Calculus after AP Calc?

Pre-College Issues High School Life
1

<p>Hi,</p>

<p>I just finished sophomore year, and next year, I was thinking about taking Calculus III and IV at Columbia. This year, I took AP Calculus in school, Linear Algebra online and I will take an Electricity and Magnetism (post - AP) class this summer at Columbia. However, my courseload next year is already going to be hard (I think), so for those of you who have dual enrolled/taken Multivariable or Differential Equations, what is the workload like? Is the material really hard to learn?</p>

<p>Also, would Calc III/IV look better than any of the classes I'm taking next year? Should I drop an AP to make time for this evening class?</p>

<p>Honors English 11
AP Government
AP French
AP Chemistry
AP Computer Science
AP Statistics
AP US History
AP Literature </p>

<p>Thank you SO much :)</p>

2

<p>I think Calc III/IV would make a much stronger application than AP Statistics. We’ve got a good group of kids in my school every year who finish Calc BC as juniors … the ones who are celebrating the end of a year of misery sign up for AP Statistics, and the ones who actually want to learn more math take the joint enrollment college calculus course thing offered by our school. You can guess which one’ll look more impressive :P</p>

<p>Anyway, I can’t say anything about Columbia, but we do distance learning with Georgia Tech at our school and everybody says it was much easier than AP Calculus. Then again, the caliber of students at GT isn’t exactly on par with Columbia, haha.</p>

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<p>The workload for college classes isn’t that great, though it does take up a chunk of your time in the evening.</p>

4

<p>That’s true. I could save Calc III/IV for senior year, but I would really prefer not to. AP Statistics is a good GPA boost, but maybe I could self-study for the exam and focus on my other classes? Would you say all the classes are doable? Especially junior year? </p>

<p>Thank you notamushroom :P</p>

5

<p>I self-studied AP Stats. Definitely doable.</p>

<p>The kids at my school who feel the need to go beyond BC Calc do a dual enrollment thing with NC State. I would say it’s much more productive than a year of AP Stats. I’m doing that. We’ll see how it goes.</p>

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<p>AP Stat is very basic</p>

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<p>@TCBH: Do you have any experience with multivariable? Is it as hard as its name :p</p>

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<p>I’m taking it right now. We’ve gone through 3-D coordinates, vectors, and cross/dot product.</p>

<p>I don’t think it’s much more complicated than single variable.</p>

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<p>@gcf101: haha I like your tags :slight_smile: If you have any advice since you love math :P</p>

<p>Thanks TCBH :slight_smile: Congratulations on UCLA, it’s a great school!</p>

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<p>I have been placed in Algebra 1 in 6th grade when I moved to America. I just followed the progression, with a little acceleration on my own and I finished Multivariable by the end of Sophomore year summer.</p>

<p>Multivariable is VERY different from the stuff you have learned. But since you have taken Linear Algebra, it shouldn’t be so much of a challenge since you have learned a lot of knowledge regarding vector manipulations. Basically you get into a lot of different integrals that doesn’t find “area under a curve” but defined differently. Calculus 3 is much more applicable, looks much more complicated and fun, if you like math. </p>

<p>Material hard to learn? Well if you have lined up like 8 AP classes, you are definitely not a dumb person. There isn’t any math that’s hard to learn, it just takes time to absorb. Calculus 3 is very straightforward if you have a good instructor. </p>

<p>After the 3 basic calculi, you progression would pretty much look like:</p>

<p>Ordinary differential equations -> Linear Algebra (but you know this) -> Complex variable -> Numerical analysis -> Partial differential equations -> Stochastic processes</p>

<p>That’s the engineering math side. Pure math gets weird, stuff like modern algebra, rings fields and groups. </p>

<p>That’s just my experience.</p>

11

<p>@TCBH</p>

<p>You haven’t seen anything yet. Wait until you get to line integrals, then more intense line integrals. Eventually Green’s and Stokes theorem. </p>

<p>I take you haven’t done double/trip/quad integrals yet. Those are really similar to what you learned in normal calculus except you just integrate something with different respect to several variables, several times.</p>

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<p>Thanks kidwithshirt! your advice and progression is really helpful. I like math (thinking about physics/math dual major), so hopefully Calculus III will be kind of fun. :P</p>

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<p>If you like math, especially going on a physics path, why don’t you use your summer and read over some Ordinary differential equations stuff? I just took the class at my local U. and it was a complete waste of time. I could have read the material in a week and a half, instead of suffering through waking up 6am in the morning and a dreaded test twice a week. </p>

<p>EDIT: I forgot to mention that Ordinary differential equations only requires the knowledge of series, a little bit differentiating with respect to x and y, i.e df/dx df/dy. Most people have studied this in Calc BC. </p>

<p>What you basically do in ODE is you get to solve things like d2y/dx^2+dy/dx+10y=cos(x) for y. You get something similar to (y=Acos(x)+Bsin(x)+xcos(x) (not the real answer, just made it up). And it’s kind of interesting you get a first and second order derivative added together in one equation and solve for the original y.</p>

<p>I have a ton of examples of ODE’s applications. After ODE, you can go on to Partial differential equations, with which you could really start to model things about real life. A lot of fluid dynamics stuff is based on differential equations, from fluid dynamics you get a lot of branched applications, like aerodynamics (air is fluid). It’s interesting that economics and human behavior is close to fluid dynamics (traffic theories).</p>

<p>There’s a ton you can do! Don’t like stupid AP Calc tests ruin your experience with math. Remembering integrals isn’t everything.</p>

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<p>Hmm. This summer I’m doing Linear Algebra and taking sort of a post-AP Physics class with calculus, but I would like to get ahead and learn more. With Ordinary Differential Equations, what books would you recommend? Do you have any recommendations for Multivariable also? It sounds really interesting. </p>

<p>Are you an international student then? Have you applied to college yet? </p>

<p>Thank you! :)</p>

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<p>

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<p>Oh I know, we’ve only had two lectures so far. Actually the class I’m taking right now is only the 1st quarter of MV Calc.</p>

<p>No integrals until the class I’m taking in the fall.</p>

<p>EDIT: I also took Differential Equations, and I agree that it’s not the most exciting class.</p>

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<p>Glad there is some one interested in math. There is too much negative stigma attached to liking math, but I have handled it well since I don’t even take math in my school anymore =D</p>

<p>Have I misread you, that you haven’t taken Linear? If so, put it off until you took ODE.</p>

<p>I had been recommended a ton of textbooks for this stuff. Basically when you get to math at this level, there are two types of textbooks: one that shows you how to do the problems, and one that shows you why you are doing it (applications). </p>

<p>I would love to take the latter approach, which teaches based on a discovering process, much like reinventing the wheel, then the axles, then build a car. </p>

<p>Have you heard of the MIT online course program? They have a lot of free class notes. But for basic math classes they have video lectures, which is awfully cool. I found this with a buddy a couple weeks ago and we were just going to listen to linear algebra lectures. </p>

<p>This is the “most viewed” page. You will see ODE and linear on the top courses.
[Free</a> Online MIT Course Materials | Most Visited Courses | MIT OpenCourseWare](<a href=“http://ocw.mit.edu/OcwWeb/web/courses/visits/index.htm]Free”>http://ocw.mit.edu/OcwWeb/web/courses/visits/index.htm)</p>

<p>If you have itunes, you can find all the lectures through “iTunes U.” I downloaded all of them at once with my U.'s fast internet. </p>

<p>Books? I used a traditional textbook. But after taking the class the consensus is that textbooks suck. You need to read treatise and writings of mathematicians who “gets it.” They show you what the hell you just learned instead of learning strange methods to solve problems, which you don’t understand what the importance is.</p>

<p>I was recommended with this:
[Amazon.com:</a> Ordinary Differential Equations: Morris Tenenbaum, Harry Pollard: Books](<a href=“http://www.amazon.com/Ordinary-Differential-Equations-Morris-Tenenbaum/dp/0486649407]Amazon.com:”>http://www.amazon.com/Ordinary-Differential-Equations-Morris-Tenenbaum/dp/0486649407)</p>

<p>Just a side note. It is really EASY to learn math on your own. It’s not like a history or bio class in which you must memorize a lot. In reality you can go through a lot of these courses in a week or so, with absorbing 80% of the material (which is good, because think about how much you remember about Euler’s method right now? Not that much. But you still get the big picture of calculus). Why I say this is because you don’t have homeworks and tests bogging you down. Practicing is just not a part of my learning philosophy. I think getting the theory down is enough, because eventually you are going to use softwares and other aids. You just have to know what typing in a command means, instead of blindly copy and pasting letters and alphabets.</p>

<p>My friend and I counted it and it’s very possible to get a math major in a summer, getting the material down at least, without the certification or accredation, also excluding the thesis.</p>

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<p>@TCBH</p>

<p>Hmm how did you skip to ODE? The class I took had Multivariable as a requirement. Although I do have to admit there is nothing on multivariable except using partial differentiation for a tiny bit.</p>

<p>I am gearing up for stochastic process, which means I have to pump through linear, complex variable, and partial differential equations.</p>

<p>You get to see really pretty pictures in the end. Plus you use it with the stocks market. Let the money roll.</p>

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<p>MV wasn’t a requirement. I did have to learn a little partial differentiation, but that’s nothing difficult.</p>

<p>I’m trying to get ahead for this:</p>

<p>[Scholars</a> Program](<a href=“Undergraduate Program | UCLA Department of Mathematics”>Undergraduate Program | UCLA Department of Mathematics)</p>

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<p>I’m almost done with taking Linear Algebra now, I have about a month left. </p>

<p>I’ve heard of MIT’s Open Courseware but I’ve used it more for physics. I’ll look at it more for math, especially ODE. </p>

<p>I definitely understand what you mean about learning math with application. It adds a whole new light to it and makes it seem so much more real and interesting. </p>

<p>If you have any other advice, please let me know. I’m sort of new to all of this :)</p>