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April 5th, 2011, 12:47 PM  #1 
Newbie Joined: Apr 2011 Posts: 5 Thanks: 0  Going back to school? Need advice!
Hi all, I need some advice. I'm about to graduate college and am in an interesting position. I'm going to work in industry (investment banking) but have the sneaking suspicion that I'll want to come back to math. I took some in my first two years of college and then stopped for a few reasons (family stuff and a couple terribly taught classes). I'm toying with the idea of applying to Columbia's nondegree program. Seems like it offers a lot of courses but I'm a bit wary, I guess, of just aimlessly going back to take more math. Here's my background so far: Decent Liberal Arts College (freshman year) Calc 2 (A), Linear Algebra (B+) (some other semirelated courses: logic, decision theory, bit of econ) Ivy Calc 3 (A), ODE's (A) I was thinking of taking probability and algebra in the fall and then stats/analysis in the spring. Any thoughts on how I should go about doing this? Thanks for the help, Mariogs 
April 5th, 2011, 01:25 PM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Going back to school? Need advice!
Can you give more information on the classes you're considering? Probability, algebra, stats, and analysis each (though some misfortune of language) refer to a number of different classes, some very different from each other.

April 5th, 2011, 02:27 PM  #3 
Newbie Joined: Apr 2011 Posts: 5 Thanks: 0  Re: Going back to school? Need advice!
Sure, so probability requires multivariable calc, stats requires probability, abstract algebra and analysis require through linear algebra. They're the intro upperlevels.

April 5th, 2011, 03:23 PM  #4 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Going back to school? Need advice!
Is the analysis real, complex, or both? Difficulty varies (real is harder). It looks doable to me. Algebra doesn't have much in the way of prerequisites, but it does require more mathematical maturity than the classes you've had so far. "You can do it but don't let yourself fall behind"type of difficulty. (It also takes more memorization than the average math class, but that shouldn't be hard for you.) You shouldn't find the probability class too difficult, but make sure to learn it well since you'll need all of it for statistics. Most people find that level of statistics too too hard either, though I did  I did very poorly in that class and actually had to drop it. Complex Analysis is easy as long as you get the right model in your head so your intuition is right. Get familiar with the Riemann sphere, it makes understanding the class easier.* Real Analysis is hard. I did well in the class but many of my classmates did not. If it's a combined class it probably won't be that hard because you won't get far into either subject. * Bizarrely, I find this to be a case where the "triangle inequality of learning" fails: it's easier to learn the Riemann sphere and the rest of complex analysis than just complex analysis. Perhaps it's less surprising on account of its simplicity, but still.... 
April 6th, 2011, 02:08 PM  #5 
Newbie Joined: Apr 2011 Posts: 5 Thanks: 0  Re: Going back to school? Need advice!
I guess one of my concerns is that I'd kind of be drifting. Like, I want to explore more math but don't know where this would lead. Even if I really wanted to do more, I'd have to do at least a year of coursework (I'd think) and then I'd still have to apply the following year and wait for the results before being able to do anything. Any thoughts on whether this is a serious concern? 
April 6th, 2011, 10:14 PM  #6 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Going back to school? Need advice!
I took math just for fun myself  I've never worked a 'math' job in my life (I'm a computer programmer) but that's where I took my undergrad and graduate coursework. So of course *I* would say it's not a concern. Maybe others will chime in...?

April 9th, 2011, 11:37 AM  #7 
Senior Member Joined: Apr 2007 Posts: 2,140 Thanks: 0 
Welcome to the forum, Mariogs379. If you're serious about mathematics, work your way up to topology, complex and real analysis, number theory, etc. This also should help you prepare for advanced physics studies, such as theory of relativity, quantum mechanics, etc. 

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