Ive been pondering these for a while

[OrbsAndSuch]

Hello, I am a freshman in college, and i have a while to pick my major, and eventually my career, but I figured I should start thinking now. Sorry if these questions seem completely random, but this how i think, and this series of questions has turned into a sort of half-rant, but any help/advice/questions/discussion is appreciated. Let's continue:

Whats the difference between "pure" and "applied" mathematics? First thing that comes to my mind is that "Pure" math is basically concepts and theory, and "Applied" math is those theories and concepts applied to the real world. Is this correct?

Which universities have strong programs for either? I know the Berkeley has an Applied Mathematics program, but I am not sure if Applied is for me.

Ive always been fascinated with planets and stars and galaxies - space in general - and Astrophysics seems to be the right path. For years, my plan was, in fact, Berkeley for Astrophysics, but my past few Physics instructors have... desensitized, for lack of better word, my interest in Physics - the physics itself wasn't boring, the teachers were. Is this gong to be the case everywhere i go to school?

For lack of further evidence, I feel a subject change is in order.

Do differential equations have a practical application in music? (i.e. distortion of sine waves?) I know there are probably simpler ways for distortion, but differential equations have always been intriguing to me.

 

[millitiz]

For question 1, well, they are pretty much the same in the higher level. Sometimes I tend to think that Applied math is just one of the subfields in math.
About question 2, well, I am pretty sure that it is not a phenomnenon across the board. At least in my school, I really liked some of my professors, and most of them are knowledgeable, intellengent (duh!). I am pretty sure that almost none of them are boring. I guess you are probably just not that lucky.

 

[Dr.D]

Many, many years ago, I signed up for a differential equations course in the Pure Math department. We spent the whole semester talking about the properties of the solutions of
y''+k^2*y = 0
without ever actually saying what those solutions were. We proved a whole slew of properties about those solutions (I can't remember a one of them today), but we never solved the differential equation, and that was the only DE we discussed. I got a B.

The following semester, I signed up for differential equations in the Applied Math department. We talked about all manner of differential equations, but mostly we talked about the Wronskian (the subject of the teacher's dissertation). I got a C.

I decided I could not afford to take any more DE classes, so I went on to take Laplace Transforms, Fourier Transforms, and a mess of other stuff, and essentially taught myself differential equations, much of it through working on the analog computer.