<p>I suppose this question is mostly for Denzera... or anyone that has taken AM classes.</p>
<p>What would you say are the main differences between Applied Math and 'regular' Math courses? Are proofs and theory less emphasized in AM classes? Does one do <em>any</em> proofs in AM classes?</p>
<p>For example, classes like ODE or linear algebra. The 'CC' and SEAS sections seem to cover the same topics but they obviously have to differ somehow. So, how?</p>
<p>AM probably has an emphasis on how the math is commonly used. Like in calculus, an Applied curriculum might focus more on finding the extrema at the sacrifice of math theory.</p>
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<p>I didn’t know there was a CC/SEAS split on ODE; you sure there is? I took SEAS lin alg in the AM dept (w/ Spiegelman who seemed like a really nice guy), and there was nothing applied math about it. It was actually one of the easiest courses I took – mostly plug-and-chug and no real thinking (whether theoretical proofs or real-world applications).</p>
<p>Spiegelman’s Lin Alg in the AM Dept >>>> Regular Lin Alg in the Math dept. I mean, by miles. The guy is a hoot.</p>
<p>I don’t believe there’s much difference in the ODE classes. Plenty of differentials, of course. <em>rimshot</em></p>
<p>The two curricula share a lot of courses. However, a difference in the amount of proofs is spot on. In its place, AM has you do some Stat and Statistical Inference courses, and a little compsci-esque math here and there.</p>
<p>The PDEs class in AM is called Applied Math 2, and it’s a ball-buster. But fun!</p>
<p>edit:
Here’s a hint, if you have to use words like ‘probably’ and ‘might’ in response to a strict factual question, you probably might not know what you’re talking about.</p>
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<p>You’re right, because people that use absolutes in all of their phrasing know exactly what they are talking about. </p>
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<p>Its amazing how I was still right though…</p>
<p>sorry for not using enough specifics, I only use calculus when I’m writing valuation algorithms for the finance industry… so I can only humbly guess at what they teach in college.</p>
<p>im taking spiegelman’s lin alg course right now, and from what i gather from my friends taking the normal lin alg course, the only difference is that spiegelman likes to throw in some computational aspects every so often. so he’d discuss in class how computationally expensive a certain matrix operation may be, but he doesnt put that on exams.</p>
<p>yeah revolution, the other difference is that he’s awesome. 
I suppose I’m biased, having had him as my advisor for some independent research as well. but he’s a real credit to the teaching quality available in SEAS.</p>
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try that logic again…
My statement:
“Using weakening conditional modifiers on a question of fact indicates you don’t know what you’re talking about”
Your statement:
“That can’t be true, because people who don’t use weakening conditional modifiers don’t always know what they’re talking about.”</p>
<p>I made a statement, and you said the inverse was not true. We’re “probably” both right. :P</p>
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as they say, even a stopped clock is right twice a day.</p>
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<p>Oooooh, big man here. Everyone watch out. Seriously, is “writing valuation algorithms for the finance industry” supposed to somehow qualify you to talk about what the Applied Math curriculum at Columbia is like? I mean, someone who went to the departmental website and read over the list of courses could probably say more interesting things than you.</p>
<p>But of course, because you work in finance, you therefore must be some sort of higher human being. I’ve got news for you, pal. I’m currently working a project to wind down Lehman Brothers, closing out all their positions and liquidating or selling business units worth billions of dollars. I know many, many investment bankers. Some of them are smart, some aren’t, but all of y’all are jackasses. And if you all knew how to properly “valuate” things, maybe some of these investment banks wouldn’t have gone bankrupt, and I could be off re-engineering business processes or something in someplace with nicer weather.</p>
<p>All of which has sweet F.A. to do with the applied math curriculum at Columbia, which was the question here, which I have extremely personal knowledge of, and you have… bupkus.</p>
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<p>I’m not down for internet wars. I saw a post on AM, I thought it was an interesting question, I wanted to give my two cents on it and see what others had to say. If you’ve interpreted my posts in any other way then I apologize for not disclosing. But from now on I’ll disclose all of my posts.</p>
<p>DISCLAIMER: The information contained in this response is probably… (I’m sorry) is DEFINITELY less accurate than Denzera’s response. If you have to choose between our responses, even if they are the same, choose his it’ll be more accurate and serve your needs to a greater extent.</p>
<p>GS_Banding: Sorry for the thread hijack, it’s all yours again.</p>
<p>Thanks for the replies. I’ll try my hand at AM-PDE next semester.</p>
<p>C02, I’m going by ODE classes listed here (E1210, V3027):
[Fall</a> 2008 Subject: Mathematics](<a href=“http://www.columbia.edu/cu/bulletin/uwb/subj/MATH/_Fall2008.html]Fall”>http://www.columbia.edu/cu/bulletin/uwb/subj/MATH/_Fall2008.html)</p>
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<em>laughs</em> ok, clearly i’ve been way too much of a jerk myself.</p>
<p>just understand, we have a lot of random people coming along here every day who decide to post like they know what they’re talking about, and it ends up confusing the prospective students. GS_Banding is more of an old hand, and that’s less of a risk with him. But the next 5 people who ask about how interviews are handled at Columbia may get 5 different answers, unless the actual students/alums here get to the question first. So we’re doing our best on quality control.</p>
<p>While your comment was directionally correct, it wasn’t precisely correct, and those subtleties are mostly what GSB was asking in the first place. A degree is a collection of courses, and between AM and pure Math, a lot of those courses overlap. The difference is in which other classes are required (and which are strongly suggested), rather than the teaching methodology or point-of-view which might emphasize, as you say, “finding the extrema at the sacrifice of math theory”. So in the place of Topology, an AM student might take Statistical Inference, but both are grounded by the prerequisite of the Analysis & Optimization class that both majors require - which is taught emphasizing the same things to both groups, indeed is the very same class. See what I mean?</p>
<p>His original specific question was,
The answer is, only by the teachers who are teaching them, and their particular styles. Linear Algebra covers the same ground, and ODE covers the same ground, regardless of which department it’s in. (that may not be transparently obvious but in my experience it is indeed true). I found Spiegelman to be a much better teacher than, say, Sean T Paul, so I took the AM class. In fact I’m pretty sure they use the same textbook.</p>
<p>I’m picking up what you’re throwing down, I can see how that is obnoxious. I’ve followed the Columbia forum for a few months now and I’ve seen GS_Banding so I know he’s old school.</p>
<p>Yeah, I’m in Speigleman’s lin alg too, which is far far far superior to anything in the English as a second language pure Math teachers your are going to get. If you can get away with taking E3101 in your major, do it.</p>
<p>i feel a bit late to the party here but i have to do this…</p>
<p>SPIEGELMAN IS AWESOME!!</p>
<p>best math teacher i ever had at CU hands down</p>
<p>nice to see denzera finally get riled up …its quite a rarity </p>
<p>also lukejdavis…it would be nice if you sortof introduced yourself so that we would know whether or not you know what you’re talking about (i don’t mean you should tell us your name or anything)…the problem is that alot of HS kids come on the boards and act like they know everything about columbia and start arguing with the students/alums…though you’re obviously not a highschooler being in finance doesn’t qualify you to talk about columbia</p>
<p>Why is everyone big fans of Spiegelman? Just wondering. I actually only went to LinAlg the first day, and didn’t go to any other sessions because I thought the class was incredibly easy and pointless. I ended up having to take the final in his office (must have been a scheduling conflict), and talked him a bit, and he stood out as a genuinely nice guy.</p>