to take Modern Algebra at the Univ. of Minnesota.

Has anyone taken this course before? I've heard that topics such as rings, fields etc are helpful in terms of learning HEP Theory.

If you've taken this course before how much of an exposure did you get on Lie algebra (if at all) ?


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Re: Modern Algebra

Postby Juston » Tue Jan 20, 2009 11:49 pm

As far as the math department at my school is concerned, Lie algebras are a graduate level subject. Obviously, I can't say the same for other schools, but it may be easier to take or audit a graduate physics course that covers Lie algebras.

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Re: Modern Algebra

Postby WakkaDojo » Wed Jan 21, 2009 12:52 am

In my undergraduate studies of abstract algebra we did not encounter Lie algebra or Lie groups, and I took a two part course on the topic. There are a lot of elements in this field of mathematics (no pun intended), so perhaps whichever advanced topics (for an undergraduate) you cover are dependent on the professor.

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Re: Modern Algebra

Postby dsperka » Wed Jan 21, 2009 2:30 am

My personal advice would be this: If you are taking modern algebra to gain background that will be helpful for physics, don't do it. If you want to take a PURE math class, then by all means. I took modern algebra because I thought it would be helpful, but found it to be so boring that I couldn't put any effort into it and ended up getting a C. I'm sure youd be better off learning it from a physics professor if and when you need to. If you haven't already, take an advanced physics class related to HEP, like particle physics or maybe QFT if youre up for the challenge.

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Re: Modern Algebra

Postby PhysicsPdx » Wed Jan 21, 2009 12:48 pm

To get to Lie Algebras you need to first understand groups, then fields and rings. Both group and ring/field theory courses can be amazingly rewarding, if you're willing to undergo a massive shift in your thinking... away from your physics brain and toward your proof based, abstract math brain.

As the previous poster said, if you want to learn Lie Algebras so you can apply it to HEP theory, then take it through your graduate physics department or learn it on your own in the context of your research/classes. It would be a miserable experience to wade through all of the underlying mathematics if all you want to do is apply it vs. really understanding the underpinnings. It comes down to your motivations. I can tell you firsthand, the professor and students aren't going to care that you're well versed in physics, or especially that all you want to do is apply the material, you'll simply get broadsided and fight to keep up. So, be honest with yourself.

I hope it helps.

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Re: Modern Algebra

Postby naseermk » Wed Jan 21, 2009 1:49 pm

PhysicsPdx wrote:It would be a miserable experience to wade through all of the underlying mathematics if all you want to do is apply it vs. really understanding the underpinnings. It comes down to your motivations.

I do not really like working with stuff if I do not have a good grasp of the foundations. When it comes to 'proof based, abstract math brain,' I really enjoyed the challenge posed by Real Analysis.

Summing it up, I do want to learn its application to HEP, but, at the same time I want to have a good grasp of its foundations as well.

Thanks, PhysicsPdx for helpful comments ( I have no exposure at all to Lie algebra and did not know that group, ring / fields form the foundation for Lie algebra). Hopefully, that'll change by the end of the semester :D

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Re: Modern Algebra

Postby YF17A » Wed Jan 21, 2009 9:31 pm

I'll add my two cents from the HEP theory side: you don't need rings and fields to take a first pass at Lie algebras. You do need groups, since Lie algebras are essentially "infinitesimal" group elements - their algebraic structure is just a vector space, which we're all familiar with. And I wouldn't recommend staying away from classes with the name "algebra" in them. Pure abstract algebra is indeed a long and painful bore, but "algebraic topology" and "algebraic geometry" are MUCH closer to our field.

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Re: Modern Algebra

Postby InquilineKea » Thu Apr 01, 2010 1:38 am

Wow, I identify a lot with this thread too. Unfortunately, I went all the way to become a math major, and this certainly hurt my GPA. Although I do recognize the intrinsic significance of math, I'm just better at thinking intuitively than analytically.

I've realized that it's far more rewarding just to "learn the math as I go". Oftentimes it's more rewarding to learn the application first and then to learn more about the theory. E.g. Schrodinger's equation first, and then partial differential equations second. Though if I had EQUAL interest in both fields, then it would probably be better to learn the theory first and application second. E.g. learning quantum mechanics first and then learning physical chemistry, which is really a special case of QM. This would make physical chemistry more rewarding, since it's unified, and not just a bunch of ad hoc facts (learning things by means of ad hoc facts isn't rewarding either, which is why I don't like the way they teach biology or history).

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