Applied Math: Areas of Study & College Focus

[thrill3rnit3]

What are different areas of study in Applied Mathematics?

That's what I'm planning to do in college but I'm trying to figure out which area I'm going to focus on.

 

[maze]

The field is huge. A few of the bigger subdisciplines include

Numerical Analysis
PDE
Optimization
Network Theory
Applied Probability

 

[thrill3rnit3]

I see. Which is the more popular one?

 

[maze]

dont worry about specalizing until you have taken the standard maths for beginning undergraduates (various calc classes, linear algebra, etc)

 

[thrill3rnit3]

I already took those classes in a nearby junior college.

so when I hit the university after high school i'd probably be jumping in right into the major requirements.

 

[thrill3rnit3]

Also, which specialization offers more opportunities outside research?

 

[maze]

Each of these areas is huge in both academic research and industry application. For many positions a masters or phd is necessary, so you may not want to specialize until late undergrad or graduate school, should you decide to do that.

I would recommend studying real analysis and numerical linear algebra next.

 

[thrill3rnit3]

I heard real analysis is a hardcore math class. But I'm looking into getting a book and self-studying while I'm still not in college.

Meanwhile, "numerical" linear algebra? What's the difference between regular linear algebra and numerical linear algebra? I already took the linear algebra course offered in the community college so I'm just wondering...

EDIT: Nevermind about the numerical linear alg. question. I did a search on google and found the difference.

What are good institutions/universities for applied mathematics? both undergrad and grad.

 

[maze]

Check out Gilbert Strang's linear algebra video lectures (first lecture here) at the MIT OCW site online. It's not numerical linear algebra, but it is probably a more advanced level than you have already seen, and probably a prequisite for understanding numerical linear algebra. Plus the lectures are great. If you already know linear algebra at that level, then I recomment picking up Numerical Linear Algebra by Trefethen and Bau,
http://www.comlab.ox.ac.uk/nick.trefethen/text.html

 

[thrill3rnit3]

What are good institutions/universities for applied mathematics? both undergrad and grad.