What is Linear and Abstract Analysis and How Are They Applied in Science?

[Lonewolf]

Next year I have the option of studying these two courses. What are they about, and what are they used for? Has anybody taken courses in these, and if so, what did you think of them?

 

[quantumdude]

Do you mean "Linear and Abstract Algebra"? If so, then that would make more sense!

My answer would depend on your major. If you are majoring in math or physics, then you will need to take both of them. If you are in engineering, you will only find Linear Algebra useful.

I took both of these courses, and as a physics grad student I find them indispensable. My thesis is on effective field theories for hadrons, and one must have a solid foundation of vector spaces and group theory for that.

 

[Lonewolf]

Nope, it's definitely analysis. We've got separate options for abstract algebra and linear algebra.

 

[damgo]

How weird... could you post the course description? Probably it is something like a real analysis course, which I would highly recommend. But from those names it's hard to tell -- are you in the States?

 

[Lonewolf]

The course descriptions are linked below

http://www.mcs.le.ac.uk/Modules/MA/MA2121.html

http://www.mcs.le.ac.uk/Modules/MA/MA2151.html

I like the sound of them, but I'm not sure what exactly they involve, and searching on the web for them wasn't exactly fruitful. We've got real analysis as separate first and second year modules. I'm from the UK. We don't have majors or things like that. We just do a degree course in a subject.

 

[HallsofIvy]

HallsofIvy

Thanks for the links.

"Abstract Analysis" looks to me like a fairly standard analysis course (perhaps a second year of analysis- I didn't look for prerequisites.)

"Linear Analysis" looks more like what I would call "Functional Analysis", generally speaking more "abstract" and more difficult than "Abstract Analysis"!

 

[Lonewolf]

Thanks for the input. I think I'm going to take them both. Is there any use for either of them in applied mathematics? I don't really want to take something that can't be used outside pure maths. The linear analysis course seems the more interesting of the two at the moment, although that could change once I take it...

 

[HallsofIvy]

Certainly, I would recommend taking the "abstract analysis" course first. It will definitely help you in taking the "linear analysis" course later. (Remembering that the best thing you can do is talk to the faculty who actually teach the courses for their recomendations!)

As to how much use they are in "Applied Mathematics", that depends strongly on what you mean by "applied mathematics"- an unfortunately vague term! Some people use "applied mathematics" to mean the theory behind the kind of mathematics used in applications. Certainly, if you consider yourself a mathematician of any sort you should have as much anaysis as possible. Functional Analysis (what, I think, is your "linear analysis") is used in developing the theories behind solution methods for differential equations, among other things, but are not really necessary just for using those methods. Again, think about exactly what YOU want to do and talk to the faculty.

 

[Lonewolf]

Thanks a lot for your advice. I'll go and arrange an appointment to discuss it with a member of the faculty. I meant applied to some area of science, e.g. are they of any use in theoretical physics?

 

[damgo]

Yes! If you get advanced enough, most areas of math are useful in theoretical physics. But analysis is especially useful.

 

[Lonewolf]

Wow, that's pretty cool. At least the stuff I'm learning is only seemingly useless