ℝolliℵg M∀th Thr∑a∂

Thanks. Just found it here too: http://www.dartmouth.edu/~matc/MathDrama/reading/Hamming.html
Along with :http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html

Top level is here: http://www.dartmouth.edu/~matc/MathDrama/reading.html The Geometry in Art and Architecture link looks really nice.

OK, that was well worth reading. Thanks, guys.

we should do reading group some time. my greatest regret is not having taken a course in complex analysis.

Took me much longer than I would have liked to grok what was going on in that subject. btw, did you see the thing in Vanity Fair about the guy who reverse engineered device Jan Vermeer used to paint his masterpieces?

like "girl with a pearl earring"?

Yes, only the one that he reproduced was The Music Lesson.

I linked it on some art thread where I don't think anyone looked at it but I'll put it here too: http://www.vanityfair.com/culture/2013/11/vermeer-secret-tool-mirrors-lenses

Anyway most important thing about complex variable

this is the book i wanna read

http://usf.usfca.edu/vca//vca.jpg

Things:
Assumption that the derivative of a function does not depend on the direction you are coming from is a pretty strong one which is why analytic functions have so many things you can say about them.

Function log z can't be defined without branch cut and related fact that integral 1/z on a loop is non-zero

You spend a lot of time switching back and forth from complex variables to rectangular coordinates to polar coordinates.

Have a copy somewhere. It's pretty nice, spends more time trying to generate intuition than most.

Just came across notes on branch cuts by my advisor's advisor: http://math.mit.edu/classes/18.305/Notes/n00Branch_Points_B_Cuts.pdf

heh, a prof in my dept wrote a 1200 page, 2 volume book on the complex logarithm

Really? Who was that?

http://ebooks.cambridge.org/content/978/05/1156/619/6/9780511566196i.jpg

they're enormous

Visual Complex Analysis is terrific (especially if you haven’t been exposed to Michael Spivak’s Calculus or “Baby Rudin”)!

Book club?

http://www.madore.org/~david/math/hyperbolic-maze.html

super down for a book club. would have to start after finals tho

I’d participate!

I started reading the recently published Computability: Turing, Gödel, Church and Beyond edited by Copeland, Posy, and Shagrir. It’s a servant of all. But so far, so good. Especially enjoyed Martin Davis’ essay, “Computability and Arithmetic.” It explores Hilary Putnam and Yuri Matiyasevich’s work on Hilbert’s tenth in a comprehensible way.

super down for a book club. would have to start after finals tho

Good luck!

by servant of all you mean written for a too-general audience?

and thanks!

not sure how much brain i have to tackle another math topic at the moment, but i'm for a reading group as a general notion and i'd try to follow along a bit at least.

i started skimming along the complex analysis stuff and not-incorrectly thought "fibration" so i'm glad i'm building some intuitions.

re. that computability volume, a, uh, friend of mine has to write a review of it pretty soon, so any tips on what worked/didn't from your point of view would be appreciated (my friend hasn't started reading the book yet but the review is overdue, story of his life)

http://i.imgur.com/gxC8u1S.png

why do they schedule exams at 9am? who can even think that early?

http://math.berkeley.edu/~wu/AMS_COE_2011.pdf

Professional development (PD) for in-service math teachers is
generally taken to be \feel-good sessions". Some believe that its
main goal is to give teachers encouragement and sharpen their
pedagogical skills.
Others believe that teachers should be exposed to fun mathematics
(such as the Konigsberg bridge problem or taxicab geometry),
even in the face of their inability to deal with bread-and-butter issues
such as how to teach fractions, why negative times negative
is positive, what similarity means, or why the parallel postulate
is important.

anyone want to take a stab at 'why negative times negative is positive'? seems like a good one.

because negative divided by positive is negative.

i think algebraically it follows from that

"what is division?" is a good problem that i think i've raised on this board before. does 20/4 = 5 mean that if we divide 20 into 4 parts each part is 5 units large, or if we divide 20 into parts that are 4 units large we get 5 parts?

or how about this: if multiplication is defined as repeated addition, then multiplication by a negative is repeated subtraction, and subtracting a negative is obviously positive

"If any single quantity is marked either with the sign + or the sign - without affecting some other quantity, the mark will have no meaning or significance, thus if it be said that the square of -5, or the product of -5 into -5, is equal to +25, such an assertion must either signify no more than 5 times 5 is equal to 25 without any regard for the signs, or it must be mere nonsense or unintelligible jargon."

Baron Maseres otm

Use complex numbers. Rotation twice by 180 degrees is the identity

LOL imo if you're using complex numbers to justify arithmetic you've won the battle but lost the war

Well, take out the complex numbers but keep the argument.

or how about this: if multiplication is defined as repeated addition, then multiplication by a negative is repeated subtraction, and subtracting a negative is obviously positive

― the late great, 11. december 2013 00:48 (1 hour ago) Bookmark Flag Post Permalink

This isn't logical, right? Surely -5 - -5 5 times is +20?

that's because what you just described is -5 - (-5) - (-5) - (-5) - (-5) - (-5), no?

should i say subtracting a negative is the same as adding?

tbh i don't completely understand the objection frederick

Seems there are plenty of ways a mathematician could convince himself of why it has to be but not clear what is the most obvious common sense explanation for the layperson.

Actually I might have an idea. But there is not enough room to write it in the margin of this thread.

Oh, I get it. You're right. My fault.

you can just do basic arithmetic on the integers as an additive group, just teach your kids group theory ;-)

for division i guess you either need a euclidean ring or a fullblown division ring, in which case division is just multiplication by inverses

If you believe -1 x a is -a, then -1 x -1 is -(-1), and negative negative 1 is plainly 1.

But once you believe -1 x -1 = 1, I think you believe that a negative times a negative is a positive in general.

elegant

we had to prove all this bullshit in my first real analysis class, to give the impression of "rigour"--but we didn't even construct the real numbers (using dedekind cuts, etc), just stated the Completeness property as an axium--such a waste of time

Think it might be useful to think of multiplication as making a copy or n copies of something to replace the thing and multiplication by -1 as making an inverted copy. So say you have a white disk than multiplying by -1 you replace it with a black disk and vice versa, or better yet you have an Othello token and just flip it over.