Self-Study Group: Join Now Before Semester Ends!

[Jacobpm64]

Well, I was following a thread about a self-study group, but the op of the thread hardly ever gets online, so I'm wondering if anyone still wants to do this, as my semester is almost over, and I'd have time over the summer to try to study something.

EDIT: I am referring to the post by studious.

 

[djeitnstine]

I remember that thread...

what subjects/level of work are you referring to? I would enjoy an advanced math directed towards engineers and physicist group anytime after finals. That means sans the proofs etc. =]
Just in case anyone is interested topics for that are
PDE's
Fourier series
Navier-stokes equations etc...

 

[Jacobpm64]

i'm a math major/physics minor... That could be interesting for me.

I've had a really basic course in PDE's that just covered like.. finding product solutions of the heat and wave equation.. tackling different boundary conditions and stuff.. also did a little with laplace's equation... and i did a good bit with Fourier series in that course.

However, I'm interesting in whatever.. either pure or applied math.. and getting a heads up on some physics courses... However, I'm more interested in mathematics :)

 

[djeitnstine]

Ok, this is good I'll pm you my info. My interests also lay in learning fluids. Basically I want enough foundation to tackle these extremely hard courses coming up. Although advanced math is not "extremely hard", everything I've heard about the professor is that she makes it hell.

Btw, how would you like to time this? My finals end next week. Also how large would you like this group to be? Would you like to wait for others before we begin...etc. just let me know what's good for you I'm up for anything =]

 

[durt]

I'm down for this. Fluid/continuum mechanics sounds cool, though my interests are pretty broad so anything really is ok with me.

 

[Jacobpm64]

well, i don't know if i wanted to organize it :P

I was hoping the guy "studious" who opped the original post was going to come around more often and be able to take initiative.

However, I mean, we could all just work together.

I'm cool with anything after May 8th. (that's my last day of finals)..

Then i'll have the entire summer to do whatever.

 

[djeitnstine]

well, i don't know if i wanted to organize it :P

I was hoping the guy "studious" who opped the original post was going to come around more often and be able to take initiative.

Ok well if that's the case I guess I can take a stab at organization. I'll do a bit of research to see how we can make this successful. Also I suggest not making the group too large. I have found that large groups can become counterproductive. So let's just work in 'cells' of 5 and just cross reference with other groups (if there is more than one)

 

[Jacobpm64]

i agree with not making the group too large.

Yeah, so, perhaps once you do a little research on how to work this thing out.. we can start talking to people from the other thread and trying to grab more people.

What's your background?

 

[Qubix]

my interest, for the moment, would be quantum mechanics (also interested in classical mechanics , relativity, particle physics).

 

[djeitnstine]

@Jacobpm I'm a Sophomore turning Junior Aerospace Engineering student, concentration propulsion =] at Embry-Riddle

what about yourself?

 

[Jacobpm64]

senior math major/physics minor.

 

[djeitnstine]

Ok good tagging along with you for advanced math should be good then. Just need to keep this thread afloat til we get enough people.

 

[naele]

I'd like to express my interest in a study group and I'm willing to help organize. I'm not quite at the level as both of you. I've taken a full first course in calculus through multivariable/vector analysis. I would be interested in the following subjects: linear algebra, classical mechanics, electrodynamics, elementary real analysis.

Tangentially, if anybody wants to self-study any chemistry topics I'm a senior chemistry major getting ready for the chemistry GREs, so I would be willing to do that as well.

 

[Jacobpm64]

well I'm going to be studying real analysis myself regardless if someone else wants to or not.. I've already bought a book for the summer.. so .. if you want to tlak about it during the summer we can, but i suggest we keep the real analysis out of the main group.. because it seems to be more oriented towards pde's and heavily applied math things.

 

[naele]

Well if there's enough interest I would go ahead and make a separate thread.

 

[djeitnstine]

Ok Jacob and durt both of you seem interested enough. I have found an excellent e-book for advanced math for engineers called "Advanced Engineering Mathematics" by Kreyszig. This book contains many examples and goes through each example thoroughly. I am suggesting that we keep things coherent, thus I am proposing for only those who tag along, each will receive the book from me. Message me and I will send you a copy for evaluation.

If you have any other suggestions for books or alternative methods of working problems or studying, or even object to getting the book just post your ideas and we can work things out =]

Simply send me a PM for a copy.

Also durt what is your background?

PS. I'm still working on an online system that will work for our study group. =]

PPS. To whomever requests this book, please don't request and run. I'd prefer to keep it to those who are actually interested in this group. =D

EDIT: I also forgot to note that the book is application oriented, meaning the problem sets contain many application problems

 

[PhysicalAnomaly]

I am a second year undergrad in australia studying maths and physics. Currently working on real analysis, point-set topology and commutative algebra. Oh and some quantum physics.

I don't have much experience with applied maths (yes, I'm one of those pure snobs). But I would certainly be interested in something on mathematics of fluids if you're doing that. I am rather busy at the moment though and the timing of my semesters will be quite unsynchronised with yours. I think I might have access to Kreyzig but... might I suggest something with more proofs? XD

 

[millitiz]

I hope that it is not too late to join the group right now.
I am a Junior/senior in math and physics. Going to finish Quantum and real analysis this semester, and starting Modern Algebra and Relativity next semester. I am also interested in fluid dynamic.

 

[Qubix]

I am a second year undergrad in australia studying maths and physics. Currently working on real analysis, point-set topology and commutative algebra. Oh and some quantum physics.

Well, I'm a second year undergrad in Romania. But, as I mentioned above, I'm more interested in theoretical physics than pure mathematics. I replied to your post mostly for that "Oh and some quantum physics." part. If you've got some serious interest in quantum physics or classical mechanics, please PM me.

 

[djeitnstine]

I am a second year undergrad in australia studying maths and physics. Currently working on real analysis, point-set topology and commutative algebra. Oh and some quantum physics.

I don't have much experience with applied maths (yes, I'm one of those pure snobs). But I would certainly be interested in something on mathematics of fluids if you're doing that. I am rather busy at the moment though and the timing of my semesters will be quite unsynchronised with yours. I think I might have access to Kreyzig but... might I suggest something with more proofs? XD

:( well you see I'm an engineer so proofs and I do not mix :( the reason why I chose kreyszig is because he stays away from heavy proofing. =\

Ok so far, for fluid dynamics we have militiz and durt

For advanced math (applied) we have durt ,Jacob and Anomaly

is this correct let me know what you think. We'll have to work out the proofing bit because quite frankly as I said before I'm anti-proof...if not we can split groups =\

 

[PhysicalAnomaly]

I would prefer fluids to general applied maths but I'm fine with anything useful. It wouldn't be nice to find myself deficient in applied maths some time in the future when I need it.

Well, we could do proofs when the purer people present material and you can just ignore it. And when the anti-proof ones (boo! =P) present, they could omit proofs (and use plausibility arguments instead? XD).

 

[Jacobpm64]

I agree with anomaly.

Because I'm more interested in the "theory" of DE's and things like that :P... because I've already had a course that was heavy in application (the guy who teaches odes and pdes here is strictly an applied mathematician and doesn't do any proofs).. but i'll help out.. I don't mind :).. anomaly and I can try to be more rigorous on the side..

I'm really cool with whatever... the more knowledge I have, the more useful i'll be to myself and others.

(i'll be bored because most of my summer will consist of just reviewing all the math classes I've had to date.. and being sure i know everything from all of them.. because i may decide to take the math subject gre).

 

[djeitnstine]

Ok this is great, sounds like we'll have an awesome group. DE's with proofing will be fine, as long as I can understand how to do applied problems I'm ok.

Any suggestions as to which book we can use? I can search for some with more proofs or anyone who suggests any would be equally fine.

I had a thought as to how we could make this work, only a suggestion. What we can do is use mathim.com (http://www.mathim.com) because of its excellent use of chatrooms and latex, then have "class" sessions at (a) specific time(s) per week. Each class could be directed by one of us on a specific topic each week or day - that means a rotation of students and 'professors' =]. That way everyone gets a good understanding of the subject. After each session we have a "review" where questions are asked on the previous session's problem set. I have seen many professional online teachers use a similar method (in other areas-not necessarily academia) which has turned out to be very successful - many if not all are paid to have such online sessions.

Edit: I have to mention that this method means that everyone has to prepare their stuff before each session. I imagine this would turn out just like a real class room only you're sitting in front of the computer and you are the "professor for a day".

Let me know what you think.

Allow me to revise the list =]

Fluid dynamics: Djeitnstine, Militiz, Durt, Jacob, Anomaly? Edit: added jacob

Advanced math (applied): Djeitnstine,Durt ,Jacob and Anomaly?

-just to let everyone know I intend to do both of these sessions. so Anomaly which one(s) would you like to do? =]

We still have a few weeks before summer to start so that everyone can have the time to dedicate to this.

 

[Jacobpm64]

Go ahead and throw me in both groups.. I don't know anything about fluid mechanics.. but I've taken introductory calculus-based physics sequence.. and i know a good bit about math.. so i might be able to learn this with everyone's help.

 

[djeitnstine]

Ok you're added, but what do you think of the set up?

 

[Jacobpm64]

oh i poked around on the mathIM deal, and I really like it.

Yeah I think that's a good job. What happens though, if some section is just difficult and a certain person has extreme trouble preparing the talk about it...

or since some people have different backgrounds than others.. it might be more difficult for others.. or really easy for some.. you know?

I guess we just have to help each other out and try not to be overly stressed or anything.

 

[millitiz]

hmm. Mathim looks fantastic.
Well, actually, if there is also a math session (I assume a proof base applied math?), I would also like to join that group (and yea, I am kinda indecisive on the fluid. It doesn't sound as that attractive to me, Maybe I'll wait and see the syllabus first? And the teaching part make me really nervous, because I have basically no knowledge in Statistical Mechanic, fluid dynamic).

As for this, I think one of the ways to solve it is to have some syllabus of a sort, and people could see before hand whether they are capable to teach it. If not, he could switch it with someone else, or somethings like that.

And this'll give rise to some questions, for instance, how do we decide the syllabus?

And how about the "textbook?" It seems like there is a e-book already for the math (btw, I also have a pretty decent applied math e-text by my applied math professor), but how about the fluid? I guess it would probably going to be better if it is an e-book (free would be even better :D), or something like that.

And I think there should be a general agreement on the level. I mean even "Advance Undergraduate level" is a bit vague. And this'll associate with the syllabus, too.

For instance, how much proof should be involved in the teaching of applied math? (upper level of applied math is pretty much like the pure math).

btw, my summer comes a bit latter (maybe not that late?). It'll start from late May.

I am looking forward for it.

 

[djeitnstine]

Thanks militiz I haven't thought about syllabus yet. I should have clarified the "preparing material" part though.

My idea was, everyone gets the same book, preferably with a large problem set, or even supplement it with a book containing a large problem set. We have a set amount of pages/section(s) to read and basically one person presents a summary or a review of the material to the group. If that person does not understand it or had trouble with the material, of course we are a group so we can help each other by answering questions.

Indeed this is self study so not everyone will be able to understand immediately all of the material, but I figured having everyone get a chance to present it to the group would allow persons to bet better at the topic.

As far as a syllabus goes I can collect a few advanced math syllabi for review. But almost needless to say I hoped to cover most of my university's syllabus for preparation of that class.

Here is a summary from the catalog

Advanced Engineering Mathematics I

Line and surface integrals; vector fields with the study of Green, Gauss and Stokes Theorems; Applications of vector field theory; Fourier series.

Edit: Here is for Advanced Engineering Mathematics II, although I will not be taking it, it seems interesting and quite useful

Advanced Engineering Mathematics II (3,0)
The solution of linear differential equations with vari-
able coefficients; study of the derivation, character-
istics, and solutions of partial differential equations;
Fourier series, Fourier transform, Laplace transform,
and Green’s function; applications in science and
engineering.

 

[Jacobpm64]

your Advanced Engineering Math I sounds like our regular Calculus 4.. almost exactly... Although I've only taken calculus 1,2, and 3.. I picked up most of the stuff in Calc 4 along the way in other classes and in physics courses and what not.

But yeah i still haven't messed with divergence and curl and all that jazz.. So It's something i need to learn anyway.

There's a book entitled Div, Grad, Curl, and All That.. lol.. so that might be one to look into... https://www.amazon.com/dp/0393969975/?tag=pfamazon01-20

It supposedly develops vector calculus by looking at problems in electrodynamics, I believe.

So it's heavily application-based.

I also see it on some of the syllabi from MIT physics and engineering courses.. and a supplementary textbook (i guess to help with some of the math stuff if people get tripped up)

 

[djeitnstine]

Hmm this is interesting because I have covered mostly those topics in my previous courses. My professor did a bit of applied stuff with them so I'm no stranger to that subject and its uses.

Heh, it would be great if everyone was on the same page, but I guess that's wishful thinking...

 

[millitiz]

Well, I'll say it is less than wishful thinking though (considering we are not in the same school, or not even in the same country, I hardly believe that we would be on the same page...)
Interesting enough, those are covered in my calc 3 class (and some are in the applied math classes). However, we basically study almost everything again in a more rigorous, proof base class last and this semester (and it is really interesting) :)
For this group, are we basically following and studying the book?
So self-studying in a group?

 

[djeitnstine]

For this group, are we basically following and studying the book?
So self-studying in a group?

That is correct.

 

[millitiz]

hmm, now that I know what it is really like, I am afraid that I couldn't make it (ur, it is a bit unnecessary for me, plus I think that I wouldn't have enough time in the summer).
However, I am planning to study Particle Physics over the summer. But I guess I shouldn't make another sub group here, right? ;)
Djeitnstine, thank you anyway. Please cross my name off from the groups, and I guess Ｉ'll start another new threat on self-study group for particle physics.
And also, would you mind if I borrow your ideas on group studying? They sounds really great and would be a great guide.

 

[djeitnstine]

Sure millitiz, I'm actually happy you found the ideas useful.

 

[djeitnstine]

Re-upping that list:

Fluid dynamics: Djeitnstine, Durt, Jacob, Anomaly?

Advanced math (applied): Djeitnstine,Durt ,Jacob and Anomaly?

 

[PhysicalAnomaly]

First, I would like to point out that I will be quite preoccupied until the 20th of June. Winter break doesn't start till then. I can however still do this though I might be giving fewer lectures than receiving. Also, I haven't had a chance to check your proposed website out but I'm not sure how we'd do this in real time if that's what you're planning since I'm probably over half a day ahead.

I have already been through a course that does grad, div, curl, line and surface integrals and Stokes, Gauss, etc. This wasn't done rigorously but I doubt we'd be doing that here either. I was thinking (hoping?) that we'd all have at least done these topics since they constitute the very basics of undergrad maths, usually taken in 1st or 2nd year. (*sigh*) It would probably be counterproductive to go through all of it in detail, especially since each of you have done some (the ones that the others haven't done XD). We could do a quick run-through...

I was thinking that we'd do topics such as:

Jordan normal form, nilpotent operators, tensors, Hermitian matrices
DE's, finite difference and shooting methods, Laplace transforms, numerical methods in DE's such as WKB and Sturm-Liouville (But no advanced stuff like Sobolev spaces)
Laguerre, Legendre, Airy functions (used in QM)
Brownian motion, random walks, Markov processes, Monte Carlo methods (useful for stats and probability, statistical physics and QM)
Langrangian formulation of mechanics

 

[Jacobpm64]

you have a good list of stuff there anomaly :)

 

[PhysicalAnomaly]

Hmmm... I see one disadvantage of the chatroom - you can't record sessions. It would be nice to be able to in case a member misses a session. Also, it would be nice for revision.

 

[Jacobpm64]

Anomaly, I just typed random math stuff in the chat box in MathIM and copy/pasted it into a microsoft word document. Everything showed up well.

Works fine to me.

 

[millitiz]

I was thinking that we'd do topics such as:

Jordan normal form, nilpotent operators, tensors, Hermitian matrices
DE's, finite difference and shooting methods, Laplace transforms, numerical methods in DE's such as WKB and Sturm-Liouville (But no advanced stuff like Sobolev spaces)
Laguerre, Legendre, Airy functions (used in QM)
Brownian motion, random walks, Markov processes, Monte Carlo methods (useful for stats and probability, statistical physics and QM)
Langrangian formulation of mechanics

Hmm, now I feel very ashamed... I only know half of the listed items, and the other half of them, I either have no idea, or only remotely know/hear of them...
The worst part is that I am already a junior/senior in college, and also major in math/physics...

And if we are talking about proving them... That'll be FASCINATING! (and my quick estimation is that it could take at least an year to thoroughly go over them.)
For instance, there are linear algebra/real analysis, Differential Geometry, ODE, PDE, (Topology is probably needed in some cases) etc. They all worth at least a semester of studying. But even just thinking of it makes me exciting! Proofs, proofs, and more proofs!

Oh well, I doubt if that is ever going to be the case anyway...

 

[PhysicalAnomaly]

I don't know about them but I'll be proving whatever I do (of course, I might have to hand-wave a bit). And yeah, I'm only in my second year. =P But I don't know more than a brief definition of them. Join us. I'll only be doing this very casually - as I said, it will be while my semester is on. In fact, I think we should just start now and do it casually as a long-term hobby. I just don't see how we'll learn stuff well if we rush.

@jacob: Do the symbols appear on word though?

 

[Jacobpm64]

the symbols sure do appear on word.. because MathIM uses the latex code you type.. and makes it into images. Therefore, when you copy and paste the text from the chat window into microsoft word.. You're pasting words.. with images (the math is just like inserting a photo into a word document).

 

[millitiz]

I don't know about them but I'll be proving whatever I do (of course, I might have to hand-wave a bit). And yeah, I'm only in my second year. =P But I don't know more than a brief definition of them. Join us. I'll only be doing this very casually - as I said, it will be while my semester is on. In fact, I think we should just start now and do it casually as a long-term hobby. I just don't see how we'll learn stuff well if we rush.

@jacob: Do the symbols appear on word though?

Hmm, you are confusing me further. I thought this self studying is more on the applicational, engineer-physics type of math (and that was the reason I decided to quit, why, I already know them).
And your listed topics, although some of them are well related, some of them could be a whole field in its own right. And I don't see how it could be done in a summer, if you are thinking of anything of mathematically rigorous.
Let's just pick tensor for an example.
Tensor is in fact, related to differential geometry, or greometry in general.
So to learn tensor, one also need to learn forms. And I think it is also related to Cohomology (I think this is the word?). And since it is "differential" geometry, one also need to learn differentiation, Rienman integration, (possibly Lesbegue integration?). Of course we know how to do differentiation, integration, and what not. But what is differentiation? In what condition can we do differentiation or integration (in fact, this is where lesbegue comes in, if you know it ;D)? And also, one need to know about space, sets, open, closed, compact, etc topology.
Yea, so I am currently learning some differential geom now in an analysis class(?). And use it to prove Stoke's theorem. Needless to say, it is fascinating!
Nonetheless, I can still see that some of them are more narrowed than others, and could be done quickly (or maybe I am just not knowledgeable in those fields?)

But to be honest, except those math nerds like us, I doubt anyone is interested in step into this "mine field."

But then again, we can always make another subgroup. So it kinda depends on how people think about it.

 

[PhysicalAnomaly]

I was thinking that it would be on during semesters as well. Also, the proofs will be presented but not everyone has to understand them. The concepts themselves can be understood (intuitively anyway) without proofs. A lot of those concepts can be learned on their own (assuming basic undergrad applied maths) in the manner that physicists and statisticians do.

And no, the most general form of a tensor is not due to differential geometry. It is an algebraic object along with a multilinear mapping. But we can of course avoid showering applied peeps with 'abstract nonsense' as they'd like to call it and only learn specific tensors as used in civil engineering, relativity, differential geometry, etc. In many ways, these are the things that would be of most benefit to pure mathematicians who don't get a chance to see it in their course (because they're too busy learning about elliptic curves and homologies).

 

[millitiz]

I was thinking that it would be on during semesters as well. Also, the proofs will be presented but not everyone has to understand them. The concepts themselves can be understood (intuitively anyway) without proofs. A lot of those concepts can be learned on their own (assuming basic undergrad applied maths) in the manner that physicists and statisticians do.

Yes, I understand. I was a physics student originally, I totally understand that concepts could be learned and "proved" by hand waving ;).

And no, the most general form of a tensor is not due to differential geometry. It is an algebraic object along with a multilinear mapping. But we can of course avoid showering applied peeps with 'abstract nonsense' as they'd like to call it and only learn specific tensors as used in civil engineering, relativity, differential geometry, etc. In many ways, these are the things that would be of most benefit to pure mathematicians who don't get a chance to see it in their course (because they're too busy learning about elliptic curves and homologies).

Thanks for teaching. As I said, I was a physics students, and didn't think of taking any advance math course until this year. So yea, I guess I don't really have that deep knowledge in math (yet, I hope). But I am going to take modern algebra the coming school year, so I guess I'll learn it then?
And yes, the first(and probably the only time?) I know the tensor is within the context of relativity, where tensor is a map mapping vectors and forms, which then I kinda assume that it is related to Diff Geom. Well, where are the others?

 

[PhysicalAnomaly]

Don't worry, I'm only a second year student and only started on any serious pure maths late last year and early this year. You'll catch up in no time. You probably won't be studying tensors of algebras in a first course in algebra though. The reason I got here so fast is that I didn't take a first course... nor a second.

Yeah, they have k-tensors. I think relativity got their tensors from diff geometry. In civil engineering, they have stress tensors. That probably came straight out of multilinear algebra.

The rest of them are probably busy studying. I'm trying to do 10 questions a day. Which doesn't sound like much but some questions take a few hours of thinking to complete. What about you?

 

[djeitnstine]

Yes, studying for finals has been time consuming. I have the last four between today and tomorrow.

I'll probably end up doing my own self-studying, or perhaps millitiz can help me (with all the engineering/physics application type math) since you guys are on your way to pure math,

However, if some of you are still up for Fluid Dynamics, I'll definitely get involved in that.

 

[millitiz]

10 questions per days! Man, that is a TON of problems. Sometimes I couldn't even figure out A question for hours (I think the worst ones took me for DAYS) :).
Well, actually, I am doing some reading outside classes, but not really a lot (at least not 10 questions per day!), and btw, final is coming.
You see, 4 problems per week is a hell load of homework for our school (both physics and math). And they could easily take four five pages. So 10 problems per DAY is amazing for me :)
(How many trees do you kill per day! XP)

 

[millitiz]

Yes, studying for finals has been time consuming. I have the last four between today and tomorrow.

I'll probably end up doing my own self-studying, or perhaps millitiz can help me (with all the engineering/physics application type math) since you guys are on your way to pure math,

However, if some of you are still up for Fluid Dynamics, I'll definitely get involved in that.

I think Anomaly is suggesting some of the applicational aspects of those topics. And basically no proof involved. Although I do need to admit that the list s/he gave was quite different from what you/I expect...

 

[PhysicalAnomaly]

10 questions per days! Man, that is a TON of problems. Sometimes I couldn't even figure out A question for hours (I think the worst ones took me for DAYS) :).
Well, actually, I am doing some reading outside classes, but not really a lot (at least not 10 questions per day!), and btw, final is coming.
You see, 4 problems per week is a hell load of homework for our school (both physics and math). And they could easily take four five pages. So 10 problems per DAY is amazing for me :)
(How many trees do you kill per day! XP)

I don't always manage ten. And yeah, I only do one or two problems that take me hours/days to do. The rest are half hour/15 min problems. Get a book with hard questions and start cracking? And yeah... erm... I tend to write concisely and squeeze things a bit. I don't write cursive so it's still quite legible. I would like to say that it's elegant and short but I end up cancelling quite a bit and take the long way sometimes. It's only a few pages a day though. I probably kill a small tree per semester (more worried about the ink I use - my father is left wondering why I'm buying pens every other week). ;)

@dj-something: Don't be put off. As millitiz said, it'll be mostly the applied side of it. Even I'm not prepared to study DE's in depth. We'll go over grad, div, curl, Gauss, Kelvin-Stokes, Green first. All the topics I've mentioned are routinely studied by 3rd and 4th year students in engineering, physics and maths. I don't expect everyone to have been through real analysis (though you do have my scorn if you haven't =P).

PS Oh and I've been neglecting physics. It's terrible but maths has consumed my soul. I'm hoping that my maths experience will negate any disadvantage I'll have from neglecting physics. XD