ℝolliℵg M∀th Thr∑a∂

lol i was gonna say, i just search for 'grothendieck' and then

j. wrote this on thread ℝolliℵg M∀th Thr∑a∂ on board I Love Everything on Jun 30, 2014
every time i want to find this thread i just search for 'grothendieck'

O_0 i think this is the start of something

Has the Grothendieck prime come up on this thread yet?

What is relation between sheaf and tangent bundle? Aka How do I shot sheaf?

ack. the general notion of a sheaf i understand only through general abstract nonsense. a tangent bundle involves differential geometry or generalized smooth spaces or something, which gets dangerously close to actual numbers and spaces. i'm of no help there.

You toss it iirc

http://www.heideland-games.de/files/12-06-30_strohsackhochwurf3.jpg

pictured: mirror universe in orbit

Sterling, you got some phase planing to do!

Sorry

http://cdni.wired.co.uk/674x281/g_j/Issey_1.jpg

https://www.youtube.com/watch?v=BJ7_fFABc9s

Sterling, you got some phase planing to do!

― The Wu-Tang Declan (James Redd and the Blecchs), Sunday, August 31, 2014 9:12 PM Bookmark Flag Post Permalink

by this you mean you want me to explain my phrases more clearly?

No, just making a bad joke.

this is 100% a stupid question but still.

I used to be really good at maths in school, didn't carry it on to university, but recently I've got the urge to take it up again. I play a lot of numerical puzzles and things but I really want to do problems and spend time trying to work things out again. Yeah, I know that's embarrassing. Anyway, are there such things as maths books for adults that you can buy that have problems and examples etc or would I just be better off picking up secondary school books?

I used to be really good at maths in school, didn't carry it on to university, but recently I've got the urge to take it up again. I play a lot of numerical puzzles and things but I really want to do problems and spend time trying to work things out again. Yeah, I know that's embarrassing. Anyway, are there such things as maths books for adults that you can buy that have problems and examples etc or would I just be better off picking up secondary school books?

Yes! I recommend Strogatz's books:

http://www.amazon.com/gp/product/0544105850/ref=pd_lpo_sbs_dp_ss_1?pf_rd_p=1535523722&pf_rd_s=lpo-top-stripe-1&pf_rd_t=201&pf_rd_i=0691150389&pf_rd_m=ATVPDKIKX0DER&pf_rd_r=17CZ8R5ZTVM1NJ77SRYC

A terrific introduction to mathematics. It starts with arithmetic and ends with calculus and abstract algebra. His writing is terrific, regardless of subject.

http://www.amazon.com/Calculus-Friendship-Teacher-Student-Corresponding/dp/0691150389/ref=sr_1_1?s=books&ie=UTF8&qid=1410292988&sr=1-1&keywords=calculus+of+friendship

Is also very good. The problems within illustrate the usefulness of calculus.

Textbooks are trickier. Are you familiar with algebra or trigonometry?

Yes, both. Trigonometry was actually one of my favourite parts of the course. I'm really more after textbooks rather than books on the topic, but thank you for the recommendations.

Word. I love http://www.amazon.com/Calculus-4th-Michael-Spivak/dp/0914098918. Take it slow. :D

Whiplash of nostalgia on seeing the book front on Amazon, though mine must've been an earlier edition (as it was 20+ years ago).

Just this weekend got back into redoing my Masters from that time, which was in algorithmics so a few levels below sterling's. But so satisfying to work out an equation for "What are the points equidistant to these two points and this line", and see an set of clattering clauses snap into a simpler form.

Only have little Spivak.

You know, Calculus on Manifolds

I actually ended up folding and buying an advanced secondary school maths book BUT I have wishlisted that recommendation for later, I don't want to get into it and find I can't do any of it and then get discouraged...so thank you for the rec, much appreciated!

yeah I have discouraged myself on various occasions since graduating trying to sit down and do random math problems from The Art of Computer Programming almost completely cold.

TAOCP is my favorite non-analysis analysis textbook. Concrete Mathematics has some fun problems too.

Song about topology:
https://www.youtube.com/watch?v=chh78JcKfoA

gyac, if you have a good university bookstore or used bookstore in a college area around, you might browse through their dover books selection and see if there's anything to your liking on a given topic. many dover books are old textbooks picked up and reprinted by the publisher, and there are several that try to be inviting in among the fairly hard-nosed coursebooks (especially considering that older textbooks were a lot less hand-holdy).

^^^otm

Think even B&N has some Dover books on the shelves. Used to actually be a Dover bookstore in an office building on Lower Broadway. You could just go to the virtual store: http://store.doverpublications.com/

In addition to the maths book you might also want to pick up http://store.doverpublications.com/0486783405.html

Hello dere

spent the evening perusing the works of shinichi mochizuki

http://cdn.tokyotimes.com/wp-content/uploads/2013/02/abc-conjecture-300x2001.jpg

http://www.heidelberg-laureate-forum.org/de/laureate/alexander-grothendieck/

dudes

Wow.

But what about his prime?

Who Is Alexander Grothendieck?

^must read

Also: http://www.ams.org/notices/200409/fea-grothendieck-part1.pdf

http://www.kurims.kyoto-u.ac.jp/~motizuki/top-english.html

http://projectwordsworth.com/the-paradox-of-the-proof/

^^ more than a year old, sorry

Interesting.

Keep meaning to post this:
https://www.youtube.com/watch?v=chh78JcKfoA

Here are two Dover books I found quite useful and readable:

Advanced Calculus, by David V. Widder
Introduction to Partial Differential Equations with Applications, by E. C. Zachmanoglou, Dale W. Thoe
Mathematics of Classical and Quantum Physics by Frederick W. Byron, Jr. and Robert W. Fuller

And here are some Springer-Verlag Undergraduate Texts in Mathematics that I found readable and useful:
Finite-Dimensional Vector Spaces, by Paul R. Halmos
Linear Algebra: An Introduction to Abstract Mathematics, by Robert J. Valenza
Groups and Symmetry, by M.A. Armstrong
Basic Topology, by M.A. Armstrong

Add to the latter list
Transformation Geometry: An Introduction to Symmetry, by George E. Martin

Wow, I guess these Springer Undergraduate books cost almost twice as much as when I bought them. Guess I shouldn't be surprised.

Much discussion about whether this is actually a 2014 photo of Grothendieck but general feeling seems to be yes:

http://www.heidelberg-laureate-forum.org/de/laureate/alexander-grothendieck/

Is he going to be part of an upcoming Os Mutantes reunion in that getup?

Oh, I get it, those are his monastic vestments.

someone explain the monty hall problem to me please. i just read this

http://mathforum.org/dr.math/faq/faq.monty.hall.html

and it SORT of made sense, but at the bottom the guy gives an example of a 1000-door problem, saying that if monty shows 998 goats, your chance of finding the car out of the final 2 doors is 999/1000 if you switch. this just seems like it cannot be right. doesn't that assume that monty has no knowledge of where the car is?

wait i think i get it now

Monty does know.

it's not a 50/50 at the end because you still have the 1/1000 chance of guessing right originally. since the host shows you 998 goats, the remaining door HAS to have the car if you didn't guess right at the beginning. and the odds of you not guessing right at the beginning are 999/1000

that was fun

You got it

I just tried to write out a game-theoretic interpretation, and then I tried to apply Bayes' theorem, but I got stuck on both of those.

but yeah rly the answer is "because Bayes' theorem is true"

you got it anyway though, hooray!

monty hall is deep and subtle