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### Math crossroads: which course?

Posted: Fri Jul 03, 2009 5:44 am UTC
First off, sorry if this is not the right forum for this. I figured that the great math minds here could give me some advice, but move me if you will.
That said, I'll continue.

So I'm going to be starting my second year at university this upcoming fall. I'm an EE/Math double major doing some late schedule-reworking, and I'm trying to figure out whether it would be in my best interest to take numerical linear algebra or real analysis. Both look interesting, but the problem I'm mainly having is in not knowing what is really involved with the two fields and their applications. I've wandered around Wikipedia a bit, but it seems to turn into a giant game of link-following to find a math article in layman's terms...

Anyway, if anyone has any advice slash opinions on where I should go I'd be greatly indebted.

### Re: Math crossroads: which course?

Posted: Fri Jul 03, 2009 6:46 am UTC
Real analysis is traditionally a "pure" math course; it focuses on issues that are of concern to pure mathematicians, such as whether functions are always continuous or differentiable, but if you're an applied kind of guy you might not care so much. Numerical linear algebra is, as I understand it, extremely useful for certain applied disciplines, where it's often necessary to perform matrix operations on very large but sparse matrices (such as in computational biology).

So first you should tell us what you're interested in.

### Re: Math crossroads: which course?

Posted: Fri Jul 03, 2009 10:03 pm UTC
Does 'numerical' in linear algebra imply that you're already familiar with analyitical linear algebra techniques? If not, take the lin. alg. course hands down as it'll be more useful and, in my opinion, more interesting. If it's strictly a computational course then I suppose it would depend on your personal preferences.

### Re: Math crossroads: which course?

Posted: Sat Jul 04, 2009 12:10 am UTC
If you're an EE/Math major, take real analysis. A math major who doesn't know real analysis is like an EE major who never took a circuits class. Frankly, you should take both classes, but take real analysis first. (I say this as a professional applied mathematician who does numerical linear algebra all the time).

### Re: Math crossroads: which course?

Posted: Sat Jul 04, 2009 3:23 am UTC
Is either a prereq for some other interesting classes you can take in the spring? Are they both offered every year?

### Re: Math crossroads: which course?

Posted: Sat Jul 04, 2009 9:38 pm UTC
RA is a prerequisite for RA2, both of which are required for the math major and offered alternate semesters. I'm more of an applied guy (hence the engineering), but I guess there's no getting around a good deal of pure math as my school has no applied mathematics major. I took a course in abstract linear algebra last semester (vector spaces, Cauchy-Schwartz, Gram-Schmidt, projectors, eigenvalues, etc) and the NLA class is designed to kind of build on that and give techniques for optimization and working with different data sets given characteristics of the data (sparseness etc) as well as some more pure stuff, as far as I understand (uninformed sophomore, forgive me

As it stands now, I guess I'm going to have to drop a different class and take both. NLA is only offered sporadically and seems so practical, but I *need* RA...there goes that awesome Crypto course...

Thanks for the responses!

### Re: Math crossroads: which course?

Posted: Sat Jul 04, 2009 11:02 pm UTC
No crypto! Hey now, let's not be too hasty with this analysis decision... If you can get a first complex analysis in without having RA1, then doing RA1&2 senior year might not be too bad?

### Re: Math crossroads: which course?

Posted: Sun Jul 05, 2009 5:12 am UTC
Might not be helpful in anyway, but my RA professor always told us something along these lines:

"Yes, engineers say they don't need all this stuff because they have computers to do it for them. What they aren't taught is that if what I'm doing up here isn't true for their particular function, then their computers can spit out all kinds of nonsense that can get them into trouble. The computer doesn't know or care whether or not their function exists or is differentiable, or integrable, you see. It'll give them *something* if they ask for it. That's why you have to do this delicate mathematics, to make sure that what the computer is doing makes sense."

And then a little bit reassuring us that computer won't take the future mathematicians' jobs.

### Re: Math crossroads: which course?

Posted: Sun Jul 05, 2009 3:27 pm UTC
I don't think that actually happens. I use maple for my computer integration; if an integral doesn't converge, it tells me so. In fact, it's pickier than it ought to be! I bump into this all the time when I try to renormalize things.

### Re: Math crossroads: which course?

Posted: Sun Jul 05, 2009 3:51 pm UTC
doogly wrote:I don't think that actually happens. I use maple for my computer integration; if an integral doesn't converge, it tells me so. In fact, it's pickier than it ought to be! I bump into this all the time when I try to renormalize things.

Really? That's sort of impressive, hehe. I'll admit that he's a bit on the old side, so things might've changed since he forged those quotes/stories.

### Re: Math crossroads: which course?

Posted: Sun Jul 05, 2009 4:46 pm UTC
Symbolic math software make all kinds of assumptions. I think both Mathematica and Maple will output 0 if you ask it what [imath]\frac d{dx}\frac{df}{dy}-\frac d{dy}\frac{df}{dx}[/imath] is, even if you provide it with an explicit counterexample f. I've also noticed stuff like getting 0 from 0^x, where x is a variable, even though the programs will tell you that 0^0 is 1, and Mathematica "helpfully" plotting [imath]f(z)=\sum_{n=1}^\infty n^{-z}[/imath] (as the Riemann zeta function) over the entire plane, even though the sum doesn't converge for Re(z)<1. I've seen examples of Wolfram Alpha claiming that an obviously convergent integral or sum diverged.