Searching for Credit Options for Partial Differential Equations

[gabe_lane]

Ok so here's my summarized story.

At the end of summer should be the start of my Senior year, but i dropped out and started college a year ago. I taught myself Calc I in two weeks while taking 18 credit hours and CLEPed out of it my first semester and received a 99.4% in Calc II the next semester. I also taught my self Statics in 10 days and received a 100% in it and a 99.3% in Dynamics the next semester. I tell you this so that when I say I've taught my self a course I don't meen I skimmed over it. When I say I've taught myself a class I mean I know it inside and out.

Now recently I just completed an Independent Study of Ordinary Differential Equations through BYU in three weeks with an A+. But now my problem is that DE is the last math course that my college offers, and I'll be attending one more semester here (to finish all of the Physics courses that they offer). So my question is does anyone know of any institutes that offers a online or independent study course in Partial DE? I would ultimately like to just teach it to myself and test out of it, but in most cases, like BYU's independent study, you have to do the entire course homework and quizzes included.

I know an option is to study it myself, and then just retake an actual semester long course in it wherever I transfer to but I severely dislike the idea of retaking an entire course simply based on the preconceived notion that it's impossible to learn by yourself. After all, the textbook really is just a written version of a teacher's oral explanations. I also know MIT has their open course ware, but that's not what I want. I don't need help learning the material, I need a way to credit for it, any way I can. I'll do independent study, online course, test out similar to CLEP exams.

I love to learn, can do so quite quickly, and I love to solve problems. I really don't want to be held back this next semester (as that's why I dropped out of high school in the first place).

Sorry for taking so long. Just any options anyone knows of to credit for Partial DE while attending my current college this next semester would be very much appreciated. Please and thank you.

 

[romsofia]

There is a topic here http://www.quantnet.com/forum/threads/numerical-aanalysis-or-pde-online-courses.3505/ about it (don't know if you've seen it yet).

HOWEVER, you're going to need to teach yourself calculus three (didn't see you mention that) because PDEs are multivarible differential equations, and you're going to need to know know how to do calculus with multivarible functions! I'm going to assume knowledge of linear algebra will be helpful, but I'm taking a PDE course next semester so I can't comment too much on it.

Good luck.

 

[multiphasic]

PDE is an ever evolving discipline. I took it at one university and transferred to another and no one at my current university is familiar with the methods (canonical transformations) we used in my previous course; they use different methods.

Doubt anyone is going to let you self teach yourself PDE. Not sure you would want to either. The courses you mentioned testing out of were basically monkey see monkey do. PDE is not that kind of course. You SHOULD be learning a lot of theory in PDE and you should have no idea what you are doing at the undergraduate level, lol.

The book we used was nearly the size of a calc book (which covers 3 courses) and we of course only touched a small fraction of it.

I know an option is to study it myself, and then just retake an actual semester long course in it wherever I transfer to but I severely dislike the idea of retaking an entire course simply based on the preconceived notion that it's impossible to learn by yourself. After all, the textbook really is just a written version of a teacher's oral explanations.

Don't take my response as another "oh you can't learn it by yourself!" I hardly went to any of my classes for my undergraduate degrees (also quit HS) and completely agree with you for most course work. It's easy to learn on your own and I don't doubt you could learn PDE's on your own; however, you could study PDE's for a month and then take a test that is completely unfamiliar to you because it is a part of PDE you did not study. It's also more likely that you would spend a lot of time studying PDE's and still not understand the techniques, but that's no different from taking the course either. A good professor makes quite a difference in that course.

I think you've tricked yourself into thinking math and science are easy by skimming through a few very basic courses.

 

[gabe_lane]

Thank you both very much, good information. Yeah the only online PDE course is the one through CVN that's five grand so I don't think I'll be taking it anytime soon.

What you said made perfect sense multiphasic. Learning one method and having it be useless at another institute. BUT, I don't think math and science are easy at all, I just want to hurry up and get to where it is hard.

And I would agree with you about skimming through very basic courses except I solved two physics problems that my professor got stuck on a while back and he asked for a copy of my solutions (he has a masters degree in Physics, although he did take the more theoritcal route and the problem was very much just the tricky math.) I also solved a couple math problems that my other proffessor couldn't (he has a bachelors in Physics and a PhD in Engineering) I also solved all of the Putnam exam questions in the Calc book I used. I know I've come no where near the difficult material in mathematics, but I've always been able to solve problems out of the norm, that were beyond 'monkey see monkey do' (this line actually made me laugh I had never heard the expression before). So I have no reason, yet anyways, as to why PDE's would stump me.

So my proffesor just gave me one of his math books from graduate school and said I shouldn't have any problem going through it, its a mathematical methods for physicists book, and that will be what I study this next semester instead. Although no credit will be awared it will be fun to tackle.

Thanks again for your repsonses.

 

[gabe_lane]

So me and my proffesor are trying to find a online institute that offers an online course in mathematical methods for physicists so I can get credit for it haha. I'm having trouble with this one as well

 

[TylerH]

So I have no reason, yet anyways, as to why PDE's would stump me.

I don't know how the book you're using covers it, but it could be a lot more proofy than any of the "monkey" classes. I know my book (can't remember the name, it's a Dover reprint, if that helps) goes into the analysis stuff behind PDEs and reads more like a real analysis or Apostol's calculus book.

You mentioned the Putnam problems, how much experience have you had with proofy math?

 

[gabe_lane]

I have had VERY little if none at all, experience with proofy math. I mean in my elementary linear algebra class ocasionally there was a problem that would say prove such and such thoerm. Most the time it was just algebraicly showing that two different methods were equivilent though.

I was thinking of taking Real Analysis but I heard that was a more graduate level course, (and a hard one at that.)

Would you recommend any books or courses to warm me up to PDE's? I'm just having trouble deciding where to go next. Maybe any online courses I could take that would be beneficial, I plan on majoring in Physics, Mathematics, and Mechanical Engineering (wasn't going to but I fell in love with Dynamics so I have to explore it a little.)

Also I saw a Post-Euclidean Geometry class online, would that be something I could take at this level, or am I going to need more experience with proofs? Link to class below
http://netmath.illinois.edu/courses#402

The sections I'll be studying out of this book my proffesor gave me are
Partial differentiation and multiple integrals (about half review half new stuff)
Fourier series (heard this is really good to study)
Integral transforms (almost all review, but with one or two things added)
Partial Differential Equations (not sure how in-depth it is)
Probability (heard it helps with understanding proofy math)
any classes online that would cover similar material?

Really any direction as to classes I should take now, preferebly ones that can be found online, would be much appreciated.

And again thank you all for the answers already.

 

[snipez90]

Undergraduate real analysis is sometimes considered the rigorous foundation of basic calculus, but you can go much deeper pretty quickly. It's also typically the first proof-based college math course that many people encounter.

The textbook you mentioned sounds a lot like Boas's math methods text. In that case, the PDE treatment you get there is probably very narrow in scope. For instance, Boas' chapter on PDE is mostly confined to the use of separation of variables to tackle finite boundary value problems. Here the prerequisite chapter on Fourier series comes in most handy.

The typical undergrad PDE text will discuss several techniques for solving PDEs, including separation of variables. Integral transforms are extremely useful for solving PDEs defined over infinite intervals. In particular, the Fourier transform is probably single-handedly the most useful tool in tackling linear PDEs.

For an undergrad treatment like Strauss' PDE text, you probably only need to be comfortable with basic multivariable calculus, e.g. partial differentiation, gradient, directional derivative, etc.

Also, I should remind you that the clarity and mathematical sophistication of undergrad topics on wikipedia is extremely high. It's well worth checking out for an overview of the theory and the proofs of basic results.

 

[TylerH]

Also I saw a Post-Euclidean Geometry class online, would that be something I could take at this level, or am I going to need more experience with proofs? Link to class below
http://netmath.illinois.edu/courses#402

It sounds like chapter one would give you a sufficient introduction to the types of proofs you'll be doing in that class. AFAIK, almost all math departments require an intro to proof class as a core class of their math major. The university I've been doing dual enrollment at, Western Carolina, requires it for a math major and for anyone applying for the math masters program.

EDIT: After some research, I can tell you that it is required at UI, and is called Math 347/8 Fundamental Mathematics(http://courses.illinois.edu/cis/2011/spring/catalog/MATH/347.html?skinId=2169). Here's a list of the courses required: http://courses.illinois.edu/cis/2009/fall/programs/undergrad/las/math.html.

Really any direction as to classes I should take now, preferebly ones that can be found online, would be much appreciated.

And again thank you all for the answers already.

I recommend a proof class.

But, have you asked around to see if any of the professors are willing to do an independent study on PDEs with you? Just a hint, but it sounds like you approach independent studies as a way to get though the class with as little unnecessary effort as possible, but I doubt that's very attractive you your prospective professors. Show them you're interested, and let them know you're WILLING to do the work, but believe you can SHOW them it isn't necessary. It also helps to show intense interest in going beyond the course material.
For example, I did an independent study with a group theorist this summer, and we got to spend most of our time on abstract algebra once I showed him I knew all the proof stuff. I convinced him to waste his summer teaching me by convincing him he would enjoy it by getting to cover material he finds fun to explain. You have to appeal to their love for math. Even though, in the beginning, we had agreed that I'd take every quiz and test, in the end, I got an A+ without ever doing either. 1 or 2 proofs, and presenting them to him, was enough to SHOW I didn't need the tests. I can honestly say it was the funnest and most stimulating class I've ever taken.

Interesting coincidence: The professor I did an independent study on proof and logic with over the summer, Tuval Foguel, got his PhD. at UI at UC.

 

[gabe_lane]

To snipez90: Thank you for your advice. Do you know of any real analysis class online?

To TylerH: thanks. Yeah I'm wiling to do the work, (did all the homework, quizzes, and tests through BYU, about 6-10 hours a day just doing the homework and more). My proffesors can't do independent study with me :(, not that their not willing to (my Engineering proffesor already did with a class last semester and my Physics proffesor is this semester) but I'm only at a community college so they can't award credit to anout junior or senior level classes because we don't have them in our curriculum.

My girlfriends dad though (has his PhD in Physics) told me that I might try actually enrolling into another school and asking if they'll do independent study with me. I mean I'd love to actually take these classes, I just love to learn and I've hit the end of the rode here at my college as far as math goes.

I'll give that Post-Euclidean Geometry class a try, thanks for looking at it.

So does anyone know of any online real analysis classes than? I just have a passion for learning like I never thought possible, so I'l study it even if I can't find a class on it, but I'd prefer to get credit. Thanks again everyone for your help

 

[battousai]

Why are you fixated on taking online classes?

 

[gabe_lane]

Because I'm stuck here for another semester, and that's the only way I can get credit for the classes is online or independent study. I don't care whether they're online or not it's just that's my only option for the next semester until I transfer.

 

[hadsed]

Is there nothing else for you to take at your present university? I find it hard to believe that you've gone through all of math *and* physics in just two years... I don't recall that you talked about any physics classes, why don't you take one of those? Then when you transfer, you can really settle in and take a PDEs course.

 

[TylerH]

To snipez90: Thank you for your advice. Do you know of any real analysis class online?

To TylerH: thanks. Yeah I'm wiling to do the work, (did all the homework, quizzes, and tests through BYU, about 6-10 hours a day just doing the homework and more). My proffesors can't do independent study with me :(, not that their not willing to (my Engineering proffesor already did with a class last semester and my Physics proffesor is this semester) but I'm only at a community college so they can't award credit to anout junior or senior level classes because we don't have them in our curriculum.

Oh, I see. I assumed, because the link you gave lead to a subdomain of UI, that you go there.

My girlfriends dad though (has his PhD in Physics) told me that I might try actually enrolling into another school and asking if they'll do independent study with me. I mean I'd love to actually take these classes, I just love to learn and I've hit the end of the rode here at my college as far as math goes.

You may have waited to late to do that. Classes start the 22nd at my uni., and I assume most will start around the same time.

So does anyone know of any online real analysis classes than? I just have a passion for learning like I never thought possible, so I'l study it even if I can't find a class on it, but I'd prefer to get credit.

I SERIOUSLY doubt any college would offer that as an online class. To many struggle in person, and from what I've seen, online classes have worse pass rates than in person.

Harvey Mudd has videos on YouTube of their RA class(), so, if you prefer, you can get the lecture form of the class, but still no credit.

 

[battousai]

Universities, from where I'm at (U.S.), have something called concurrent enrollment, where students from community colleges can take classes at these universities for credit.

 

[gabe_lane]

Is there nothing else for you to take at your present university? I find it hard to believe that you've gone through all of math *and* physics in just two years... I don't recall that you talked about any physics classes, why don't you take one of those? Then when you transfer, you can really settle in and take a PDEs course.

Well I've only been here for one year, and at the end of the next semester I'll have taken all the math *and* physics course, and if I take Thermo all of the engineering classes as well in one and a half years. (I took 18-21 credit hours a semester). Last semester I focused more on engineering and only took one physics class (Engineering physics I, here algebra based phys is call general phys, and calc based phys is called eng. phys). But since I did well enough in Phys I last semester my proffesor is allowing me to take both Engineering physics II and III simaltaniously this next semester (III will be independent study with him).

Thats the problem, is I've already finished all the math classes, and some engieering and physics course, but to of completed all of the phys and eng. courses they offer (which I want to take everything I can to get a strong base) i have to stay here one more semester, which means a whole semester without math which I don't want to do.

 

[gabe_lane]

Oh, I see. I assumed, because the link you gave lead to a subdomain of UI, that you go there.

You may have waited to late to do that. Classes start the 22nd at my uni., and I assume most will start around the same time.

I SERIOUSLY doubt any college would offer that as an online class. To many struggle in person, and from what I've seen, online classes have worse pass rates than in person.

Harvey Mudd has videos on YouTube of their RA class(), so, if you prefer, you can get the lecture form of the class, but still no credit.

Oh yeah that was misleading I apologize, no I'm only attending a community college.

Ah darnet I'm always to late, thanks though.

Ok I saw one place that did real analysis online, University of Pheonix, but they needed five people to enroll and none had, so thanks for letting me know so I don't keep looking for other places that offer it.

Sweet, I'll take a look at those videos. Thanks again for all of your posts on this thread

 

[gabe_lane]

Universities, from where I'm at (U.S.), have something called concurrent enrollment, where students from community colleges can take classes at these universities for credit.

Ok cool I'll look into this. It sounded like Cornell did this but their tuition is over a grand a credit hour, and I'm to broke to do that :)

 

[battousai]

Maybe check with your local public university. Certainly much cheaper than going to a private school.

 

[hadsed]

Well I've only been here for one year, and at the end of the next semester I'll have taken all the math *and* physics course, and if I take Thermo all of the engineering classes as well in one and a half years. (I took 18-21 credit hours a semester). Last semester I focused more on engineering and only took one physics class (Engineering physics I, here algebra based phys is call general phys, and calc based phys is called eng. phys). But since I did well enough in Phys I last semester my proffesor is allowing me to take both Engineering physics II and III simaltaniously this next semester (III will be independent study with him).

Thats the problem, is I've already finished all the math classes, and some engieering and physics course, but to of completed all of the phys and eng. courses they offer (which I want to take everything I can to get a strong base) i have to stay here one more semester, which means a whole semester without math which I don't want to do.

This makes no sense; why does it matter if you finish all of them? I don't recall what your major is, but if you're even thinking about doing any kind of physics or engineering, you're going to have to take as much as you can on the subjects. Taking a bunch of math classes won't help you as much as you think. Even some areas of string theory require completely solid understanding of basic physics, and that is more important than the mathematics.

To me it doesn't make sense why you would give up any physics classes. You should take as many of them as you can, and especially for a class like PDEs, you will have a much easier time understanding them when used in a physical context. In fact, this is really true of most mathematics, unless you're not very conceptually oriented (which is not the case for most physicists I feel like).