Questions about real analysis?

It depends entirely on your interests and future plans. Different people need different things and different people like different things so as it stands your question is amorphous. I'm a physics major for example and I can't in any reasonable way predict what I will end up doing in grad school but I took real analysis simply because I love pure math (and yes real analysis would generally fall under pure math). If you mean "need" in a very general, bare minimum sense then no.

 

I took real analysis in undergrad, went on to get a phd in theoretical physics and now work as a statistician/data-miner and I can't recall a single time when real analysis has been helpful, outside of the real analysis class.

 

Hi WannabeNewton,
I think a real analysis course would be useful for a Math Phys major, but do you think it is essential? When I spoke to you before, my intention was to take the real Analysis course over the Algebra but because of more timetable constraints I am now in a position of taking differential equations and complex variables instead. I could of course take the real analysis next year, but I was just looking for another opinion on this. I have emailed my school as well.

@ParticleGrl Given that you did a theoretical physics PhD, did the real analysis not help in any way?

 

Pretty much every physics professor I've ever asked has said no, and I would have to agree with them. That's not to say you shouldn't take it if you really like the subject of course. I know you're doing a joint mathematics/physics program so regardless of whether real analysis is essential or not in the given context, you should probably check the program requirements to see if real analysis is mandatory or not as well; if it's mandatory well then that's that isn't it :)?

Definitely, definitely go with the DE and complex variables option if you are under time constraints; I'm sure your university would tell you the same.

 

I find the subject rather challenging, and I do find it interesting. I recall you mentioning that is a stepping stone to functional analysis which is pivotal to rigorously understanding QM. But I suppose I could certainly self study this.
And no, the course is not mandatory.

Just out of interest, why do you think these are more important? - more applicable to physics?

Thanks for the advice.

 

I was a double major Physics/Math so I had to take it anyways. Real analysis was (imo) a fun course, and I have had the luxury of using it in my physics courses. While, some people in physics may end up using it a lot of people will not. Theoretical biophysics for example, probably would never need it. Cosmology? Absolutely, since the key is topology and topology is kind of the mix of analysis and algebra.

With that if you have just a free space and can take if, why not? Math is never a bad thing for physics. But if you were crunched I would agree with wannabenewton go for DE/ complex variables and I would add linear algebra.

Disclaimer, I am unsure about EE.

 

Yes.

 

What Physics courses did you find it useful in?

 

Obvious answer:
Math Methods.

Less Obvious answer:
You see it pop up in various different courses. Not holistically throughout the course but in sections. Like when covering general relativity in modern physics and intro to astrophysics. When introduced to mathematical constructions like Hilbert Space, it can come in handy. And I took a math elective course called Shape of Space, which tackled the physical shape of the universe from a purely mathematical standpoint (topology) and having seen real analysis it became a made my time a little easier.

It is also part of the framework for upper level math courses which can help you better understand those courses that you would take. Analysis is pretty much just calculus again but being more rigorous in definitions, and actually having to prove statements from these definitions.

However, in my physics classes, most of my peers had not taken real analysis. They passed (for the most part) and understood the material pretty well. It is just that having been experienced to analysis I was a little more familiar with things at first and quicker. But again, if there are more pressing courses to take, get them out of the way first. I would not have taken this course unless I was a math major, at the time. But having seen it, I do appreciate it.

Hope this has helped.

 

I would also like to point out that Real Analysis is generally a bit of a heartache. So if you take this course be prepared for what lies ahead, it isn't so bad but it is generally where people are introduced to that style of math (proof writing and building strictly off of theorems).

And even though I liked it, I would not recommend the course unless you had the time and space in your schedule to fit it in.

 

IMHO real analysis is for math majors - it is where you learn to rigorously go where you previously skipped over details. It is usually an exercise in writing proofs ... as are most senior level math courses.

I enjoyed it - but I wouldn't recommend it for anyone who life goals do not include "learning to think like a mathematician". Does knowing how to prove the implicit function theorem help in real life?

 

Was going to ask if anyone wanted to elaborate, but maybe a new thread would be more appropriate...

 

"We often hear that mathematics consists mainly of "proving theorems." Is a writer's job mainly that of "writing sentences?"" - Gian-Carlo Rota

 

IMHO, real analysis is mainly for mathematical physics, like the stuff by Elliott Lieb...

 

Analysis is "just" a formalization of all the topics you took in your calculus courses. In first instance analysis won't be helpful but will help you to open your mind and will be useful when you get into another mathematical topics, but perse is not helpful in engineering.

 

I know this thread is a bit old, but I just saw another thread on PF which gave a nice counter-example to that:

Gibb's phenomenon in the convergence of Fourier series (e.g. the behavior of a truncated Fourier series for a square wave) is a practical example of the difference between "convergence" and "uniform convergence" in analysis.

Of course you can often use Fourier series without knowing that, or just knowing some cookbook recipes about windowing functions, etc - until one day your calculations don't make much sense, and you don't have any idea why....

 

a somewhat relevant post is:
https://www.physicsforums.com/showthread.php?t=579112&highlight=analysis+engineer

it really depends upon what you are interested in working on. If you design circuits, then real analysis will likely not be useful. If you end up in academia in signal processing / information theory and possibly other specializations then yes, real analysis can be useful. But I would say that of the few engineers that could use it, almost all of them could wait until grad school to take such things. Only take as an undergrad if a) you really want to for "fun", or b) you are POSITIVE that you want to go to grad school in a field where it is useful (and even then, only after talking with faculty in that field).

jason

 

Fourier Analysis is critical in a lot of problems in physics and engineering. However, it can be considered from a 'pure' math standpoint as well.

 

I would say that real analysis by itself is more interesting to physicists than useful.

Although it opens the door to higher maths that ARE useful. It opens the door to functional analysis (which is pretty cool for quantum. L2 is isomorphic to l2, which explains why different interpretations are the same), Fourier (although you don't need real analysis, it's helpful), differential geometry (which is useful in general relativity), complex analysis.