EPGY's Multivariable Calc

InquilineKea · April 12, 2007, 1:16am

Computational is similar to Calc BC. It means more problem solving and less in the way of theorems/proofs. EPGY splits the course into two, but judging from the syllabus, it doesn't appear that they really go into multivariable calculus in depth - partial derivatives come at the 34th lecture, so the real calculus part of the course doesn't even constitute half of the differential multivariable calculus course. The textbook is also a computational textbook

Also, Harvard Extension's textbook is Multivariable Calculus: Concepts and Contexts, 3rd Ed. by James Stewart. Yes, this is computational. Anything by James Stewart is computational. Check out the Amazon.com reviews as well

<a href="http://www.amazon.com/Multivariable-Calculus-Enriching-Interactive-Skillbuilder/dp/0534410049/ref=pd_bbs_2/002-2344579-3569667?ie=UTF8&s=books&qid=1176355137&sr=8-2%5B/url%5D">http://www.amazon.com/Multivariable-Calculus-Enriching-Interactive-Skillbuilder/dp/0534410049/ref=pd_bbs_2/002-2344579-3569667?ie=UTF8&s=books&qid=1176355137&sr=8-2</a>

==
Computational isn't always bad. Theoretical proof-based math takes up more time and demands you to get used to the style of the math. If you're pressed for time and aren't hardcore into math, the computational style is advisable

vin2l · April 12, 2007, 7:05am

But if I take BOTH MV differential and MV intergral from EPGY, wouldn't I get far more depth than the Harvard Extension version, and wouldn't I be far more likely to get credit?

InquilineKea · April 12, 2007, 7:26am

[quote]
But if I take BOTH MV differential and MV intergral from EPGY, wouldn't I get far more depth than the Harvard Extension version, and wouldn't I be far more likely to get credit?

[/quote]

2 years ago, I read that most Ivies don't take credit for EPGY courses. Stanford does, however. There is no equivalent of both MV differential and integral calculus in most universities - since multivariable calculus is very rarely split into two just like it is in EPGY (though I'd double check to make sure - I haven't perused the course catalogs of many universities). So you would get the same credit with a single course at another institution, or with both courses at EPGY (assuming that the university in question takes the transfer credit).

From the posts above, we see that people are managing to procrastinate the course to the few weeks before it ends. Surely, it would be quite difficult to catch up on a course that has a lot of depth.

Computational courses rarely come with depth.

It's also important to emphasize that "depth" in a course mostly comes from a student's own self-initiative. The best way to pursue depth is by doing more problems, not by relying on a course.

Also, what is your goal? Is it credit? (if so, what universities do you want to go into?) Or is it to show colleges that you're pursuing math further than Calculus BC + to pursue math more extensively through college?

<a href="http://www.stanford.edu/dept/registrar/bulletin/bulletin06-07/pdf/Math.pdf%5B/url%5D">http://www.stanford.edu/dept/registrar/bulletin/bulletin06-07/pdf/Math.pdf</a>

Okay, the reason why EPGY splits multivariable into two is to follow Stanford's model. Note that Stanford's Honors math program has one course for multivariable, whereas the regular students have to take two such courses. Note also that Stanford's Math 51a is called "differential multivariable calculus and linear algebra".

==
<a href="http://epgy.stanford.edu/courses/math/M52A/lectsums.pdf%5B/url%5D">http://epgy.stanford.edu/courses/math/M52A/lectsums.pdf</a>

Note that partial derivatives starts at lecture 35. Look at how discrete each lecture is. There isn't much depth.

Here's the lecture demo:
<a href="http://epgy.stanford.edu/courses/math/M52A/M52Alecture.html%5B/url%5D">http://epgy.stanford.edu/courses/math/M52A/M52Alecture.html</a>

I was astonished to see how easy the lecture demos were. The abstract algebra and real analysis ones were especially easy for their level. I could easily understand them with a Calc BC background.

InquilineKea · April 12, 2007, 12:43pm

So EPGY splits multivariable and integral into 2 - that doesn't seem to be too much of a problem as long as your parents are willing to pay for two multivariable courses.

The Harvard extension course is one lecture every week, for 2 hours. It's highly unlikely that you'll get that much depth out of the lectures. Neither of the courses are very much in-depth. They're both survey courses that do their job in giving you credit. At least you'll learn material in a similar way as you've learned Calc BC.

I've heard varying reviews of EGPY. Some get good instructors, some get very unresponsive ones.

==

Harvard Extension:
Dates:
Sept 20 - Jan 17

===

EPGY:
Each course is scheduled to take approximately 15 weeks to complete, although students may progress more quickly if they wish. Each course must be completed within 6 months of the student's official start-date for that course.

===
CTY:
<a href="http://cty.jhu.edu/cde/math/courses/multivariable.html%5B/url%5D">http://cty.jhu.edu/cde/math/courses/multivariable.html</a>

Individually Paced
Course Length: Typically 6 months

CTY uses James Stewart. My CTY geometry course didn't have lectures - it just had instructor help sessions.

==

The question is - do you think you need help? Or do you just want the credit?

===
Tuition:

MATH E-21a Multivariable Calculus (11648)
(Website) (Print View)
Robert Winters, PhD, Visiting Assistant Professor of Mathematics, Wellesley College.
Course tuition: noncredit and undergraduate credit $650, graduate credit $1,575.
Wednesday, Sept. 20, 7:35-9:35 pm, Harvard Hall, Room 202. Optional sections to be arranged. Fall term

<pre><code>This course covers the following topics: calculus of functions of several variables; vectors and vector-valued functions; parameterized curves and surfaces; vector fields; partial derivatives and gradients; optimization; method of Lagrange multipliers; integration over regions in R? and R?; integration over curves and surfaces; Green's theorem, Stokes's theorem, divergence theorem. Graduate-credit students complete additional computer-related or other projects consistent with the course material and their backgrounds. Prerequisites: MATH E-16, or the equivalent and general familiarity with computer use; placement test is recommended. (4 credits)
</code></pre>

EPGY:

M52A Multivariable Differential Calculus $740 Fixed-Term Two Quarters
M52B Multivariable Integral Calculus $555 Fixed-Term Two Quarters

740 + 555 = $1295

CTY:
Individually Paced Courses: Tuition for individually paced courses in math, computer science, and science (below the AP level) is based on the amount of time selected. Students who complete a course with seven or more business days remaining in their enrollment may use the extra time to begin another individually paced course. Students who have not completed their course when their enrollment time ends may re-enroll for more time.

<pre><code>3 months tuition $ 610
6 months tuition $1145
9 months tuition $1740
</code></pre>

InquilineKea · April 12, 2007, 12:56pm

Wow, Harvard Extension the cheapest?!?! Harvard SSP is so expensive, yet Harvard Extension isn't that expensive at all!

Generally, it should take ~ 6 months to complete. You should e-mail EPGY about how students choose to pursue differential + integral multivariable calculus (and how long they generally complete both courses). 2 quarters is pretty much equivalent to 6 months.

As for rigor, all three should be computational and non-rigorous. With respect to Harvard Extension, you get classroom interaction. Whether you desire that or not, is up to your personal preferences.

==
On a side note, CTY courses do not issue grades (unless things have changed since I last took them). This makes it effectively impossible for you to substitute CTY credit in for college credit. EPGY apparently does (<a href="http://epgy.stanford.edu/policyguide.html)%5B/url%5D">http://epgy.stanford.edu/policyguide.html)</a>. Harvard Extension credit may be substitutable for more colleges (but you'll have to e-mail people at the universities you're interested in to know whether such universities would really accept such transfer credit or not).

==

As a final recommendation, EPGY probably would be best. You can complete EPGY courses as quickly as you would like (so then you can register for integral multivariable calculus). As far as depth is concerned, none of them are particularly in depth - if you want depth - it's best to pursue it yourself by doing additional problems.

UNLESS

You want credit for college and the college you want to go to does not take EPGY credit (but takes Harvard Extension credit)

freeflyer · April 13, 2007, 12:06am

wow thanks everyone. you guys are hardcore.

anyway, i think i'm doing EPGY - i like its flexibility.

InquilineKea · April 13, 2007, 2:02am

On the other hand though, this may be more optimal for you:
<a href="http://www.collegeconfidential.com/cgi-bin/discus/show.cgi?8/81881%5B/url%5D">http://www.collegeconfidential.com/cgi-bin/discus/show.cgi?8/81881</a>

<a href="http://talk.collegeconfidential.com/archive/index.php/t-22179.html%5B/url%5D">http://talk.collegeconfidential.com/archive/index.php/t-22179.html</a>

See the recommendation of texas137 (the program through U-Texas).

Maximum flexibility, no need to take two different multivariable courses. Again, there is the issue of credit transfer.

<h1>LIST OF EPGY/Multivariable Calculus RELATED LINKS:</h1>

InquilineKea · April 13, 2007, 2:28am

Edit: criples, I didn't realize that the link by texas137 is now broken... =/.

mochamaven · April 13, 2007, 3:30pm

omg, EPGY BARELY gets into multivariable calc...2/3 of the course is vector algebra.

InquilineKea · April 13, 2007, 11:40pm

Vector algebra is actually quite important in multivariable calculus though. If you don't get it, a lot of the stuff in multivariable can be confusing. If you do get it (and well), the rest of computational multivariable calculus can be a cakewalk.

Problem being, that too many people procrastinate while they're still on the vector algebra. =P

mochamaven · April 27, 2007, 3:39pm

I would really really urge against taking this class...most people in my school (including me) who have taken it have not been too thrilled.

iostream · April 27, 2007, 10:55pm

yeah, the reasons why epgy blows have been enumerated several times. if you go the self-study route (which i recommend you do if you don't have access to a quality university math program that isn't going to be silly about prerequisites), i like this book: <a href="http://www.amazon.com/Vector-Calculus-Linear-Algebra-Differential/dp/0130414085/ref=pd_bbs_sr_1/102-9133948-8724120?ie=UTF8&s=books&qid=1177728690&sr=8-1%5B/url%5D">http://www.amazon.com/Vector-Calculus-Linear-Algebra-Differential/dp/0130414085/ref=pd_bbs_sr_1/102-9133948-8724120?ie=UTF8&s=books&qid=1177728690&sr=8-1</a>

hubbard's treatment of linear algebra is nice, but for a more formal treatment, axler's pretty much the bomb: <a href="http://www.amazon.com/Linear-Algebra-Right-Sheldon-Axler/dp/0387982582/ref=pd_bbs_sr_1/102-9133948-8724120?ie=UTF8&s=books&qid=1177728860&sr=1-1%5B/url%5D">http://www.amazon.com/Linear-Algebra-Right-Sheldon-Axler/dp/0387982582/ref=pd_bbs_sr_1/102-9133948-8724120?ie=UTF8&s=books&qid=1177728860&sr=1-1</a>

and after you're done with those:
<a href="http://www.amazon.com/Calculus-Manifolds-Approach-Classical-Theorems/dp/0805390219/ref=si3_rdr_bb_product/102-9133948-8724120%5B/url%5D">http://www.amazon.com/Calculus-Manifolds-Approach-Classical-Theorems/dp/0805390219/ref=si3_rdr_bb_product/102-9133948-8724120</a>

also, don't limit yourself to analysis. you may find other regions of mathematics more rewarding.

ChaosTheory · July 3, 2007, 6:03pm

I'm going to bump this up.

I need to take all of my math classes online and my school will provide credit for them. Obviously, MVC from EPGY isn't regarded very highly, but how about CTY's MVC? How about EPGY's Linear Algebra vs. CTY's Linear Algebra? Most of my knowledge will come from self-studying, so I'm looking for the more decent of the two. After that, what are your impressions on EPGY's Diff. EQ, Partial Diff. EQ, Real Analysis, Complex Analysis, and Point-Set Topology? Are they decent? I don't expect to actually learn much from them [after my experience with CTY's BC Calculus :D], but I get credit for it from my school.

Right now, here are some of the books I have:

Apostol's Calculus Volume I and II
Rudin's Real and Complex Analysis
Shilov's Real and Complex Analysis
Shilov's Linear Algebra [I'm steering away from it at the moment because I'm not very fond of determinants :p]
Axler's Linear Algebra [leaning more towards this one at the moment; an interesting approach]
Apostol's Mathematical Analysis
Topology by Hocking and Young
Topology by Munkres
Introduction to Topology and Modern Analysis by Simmons
Linear Algebra by Hoffman and Kunze
Abstract Algebra by Deskins
Ordinary Differential Equations by Arnold
Ordinary Differential Equations by Hartman
Elements of Linear and Abstract Algebra by Connell
Linear Algebra by Beezer
Advanced Modern Algebra by Rotman
Applied Linear Algebra and Matrix Analysis by Shores

As you can see, I have a fairly good library to draw from, so I will be mostly be self-studying. Right now, I think CTY might be better for MVC and Linear Algebra. Are there any other places I can take MVC and Linear Algebra online? How about the courses beyond?

iostream · July 3, 2007, 6:08pm

axler linear algebra is the bomb. for serious, i love that book. probably should supplement it with a more normal linalg book just so you know gram-schmidt and other numerical methods if you plan to test out of it anywhere.

ChaosTheory · July 3, 2007, 6:11pm

Yes, Axler's writing style is very clear. Shilov's, however, is more dense. I presume it's a result of the Russian translation.

Howard Anton's Linear Algebra, perhaps? It seems to be a more traditional book.

InquilineKea · July 3, 2007, 6:50pm

CTY isn't good. It's graded pass/fail (if I can recall correctly) and does not treat the material particularly rigorously at all. Hell, it didn't assign the hardest problems from my geometry textbook.

And take a look at the textbooks it uses. Most of the textbooks are the easiest textbooks for the particular courses at hand. EPGY's courses also uses the easiest textbooks at hand - Ross is pretty much THE EASIEST Real Analysis book you can get

CTY is only good for showing accreditation. But the fact is - the only decent courses that you can get without accreditation are the ones taught in the HONORS tracks of high-level universities.

==

And on linear algebra - it really depends on your style. (do you like clear explanations? Clear problems?). Do you want full elaboration? (even on the parts that less intelligent students are likely to miss?) You could even try one textbook for explanations and one for problems.

==
Also, care to give me the link of where you got the textbooks from? I don't have a lot of the ones you have.

ChaosTheory · July 3, 2007, 7:04pm

I think that in general, the rigor of online courses is highly dependent on your instructor. In my BC class, all of the quizzes were online and the tests were posted beforehand.

In any case, I'll probably have to go with CTY's MVC, due to the price tag on Stanford's. Both seem to be fairly similar instructional-wise, so I might just go with the cheaper one [CTY] for Linear Algebra. :D I won't be able to attend a college to take these classes due to transportation issues.

At the moment, I'm complementing Axler with Shilov; the former rarely uses determinants, while Shilov starts off with determinants and uses them throughout the book. I like Axler for now.

I'll PM you the links.

InquilineKea · July 3, 2007, 7:07pm

Think of it in terms of the market system.

People want diplomas. People hear about the system through other sources. People are risk-averse.

They do not want to take a course that they have a substantial chance of failing in.

Also, since there will be people all over the 99th percentile taking it, there will be a WIDE spectrum of abilities (those are the people who hear of CTY and EPGY - both will get a lot of those students). People in the 99th percentile include people who would fail a theoretical mathematics course (hell most Ivy League students in the non-theoretical math courses are probably at the 99th percentile) and people who actually would get something out of a theoretical math course and IMO medalists.

Hell - most of the students taking those courses just want a transcript boost. I know lots of people who took calculus in 10th grade (and of course they got A's LOLZ) who couldn't even qualify for the AIME (and who really aren't that smart - though some people do fail to qualify due to lack of practice)

The instruction you get online really won't make much of a difference. Hell, CTY courses don't even have instruction.

Holy **** - a linear algebra book that starts out with determinants?

ChaosTheory · July 3, 2007, 7:08pm

Yep, determinants start on page 5. :D

It looks like I'll just go with the cheapest options and primarily self-study the subjects. I'm assuming the higher math classes at EPGY are similar to the rest, unless anyone has had any experience and is willing to share.

Earthquake · July 6, 2007, 4:27pm

Linear algebra is useless like multivariable calculus. I did not take either of them and I went straight into Differential equations. This other girl, who is a graduated senior did the exact same thing. My school had taught us a great background in calculus, thus it was easy. I took a placement test for differential equations and I passed. I know linear algebra and multivariable calculus without ever formally learning them in school.

You should not think about price. It is pertinent that you think about choosing EPGY because the multivariable calculus for CTY was recently introduced. Howvever, EPGY has had multivariable calculus for many years; experience outweighs money.

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