ℝolliℵg M∀th Thr∑a∂

i know there are at least a couple mathematicians in the building. do mathematicians have anything cool to talk about? would be fun to hear about what research ppl are doing, or did in past lives, what courses people are taking or teaching, books we're reading, problems we're stuck on etc

i'm in my last year of undergrad program in pure math right now, currently taking general & alebraic topology (with a total madman who looks like this http://upload.wikimedia.org/wikipedia/commons/thumb/2/25/Daniel_Wise.jpg/220px-Daniel_Wise.jpg), real/functional analysis, and probability. kind of toying with the idea of pursuing grad school. i've taken a couple grad courses so far & they've gone down pretty smoothly, and there are a lot of opportunities to teach math at CEGEP (2 year mandatory pre-university program) and a masters degree is the only requirement. buuuut idk. currently applying for funding to do some research in geometry & topology with a postdoc this upcoming summer. will be spending this weekend trying to understand automorphism groups of covering spaces ^_^

We could discuss whether there is a satisfying proof for the Nilsson Conjecture.

my own contribution: why does well-being look like this?

xp never heard of it!

viz 1 is the loneliest number

oh lol -_-

exactly

i am a dormant mathematician

xp now you have ammunition for chatting up a mathematrix at your next conference

i teach math

cool! how is it?

high school?

yes. prealgebra through AP calculus. it never fails to surprise me how much easier it is to teach "hard math" than it is to teach "easy math"

i'm teaching logic right now, to the least academically prepared students i've ever taught (it's not a huge difference, but it's significant), and that seems to be otm.

the extra complement of math that people generally take to get into a university, even if it stops right at or just before calculus, does seem to make a huge difference in terms of experience, comfort, confidence, mastery of working with forms and symbols.

How are we supposed to search for this thread title?

Somebody pointed out recently that the Notices of the AMS are online and free which is great for people like me who are not in academia anymore and don't get a paper copy. Been meaning to read through the article on Beethoven's Metronome: http://www.ams.org/notices/201309/rnoti-p1146.pdf

Also recently bought a copy of Best Writing on Mathematics 2012 which is very nice and pitched at a similar level, the article on Math and Music was very interesting, written by a guy who is both a practicing musician and research mathematician.

mathematical dorks should be able to remember 98225

thats an elegant number

Yes!
225 is square of 15. (Which you can remember as fact in itself or as exemplar of (10 + x)^2 = 100 + 20x + x^2.
98 is multiple of 7 and figures in the decimal expansion of 1/7 if you think about it.

you are ridic

Let's see if I can do this:
100 = 2 mod 7 so 100^3 = 8 mod 7, 100^3 =10^6 = 1 mod 7 so 7 should repeat with 6 digits
1/7 = 7/49 = 14/98 = .14 * 100/98 = .14 * 1 /(1.0 - 0.02) = .14 * ( 1.0 + .02 + .0004 + ...) = .14285(6+1)..

currently participating in a seminar on homotopy type theory and learning the rudiments of algebraic topology. been spending time with v/a Theory and Applications of Categories reprints.

Really? Where?

the seminar? at the cuny grad center http://nylogic.org/homotopy-type-theory-reading-group

didn't realize that someone else on the board would have an interest in this!

Are you enrolled in any kind of graduate program at CUNY or elsewhere? What about the other people in the seminar?

the seminar is open to the public, like lots of cuny things actually. i'd say its only about 30% people with any current relation to NYU, grad students included. v/a former students/phds, as well as just a cross-section of ppl currently just employed but with a math background, as well as maybe students at other campuses.

we're meeting in the eves biweekly to make it feasible for people who work

Thanks. By NYU I assume you mean CUNY or CCNY, although there are probably people from NYU there too.

Also how long does it go for: two hours,

oh yes by nyu i meant cuny. goes about 1.5 hrs and then some people go off to the pub afterwards for however long. there's a google group too https://groups.google.com/forum/#!forum/hott-nyc

whats yr maths background and how does it bring you to HoTT?

'how did you first know christ?'

pretty much

constructivism had that flavor

How are we supposed to search for this thread title?

yeah sorry, had that thought while making the thread but couldnt resist lol. bookmark it, i guess?

s clover we should def homotope it up itt, stoked. what books are you reading? my course is based on munkres (<3) but prof is doing some additional topics, so far i've only looked at hatcher... it's all very intense, though. i slayed point-set but algebraic topo makes me feel v dumb

had some halfbaked thoughts while hi the other day about some group theoryish intepretation of (basic) music theory. trying to figure out how to make like, arpeggios/chords subgroups of keys/scales?? i don't know enough group theory tho

Don't have much background in this area per se, but have some background in math in general, was on the math team in junior high and then at the Bronx High School of Science, undergrad degree in math at Yale and graduate degree from NYU. First professor I had Freshman year was topologist William S. Massey, at graduate school I took the topology course from Sylvain C, but it was kind of easy and I didn't really learnd too much and most of NYU is about applied math anyway. Actually guy who wrote that music and math paper did a post-doc in topology at NYU, now he is at Lehman College. Sort of curious about this topic but more importantly like the idea that it is free and of being on an equal footing with the other students, other people not currently in academia but presumably mathematically literate - have toyed with idea of going back to finish (start?) thesis and get PhD now that my advisor is the chair but don't really want to deal with have to crank out research-level material, plus I didn't always like the Eloi vs. Morlocks setup of formal grad school, as I recently discussed with former ilxor Casuistry.

I don't know how much higher math you really use to understand music or music theory, the article I was talking about basically says that he thinks a lot of mathematical research on music is sort of bogus, drawing a picture or creating blinking lights that sort of looks like what music is doing. To him the most interesting thing seemed to be the way the similar processes of collaboration jazz improvisation and mathematical research.

i teach high school math but im an econ undergraduate and yall are simply adding fuel to the fire that rages inside me that i shd not be teaching math

plus I didn't always like the Eloi vs. Morlocks setup of formal grad school,

what does this mean?

xp would u rather be teaching econ? my first major was in econ, then i was like ah fuck it and turned my math minor into a full major

The few mathematical ideas I use to think about music are:
*Thinking about the twelve semitones as the Abelian group Z12. (supposed to be a subscript)
*Looking for least common multiples when counting out polyrhythms
*Realizing that the names of the intervals are Ordinal Numbers and
*Realizing that sometimes there are Fencepost Problems in either counting out beats or even in that the octave is the same as the one, which is why some people talk about a heptatonic scale

*Thinking about the twelve semitones as the Abelian group Z12. (supposed to be a subscript)

yeah this was basically the extent of my ruminations lol

well hey you know

http://en.wikipedia.org/wiki/Set_theory_%28music%29

Fully funded PhD student with good background (perhaps trained abroad) and famous advisor, who can sail through qualifyings, has good chance of helping advisor push out papers and securing post-doc and just generally burnishing his legacy = Eloi
Rest = Morlocks

hmm, in the humanities the 'fully funded' part of the distinction doesn't really apply anymore at lots of places, programs looking to trim, improve graduation rates/times etc. figured maybe they should only admit those who they could fund

the other part, though…

Someone told me Hindemith was into group or set theory as it applies to music but I couldn't find a reference. Maybe that Wiki page will have.

Telling you, that Fencepost thing saved me some headaches.

Oh yeah, one more thing
*Thinking about musical entities as partitions- triads as partitioning into three (with the fourth being a "generalized, augmented third*), seventh chords as partitioned into four (with the second between the seventh and the octave as a *generalized, diminished third*)

homotopy type theory isn't exactly homotopy theory bear in mind -- its this wild new realization that homotopy theory is precisely isomorphic to that branch of logic known as martin-lof type theory, and this all works only in a constructivist setting. so you have math/logics ppl without much topology background (hi!) and topology people trying to understand type theoretic notation all sort of in the mix together. i have a coworker with some topology so he's good at explaining things like fibrations and fundamental groups etc. oh right and the other part of the hott project is now you have a setting in which the claim is you can do the foundation of _all maths_ as an alternative to set theory, so eventually (tho it may be 6 mos before we get there, if we can keep up the momentum) we'll stop just building up the theory and do applications and use it to do classic results in e.g. actual homotopy theory, set theory, category theory, analysis etc.

the hatcher book is very approachable but it does sort of require someone with a bit of background to explain what he means by certain things, since the geometrical intuitions aren't totally obvious without someone drawing things or waving their hands or etc. to illustrate movement.

sounds cool xp

xp would u rather be teaching econ? my first major was in econ, then i was like ah fuck it and turned my math minor into a full major

― flopson, Saturday, November 9, 2013 4:53 PM (17 minutes ago) Bookmark Flag Post Permalink

there are many things for which i am better qualified to teach. don't get me wrong, i know the hs curricula v well, i just didnt take much advanced math and sometimes feel like i am training my kids for a sport ive never seen or played before. being the good economist, tho, i know my comparative advantage is in the high-need HS math field rather than the social studies or journalism positions i'd have an absolute advantage in.

Now I remember the problem with math, you have to beef up all this apparatus, before you can really understand or prove anything- except for trivial variations on the proofs in the book with slightly different initial conditions- let alone do a calculation, for what seems like an eternity.

Right. Turtle will eventually break the table too.

have only just noticed that this is the average of the two values. is that always true?

yeah, trivial

yes bcz of yr post at 16.22 london time

https://www.youtube.com/watch?v=tS8oyl1gygs

Slight variation on the problem: instead of limiting ourselves to 2 measurements and 2 animals, imagine we could do a million measurements. For each measurement we select at random two animals from the total animal population of earth. We place one animal on the floor and one on the table (assume table is of infinite strength), and measure the distance between the top of the floor animal to the top of the table animal (which could be a positive or negative number). Given measurements M1 through M1000000, what is our best estimate of the actual height of the table?

51"

Bear in mind that if we select 2 million animals at random from total earth animal population, its likely that most or all will be bacteria and hence of negligible height.

bacteria aren't animals!

You're right. Please disregard my previous statement. It seems the most common animal will be an insect, whose height may or may not introduce significant error in our measurement, depending on the height of the table.

Come now Let us be crooked but never common.

Challenging myself to figure out why this works:

https://pbs.twimg.com/media/FmBgdAxWAAA_O_h?format=jpg&name=small

Happy to explain if you don't figure it out

Oh, I'll let it percolate in the back of my mind for at least a day or two before relenting and looking for hints. Interestingly this trick doesn't preserve the remainder of the number after division by seven in the general case. Only in the case of remainder zero. So its not a perfect modular algorithm.

Took me a few minutes of percolating but it makes perfect sense now.

Thought of two ways to do it. One is more obvious and clear, one is slightly fancier but more interesting. They both amount to the same thing anyway.

Can’t believe I never came across that before. I did spend time long ago thinking about why the decimal representation of one seventh is what it is though.

Not much percolating in my brain yet, except a vague idea that the equation 5 * 10 - 1 = 7 ^ 2 is somehow involved.

facts

as a physical sciences person i suck at number theory. here’s how i can prove it for numbers between 100 and 1000, no idea how to generalize to the result. pretty sure a slick method would use mod but as i suck at number theory idk how to do that

suppose you have a three digit integer with digits p, q and r which can be written 100p + 10q + r

using chika’s method we drop the last digit r and divide by 10, then add 5r. assuming this new number is divisible by 7, we can write

10p + q + 5r = 7m, where m is some rando integer

multiply both sides by 10 to get

100p + 10q + 50r = 70m

to reconstruct our original integer, we subtract 49r from both sides to get

100p + 10q + r = 70m - 49r

since 70 and 49 divide by 7 (and m and r are integers) we’ve proven 100p + 10q + r is divisible by 7

some distance still to go before i’m as slick as a 12 year old math whiz

actually maybe it’s not as hard as all that - with a four digit number i think you just get 700m on the other side, 7000m with five digits, and so on?

sadly i think you always get a -49r and never a 490 ;_;

er no, scratch that, i think you always have 70m, just bigger and bigger junk in front of the 50r to keep track of

One way:
Think instead of just peeling off the last digit, multiplying it by 50 and adding it back to the rest. This will just be ten times the number in the suggested trick and is divisible by seven if and only if that number is. If the original pieces were p and q mod 7, the new number mod 7 is p + 50q = p + 49q + q which is again p + q mod 7, so the operation does not change divisibility by 7

yeah see that’s slick, i understand it but i just can’t generate math like that

Other way:
Do the actual trick as specified, divide one part by ten and multiply the other by five, so p/10 + 5q. What is integer division by 10 mod 7? Well, 10= 7 + 3. What is the multiplicative inverse of 3 mod 7? 3 * 5 = 15 which is 1 mod 7 so 5 is that inverse. In this case the new number is 5p + 5q mod 7 which again is divisible by seven if and only if the original number is

Basically this is a further generalization of the principle that makes the divisibility tests for 3,9 and 11 work, except none of us have ever seen it before, unless someone has, please speak up if so.

I don't think I follow your second explanation there, James, but the first one is basically what popped into my head as I was walking my dog this evening.

Here's how I phrased it to myself in order to convince myself that it has to work:

The algorithm as stated (taking the last digit, multiplying it by 5, adding it to the remaining number, and then dividing by 10) is equivalent to another hypothetical algorithm (finding the multiple of 49 which when added to the original number produces a multiple of 10, and then dividing out that factor of 10). Because neither of the steps in the hypothetical algorithm change the property of being divisible by 10, neither does the original algorithm.

Sorry, that last sentence should have read "property of being divisible by 7".

Has to do with groups and rings.
https://www.maths.usyd.edu.au/u/UG/SM/MATH3062/r/lect1.pdf

https://s3.amazonaws.com/saylordotorg-resources/wwwresources/site/wp-content/uploads/2012/06/MA111_Z6and-Z7.pdf

Yeah, I recognized it had something to do with theories of modular arithmetic, but was not well versed enough in that subject to follow the condensed explanation.

I think my garbled my explanation, but hopefully the gist comes through.

Clearly I should go to bed.

In mod 7 arithmetic, dividing by 10 is the equivalent multiplying by 5 is the gist of it.

Basically this is a further generalization of the principle that makes the divisibility tests for 3,9 and 11 work, except none of us have ever seen it before

Well, yeah, but the "multiply last digit by 2 and subtract from the rest" test for divisibility by 7 is well-known, and that test is to 21 as Chika's test is to 49.

Didn’t remember that one but -2 is 5 mod 7 so it makes sense.

Arguably subtraction is harder to do mentally than addition, so Chika’s method seems easier.

Fair enough. Although multiplication by two and then subtracting a really small number is (slightly) easier than multiplying by five and adding a larger number.

It’s kind of fun once you know this trick to come up with other rules for checking for divisibility.

For example to check for divisibility by 29, you can take the last digit, multiply by 3, add to remaining part of the number, and just keep doing that until you get to 29 or a number which is less than 29.

RIght. I never knew the trick for divisibility by 13 before last night and of course it fits the same pattern.

Multiply last digit by 4 and add, because 39.

Yup

When I was 15 I did this— it was so funny watching them be mad, claiming I was a computer or cheating. Nope, just a genius.

Small world I see this on twitter.
pic.twitter.com/rQtxX3eoaq

— @chloe21e8灭绝公主 (@chloe21e8) April 21, 2023

posting quean

!

Do we know whether she was also posting the questions? Seems perhaps a bit too convenient that people just happened to ask about some rather contrived integrals that just happened to have neat and tidy solutions that one poster knew the answer to.

Certainly seems possible.

i enjoyed this thread about zero:

This meme is very very funny, but it is also inviting a serious explainer 🧵 from yours truly about 0 in Sinitic languages (there'll also be something funny later on). 😂 Let's go! 1/ https://t.co/I3vEGnNS7Z

— Egas Moniz-Bandeira ᠡᡤᠠᠰ ᠮᠣᠨᠢᠰ ᠪᠠᠨᡩ᠋ᠠᠶᠢᠷᠠ (@egasmb) May 21, 2023

also have enjoyed videos recently from math youtuber @Domotro

That was good, thanks.