0 Talk

Paul September

Forwarded Message -----
From: "Philip Liplip Vuong" <pvuong@stanford.edu>
To: "Paul Ponmattam" <windshrike@gmail.com>
Sent: Sunday, September 26, 2010 3:39:47 AM
Subject: P.207 #2

Merry xmas:

http://www.youtube.com/watch?v=JGZylXfoSzg

http://www.youtube.com/watch?v=C8Tpv97gqt0

http://www.youtube.com/watch?v=dokzGDphquA

Forwarded Message -----
From: "Philip Liplip Vuong" <pvuong@stanford.edu>
To: "Paul Ponmattam" <windshrike@gmail.com>
Sent: Saturday, September 25, 2010 3:14:06 AM
Subject: Fwd: Mentorship of a high school student

Dude, for the record, if you were one school grade lower, I would have also tried to find you a mentorship. I still can, but I do not know how much work you can get done before you leave for college.

Forwarded Message -----
From: "Richard Guy" <rkg@cpsc.ucalgary.ca>
To: "Philip Liplip Vuong" <pvuong@stanford.edu>
Cc: rkg@math.ucalgary.ca
Sent: Saturday, September 25, 2010 1:39:36 AM
Subject: Re: Mentorship of a high school student

Philip,
I would be happy to see Julian at any time.
My email is rkg@cpsc.ucalgary.ca
My office number is 403-220-6314. R.

On Fri, 24 Sep 2010, Philip Liplip Vuong wrote:

> Dear Professor Guy,
>
> Hi, my name is Philip Vuong, a graduate of Stanford's undergraduate abstract math program, and I would like to ask if you can please help in finding a mentor for a student I've taught at Stanford's Number Theory camp. Julian Salzasar, a Calgary student entering his 10th grade of high school, is one of the brightest students I have ever met. He is naturally smart: even though he did not know proofs on the first day, he instantly understood every concept and succeeded in proving (beautifully) some of the class' most difficult theorems. Moreover, he is a hard worker who is passionate about mathematics: for the entire camp, he has sacrificed all his leisure hours doing extra-curricular proofs and material with me. Even now he is learning additional mathematics from me and doing proofs for fun.
>
> However, I fear that the high school education system will neither help him in his proof skills nor challenge him. Also, my job in Taiwan prevents me from devoting the necessary time to teaching Julian. Thus, I would like to find someone at the University of Calgary willing to foster his abilities and guide him in his studies.
>
> Currently, he is familiar with basic proofs and concepts (e.g. contradiction, induction, equivalence relations, bijections), introductory number theory and applications(e.g. FTA, congruences, Euler's Theorem, Pick's Theorem, Farey Sequences, Conway's Rational Tangles), introductory group theory (e.g. Cauchy's Theorem, Lagrange Theorem, dihedral, permutation, and R_p groups, isomorphisms, and quotient groups) and some elementary set theory (e.g. diagonalization process, basic cardinality, extensionality, Russell's paradox). An example of some of his group theory studies is at (attached as images):
>
> http://mathdojo.wikia.com/wiki/Julian_Homework_1
> http://mathdojo.wikia.com/wiki/Julian_Homework_2
> http://mathdojo.wikia.com/wiki/Julian_Homework_3
> (he is still working on homework 4 and 5).
>
>
> Although I know that the University of Calgary math department is very busy, do you know any faculty members or graduate students that are generous and willing enough to meet with him, perhaps on a weekly basis, and talk with him about mathematics? It would mean so much to me if you can find someone to meet with him even for an hour. I am sure if you talk to Julian for just an hour, you will realize the potential that he has.
>
>
> Thank you very much for your time,
>
> Sincerely,
> Philip Vuong
>
>
>
> P.S. I am glad that I finally found an article like your paper, "The Law of Small Numbers." Thank you!!! I finally have a list of examples where patterns eventually break down: I posted them on my door to spite my humanities and science housemates. I've also memorized example 13 in case I get into heated arguments involving "proof" by finite testing.
>
>
>

Original Message -----
From: "Paul Ponmattam" < windshrike@gmail.com >
To: "Philip Liplip Vuong" < pvuong@stanford.edu >

Sent: Tuesday, September 21, 2010 11:20:11 AM
Subject: Re: Schedule

should we try to have the meeting later, say tomorrow at the same time, if its not working?

On Mon, Sep 20, 2010 at 10:59 PM, Paul Ponmattam < windshrike@gmail.com > wrote:

On Mon, Sep 20, 2010 at 10:14 PM, Philip Liplip Vuong < pvuong@stanford.edu > wrote:

3.5

Original Message -----
From: "Paul Ponmattam" < windshrike@gmail.com >
To: "Philip Liplip Vuong" < pvuong@stanford.edu >

Sent: Tuesday, September 21, 2010 7:42:03 AM
Subject: Re: Schedule

954 296 8706
but do you mean 11pm tonight(as in 3.5 hours from now) or 11pm tomorrow night?

I'm fine with the Df(x y) = 0 for a critical point etc, but what I really seem to be having trouble with is setting the problems up like #2 on p207
I set it up, then found the jacobian but I couldn't find solutions for Df(x y) = 0 except at x=y=z=0, which is the minimum solution I think(volume 0),
so either my factoring abilities suck or I messed up the setup.

On Mon, Sep 20, 2010 at 2:13 PM, Philip Liplip Vuong < pvuong@stanford.edu > wrote:

Btw, I am calling you at 11PM your time (what is your number again?). If you would like to rearrange this for another day, please let me know.

Original Message -----
From: "Philip Liplip Vuong" < pvuong@stanford.edu >
To: "Paul Ponmattam" < windshrike@gmail.com >

Sent: Monday, September 20, 2010 3:30:02 PM
Subject: Re: Schedule

I wanted to save the extremun problems until Leon Simon's analysis notes so that we can go over compactness. But...how to find max and mins are incredibly important. Even though you may not get the proofs, you may be able to get the problems and some sort of intuition. Sure, you should definitely do the extremun problems. As for 2nd derivatie test and lagrange multipliers, they are (especially the lagrange multipliers) incredibly important (though I wish I can teach you eigenvalues first). Definitely do them to you heart's content : ).

Integration is not easy.

I have no class to teach until the afternoon, evening. I think I can remember to wake up at 11AM to give you a skype call. Forgot your number though. How about my tomorrow 11AM?

GREAT IDEA for the class. Btw, great minds think alike: I will forward you a class I am introducing to the EDGE school's curriculum.

No worry about the files: I prefer higher quality above size, so don't be afraid to supersize.

Btw, posted 3 videos for the last two homework questions.

http://www.youtube.com/watch?v=8Y7fjcAtR2g
http://www.youtube.com/watch?v=vJRMr5xx7sA
http://www.youtube.com/watch?v=pCCpQA3dT5I

Forwarded Message -----
From: "Paul Ponmattam" <windshrike@gmail.com>
To: "Philip Liplip Vuong" <pvuong@stanford.edu>
Sent: Thursday, September 16, 2010 11:11:02 AM
Subject: Re: Schedule

Hey Philip,
So I did most of PSet 5, i didnt get 6 or 17a.
6 (on page 143) I'm pretty sure is just the 4d cross product, but I didnt get one thing. You know how when you take determinants, the signs for each value in the matrix change? Like in a 4x4, it would be

+ - + -
+ - + -
+ - + -
+ - + -

So when I take the determinant of the 3x3 in the lower right, for that determinant do I use the
- + -
- + -
- + -

from the 4x4, or do i use the

+ - +
- + -
+ - +

thats for a standalone 3x3?

Okay so other things:
Leon Simon did send me the handouts, but not just the handouts.
He sent me a whole pdf copy of his 'Intro to Multivariable Mathematics' ( I attached it in case you want me to work out of that instead of Shifrin)

So I'm not sure what to put in the wiki b/c we haven't really had meeting lately, and youve put up most of the things before that, so should I just start putting the email logs/scans so far on there?
I saw what you said about studying for the GRE's, and I was going to suggest a meeting soon b/c we haven't had one in a while, but in light of the GRE's, just let me know when you'll be free again.

I'm pretty sure that tomorrow I'll be free to complete PSet 5 (Linear algebra 2):p.168 4a,5,6,7,8, 14a,b,c, p.221, 2, 3a, b, 4a, 5, 6., so hopefully I'll have that in by then.

Is least squares necessary? I'm a little anxious to start integration, but if its really important, then ok

I watched the videos, they were awesome, and I'm pretty happy you didn't make me try and get the adding 0 thing on my own, that might've taken a while, I get that proof now.

Hm I feel like I'm forgetting something, but I'm not sure what it is, so thats all for now I guess

On Sun, Sep 5, 2010 at 3:05 PM, Philip Liplip Vuong < pvuong@stanford.edu > wrote:

3. Good! You should distinguish that the delta associated with f(x)'s epsilon need not be the same associated with h(x)'s epsilon, but then again, we can always choose the smaller delta as the fixed delta. You got the key step (the hint), just be sure to rewrite in ||(g(x)-l||< epsilon for ||x-a||< delta form in the last step.

4. Multiplication....I remember this tricky bastard. One of the best moments of my life is when I realized this super unintuitive trick (took me about a week). Add zero: ||k(x)f(x)-cl|||= ||k(x)f(x)-k(x)l+k(x)l-cl|| Now use triangle inequality in a smart way along with the given epsilon limits.

Physics...read rest later...3AM.

Forwarded Message -----
From: "Philip Liplip Vuong" <pvuong@stanford.edu>
To: "Paul Ponmattam" <windshrike@gmail.com>
Sent: Sunday, September 12, 2010 12:13:02 AM
Subject: Ne hao mah!

Decided to demonstrate question 4 since it is very pretty and not obvious:

http://www.youtube.com/watch?v=a-CpIK6UuWI
http://www.youtube.com/watch?v=NhVwHHBby_g

Most of stuff setup/settled into job so I can go back into working on the dojo. Up for Skype meeting?

Also, do not worry if you can only get a few problems/not all of them. As long as you ask me questions about the material and understand it, then you are getting the material. Some questions, like #4, on hindsight, is unfair (adding some magic term and applying ideas behind compactness theorem even though it was not yet taught in that chapter). By the way, did Leon Simon ever respond?

Original Message -----
From: "Philip Liplip Vuong" < pvuong@stanford.edu >
To: "Paul Ponmattam" < windshrike@gmail.com >
Sent: Thursday, September 2, 2010 9:59:13 PM
Subject: Re: Schedule

Whoops forgot to answer other question:

I will be teaching, typically, from 4pm to 9pm (so 4am to 9 am your time) on weekdays and at worse, 9am to 5pm weekends (pretty sweet teaching deal until grad school). Anytime, except those hours are doable.

Original Message -----
From: "Paul Ponmattam" < windshrike@gmail.com >
To: "Philip Liplip Vuong" < pvuong@stanford.edu >
Sent: Thursday, September 2, 2010 11:27:50 AM
Subject: Re: Schedule

Hi Philip,
Sorry bout the last couple weeks, I got sidetracked for a short time, but then my life got taken over by the 900 or so pages of summer reading I had to do, but thats over now.

So I kept working on the epsilon-delta stuff you gave me before, I did #3(attached) and failed to get #4(also attached), I'll start doing #5/#9 tomorrow then.
I also did 1-4 from the curves PSet(attached), but I only really got 11B so far, I'll keep working on those to finish all the problems in the revised PSets.

Oh I also emailed Leon Simon today, and should I edit the meetings on the gmail calendar, or start editing them on the wiki? Or both

The time difference is 12 hours I think, so if I call you at 11 at night like the meetings have been that won't be a problem, or will you be tutoring then?

On Tue, Aug 31, 2010 at 8:22 PM, Philip Liplip Vuong < pvuong@stanford.edu > wrote:

Hey Paul,

If you can get the majority of the following work done, then you will have a complete Freshman semester worth (derivatives and linear algebra) of Multivariable calculus:

Pset 3:
p.79 1, 2, 3, 4, 5, 9.

Pset 4 (Curves): p .117, 1, 2, 3, 4, 7a, 8b,11

PSet 5 (Linear algebra): p .142, 2, 3a, 4 (must know for real world), 5, 6, 17. p.155, 2a, b. 3a, 3b, 4,

PSet 5 (Linear algebra 2):p.168 4a,5,6,7,8, 14a,b,c, p.221, 2, 3a, b, 4a, 5, 6.

PSet 6（Linear Algebra 3: Least squares, skip to 5.5. Least squares is one of the greatest achievements in applied mathematics, right after the simplex method): 1, 2, 3, 4, 5, 7, 8, 12, 13, 14.

PSet 7 (Intro integration and Linear Agebra 4) p.273, 1, 2, 3, 4., p.421 1,2,3,4, 7

PSet 8 (Eigenvalues): p.433, 1a, b, i, 3, 4, 5, 6 , 13.
Cool applications: Using diagonalization and 6a, find [1 -1; 1 1] raised to the 2525 power. Finally, to complete the entire freshman first quarter, rewrite example 2 on p.438, which is an eigenvalue proof which is an alternative to Dana's proof.

I will send you a phone number once I set up Skype today.

Forwarded Message -----
From: "Philip Liplip Vuong" <pvuong@stanford.edu>
To: "Paul Ponmattam" <windshrike@gmail.com>
Sent: Monday, September 6, 2010 3:05:32 AM
Subject: Re: Schedule

Physics...read rest later...3AM.

Original Message -----
From: "Philip Liplip Vuong" <pvuong@stanford.edu>
To: "Paul Ponmattam" <windshrike@gmail.com>
Sent: Thursday, September 2, 2010 9:59:13 PM
Subject: Re: Schedule

Whoops forgot to answer other question:

Original Message -----
From: "Paul Ponmattam" <windshrike@gmail.com>
To: "Philip Liplip Vuong" <pvuong@stanford.edu>
Sent: Thursday, September 2, 2010 11:27:50 AM
Subject: Re: Schedule