ℝolliℵg M∀th Thr∑a∂

maybe

maybe not

:-(

http://math.stackexchange.com/questions/1220953/a-difficult-integral?stw=2

Enjoyed both those problems from a month ago.

Do you guys know the formula for generating Pythagorean triples?

yeah, a^2 + b^2 = c^2

That is the equation they must satisfy, yes, but there is a simple way to generate the integral trios (a,b,c) that will work.

The way I learned to derive it in high school used number theory 101 but there is also a geometric demonstration I just came across.

i saw it in a geometry summer course but don't remember. care to demonstrate?

attempt some putnam problems: http://kskedlaya.org/putnam-archive/2014.pdf

a friend gave me the statement of a top-secret combinatorics theorem he proved. can't share the deets but it's so elementary i couldn't believe it wasn't already done or a special case of something else. been fudging my way through a proof all weekend

gotta check those untranslated soviet math textbooks for those things iirc

I never did contest math in HS and I'm still only at best a fake fake mathematician (i.e. a programmer who actually enjoyed theoretical CS classes) so Putnam problems just seem unattainable to me

there was a putnam prep class at my undergrad you could sit in on, mostly just watching in disbelief as the prof, a hyper-intense russian graph theorist, crushed every problem in a matter of seconds

http://jwilson.coe.uga.edu/emt668/emat6680.f99/challen/proof/proof.html

Proof by calculus: "This proof requires calculus, so we'll skip it."

otm

Archimedes frowns.

hint to flopson: use stereographic projection.

Thanks to caek's post here: academic language is often purposely obfuscated I read Timothy Gower's Mathematics: A Very Short Introduction a while back, which blew my mind as some kind of masterpiece of popularization, which eventually led me to the Princeton Companion To Mathematics which he addeds and sort of takes the same spirit and enlarges it a thousand-fold with tons of useful explanations of advanced mathematical subjects without diverging into the usual bifurcation of either oversimplification + dodgy metaphors or too much technical detail.

Of course, it is kind of a different thing not a popularization.

Well that's now on my mental wishlist

Maybe you are near a library that has it?

lol the first copy i stole from the internet still has editorial markup in its margins

PUP: Tim would
like to keep
‘brackets’ as even
he, as a
mathematician,
would say
‘brackets’ rather
than the more
formal
‘parentheses’. OK?

i never call them parentheses in math

In addition to referring to the class of all types of brackets, the unqualified word bracket is most commonly used to refer to a specific type of bracket. In modern American usage this is usually the square bracket and in modern British usage this is usually the parenthesis.

"addeds" should be "edited" of course.

speaking of popular mathematics, has anybody read courant's "what is mathematics?"

my dad swears by it, was wondering if anybody here could give it a thumbs up or down

for comparison, last two pop math books i read were morris kline's "mathematics for the non-mathematician" and stewart's "concepts of modern mathematics" (ian, not james)

Mega thumbs up for Courant and Robbins, and for Gowers. Not for Kline or Stewart.

Wazzabout Geometry and the Imagination, Hilbert and Cohn-Vossen?

obv a classic

i enjoyed both kline and stewart, though i ultimately felt stewart lacked depth. kline was a little dry, i guess

They're not super well-informed, that's all.

You might enjoy Plato's Ghost?

damn, too late for a PIDMAS joke

what do you mean, euler?

"plato's ghost" sounds great!

Wow, lot's of rave reviews for Plato's Ghost on Amazon, including yours.

I just mean that Kline esp didn't know his stuff very well.

Plato's Ghost is fun! but haha a uh friend of mine is quoted about it by the publisher on the Amazon page. positive quote

xp eek

Hm. NYPL has Plato' Ghost but it is completely different book.

Plato' Ghost must haunt me now

my kids thought it was a scary book when they were littler. we had to hide it

that VSI is kind of a miracle. every other VSI (including the cosmology one) is shoddy or cursory or biased or otherwise weird. but that is afaict an effective, readable and serious introduction to professional higher mathematics. and it's like 50 pages. i should definitely take a look at his princeton companion.

the more traditional NPR pop maths book i liked most recently (i.e. published in the last 10 years) was zero: biography of a dangerous idea. good book.

Some are better than others. The one on Galileo has a strange angle to push, one on Newton is pretty good I think.

Maybe you are near a library that has it?

― Lemmy Cauchemar (James Redd and the Blecchs), Saturday, May 16, 2015 11:41 AM (3 hours ago) Bookmark Flag Post Permalink

work for UW now so I can abuse my library privileges for it I guess.

Newton one was written by head of the Newton Project.

Author of Galileo book was no slouch either, although now I can see the book was not written to be a short course.

Of the little pop math I've read recently, I liked Ekeland's "Mathematics and the Unexpected".

I just read the VSI on antisemitism and it was very weird, more a history of the Holocaust than anything, but it had a couple of outstanding chapters that made it worthwhile. gonna read the german philosophy volume next.

that was just about the VSI series. obligatory math content: Mathematics Under the Nazis by Sanford Segal is fascinating

the german philosophy one is just a reprint of an old scruton book iirc, would give it a pass

was looking at one by Andrew Bowie ?

who I don't know, but I want some guidance on where to start with german idealism re. the rise of German anti-semitism in particular

oh, it seems they've replaced the old one i read then

Have always seen those Morris Kline books about, never read one. This other guy Carl B. Boyer looks like he might be good though