Hello, Im 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. Lets 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 im 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.