Easier for self-study: Analysis or Algebra?

[nicksauce]

I am a physics major doing a minor in math going into my last year in the fall. I want to learn both algebra I and analysis I, but my schedule doesn't allow for it, so I want to take one of them in the fall and self-study the other during the summer. In your opinion which would be easier for self-study?

 

[noospace]

What material do they cover and what are your interests.

Personally, I majored in physics/mathematics and took algebra over analysis.

The main use of analysis in physics is probably residue calculus which I taught myself when I needed it.

 

[Poop-Loops]

Residue calculus? Is that stuff with like the Cauchy theorem where you have imaginary (and I think real ones work too) poles in the denominator and you are integrating over it? With Jordan's lemma and such? We learned that in the Mathematical Physics series in my school.

If your school offers that class, TAKE IT. You'll likely learn a bunch of stuff you never knew would be useful without going through the whole class for it, so if you like algebra over analysis, for example, you'd still learn what you need in Math Phys while taking the math classes you want.

 

[SCV]

Residue calculus? Is that stuff with like the Cauchy theorem where you have imaginary (and I think real ones work too) poles in the denominator and you are integrating over it? With Jordan's lemma and such? We learned that in the Mathematical Physics series in my school.

If your school offers that class, TAKE IT. You'll likely learn a bunch of stuff you never knew would be useful without going through the whole class for it, so if you like algebra over analysis, for example, you'd still learn what you need in Math Phys while taking the math classes you want.

...and he would not even learn residue calculus in analysis (as it belong in Complex Analysis).

 

[nicksauce]

What material do they cover and what are your interests.

Personally, I majored in physics/mathematics and took algebra over analysis.

The main use of analysis in physics is probably residue calculus which I taught myself when I needed it.

Algebra I:
Sets, functions and relations. Methods of proof. Complex numbers. Divisibility theory for integers and modular arithmetic. Divisibility theory for polynomials. Rings, ideals and quotient rings. Fields and construction of fields from polynomial rings. Groups, subgroups and cosets; group actions on sets.

Analysis I:
A rigorous presentation of sequences and of real numbers and basic properties of continuous and differentiable functions on the real line.

Interests? Still pretty broad at the moment... but something along the lines of astrophysics/cosmology/strings/particle. I hear that group theory and such are important in theoretical physics which I assume one would need a good background in algebra to study. However, I want to learn analysis if only to have a more rigorous mathematical background, and learn how to prove things properly. I am taking a course in complex variables at the moment actually, so we are learning about residues there.

 

[k3N70n]

My guess is Algebra would be much easier to learn on your own.
But I struggled a lot more in Analysis then Algebra so that could just be my bias.

 

[JasonRox]

I would vote Algebra is easier too.

 

[mgiddy911]

The beginning of that Algebra course looks to be a bit of number theory before jumping into the abstract algebra. That part should be cake to learn on your own. Bu as it gets more abstract and delves into Rings Fields and Groups then you might need to slow down and really make sure you are understanding the concepts.

I have yet to take Abstract Algebra ( have done number theory though ) but I have done Real Analysis and found it to be the toughest math class I have taken no counting currently taking E&M.
That is not to say you can't teach it to yourself, but I think it would be better learned in a classroom. However for both of these classes you may struggle to see their connections to any of your physics classes at this point.

 

[Dmak]

I've been studying both on my own for quite a while now both are very studyable subjects although you will probably find one more interesting than the other depending on your preference.

 

[noospace]

Do analysis.

I have the same interests as you and I would say that in retrospect taking algebra over analysis was a bad decision. Yes, lie groups and lie algebras play an important role in advanced theoretical physics like particle theory, but you won't be covering that; just finite group theory which apart from some niche applications like studying the vibrational modes of molecules is not particularly useful for physics.

You can always go back and do a course like that later. See if your department has any courses in continuous lie groups and lie algebras. They would definitely be worth taking if you're interested in particle theory.