Mathematics - 2017-03-30 (page 1 of 2)

Balarka Sen

00:26

O_o

BAYMAX

The decimal numbers from [0,1] are iid random variables on {0,1,2...,9} ?

that too they are uniformly distributed ?

How this came?any idea

arctic tern

what?

Akiva Weinberger

I think so

Like, to choose a random real from $[0,1]$, you can choose infinitely many digits from 0 to 9, each choice being uniform, independent, and identical

and we don't need to worry about the $.1\bar9=.20$ thing because the odds of getting a decimal ending in infinitely many zeros or nines is 0

So, yeah, I think so

arctic tern

00:43

"decimal" is technically not a type of number, it's a way of representing a number. any number in [0,1] may be represented in decimal. the numbers in the interval [0,1] form a set, not a random variable.

Akiva Weinberger

You can make a random variable out of $[0,1]$ by choosing one uniformly at random, right?

arctic tern

presumably you mean if X is drawn from [0,1] uniformly at random, then the individual digits of X are independent identically distributed random variables which are uniform in {0,...,9}

Akiva Weinberger

Which is true, right?

arctic tern

of course.

Akiva Weinberger

And, conversely, if you choose digits like that, put them together to form a decimal, and then find the real it corresponds to, it's the same as choosing a number from [0,1] at random

arctic tern

00:45

The decimal numbers from [0,1] is not a way to say "the digits of a random variable with uniform distribution on [0,1]"

I am discussing language

BAYMAX

ok will take care from next time about calling them numbers when actually they are representations .

ok @AkivaWeinberger thanks.

arctic tern

that wasn't really the big issue...

LegionMammal978

Hmm

Just came upon an IRL issue

BAYMAX

yup@arctictern

Mike Miller

@BalarkaSen lol that it's sold in a tin can you can't see inside

LegionMammal978

00:54

Given a (filled, non-self-intersecting, non-convex) polygon, what is the minimal set of composing polygons such that a) their union is equal to the original polygon and b) their polygonal diameter is no more than a constant $D$?

And I'll have to implement this in Mathematica

Balarka Sen

@MikeMiller apparently someone exhibited an opened can, but only to find there's a smaller can inside

you can't even know if this shit is shit or not

Ask Yourself

01:41

scontent.frec3-2.fna.fbcdn.net/v/t1.0-9/…

Akiva Weinberger

Wut

Ask Yourself

Source: facebook.com/Mathematical.Mathematics.Memes/photos/…

Tim The Enchanter

02:11

@BalarkaSen The worlds greatest troll.

Will Njundong

03:02

HELP! imgur.com/RaEGDs1

I resolved this question to: $P = 3y + 2x$

I rewrote $Area = xy = 5000$ to $y = \frac{15000}{x}$
got derivative of P, and ended up with $\frac{-15000}{x^2}+2 = 0$ which forces me to use imaginary numbers, and so i think i did something wrong

Daminark

Hey @Mike!

Secret

03:20

sorry let me tidy that up first

Daminark

Kek

Mike Miller

03:38

hi

Daminark

How's it going?

CausingUnderflowsEverywhere

SOMEONE COMMENT FOR ME BECAUSE I NEED 50 POINTS:
http://math.stackexchange.com/questions/2209396/help-drawing-the-function-frac100120e-0-23t

"Grade 11 math, start from t=0 , and substitute and greater value for t each time and plot away until you have a visualy graph!"

@AskYourself who is $answered Jan 14$ and why is akiva a slut for them at 22:20 ?

@WillNjundong what's that operating system called? :o

Will Njundong

04:19

@CausingUnderflowsEverywhere lmao not the kind of question I was ever expecting in here, but it's called Linux Mint. Linux for the Win!

And I hope you do know that underflows aren't a thing ;)

CausingUnderflowsEverywhere

It's too bad what you don't know

Will Njundong

I mean I get that yes it exists, but it's hard to introduce that error unintentionally :D

CausingUnderflowsEverywhere

I got underflows when I was messing with buffers

if you visit superuser's chat then you'll see they have underflows very frequently

ask them about it

Will Njundong

aaahhh i see where you come from now

oh really?

I honestly have never seen anyone produce that type of error, and I've been involved in quite a few projects

guess im not kicking the right sacks :p

Secret

[to be done] Find a topology such that a given point in the set X is always near to every point in the set. Preliminary: Expect the topology should be highly non T1

-> omnipresence expressed in mathematical analogy

Mike Miller

04:39

@Secret If the closure of every point is the whole space then the space has the indiscrete topology.

LeGrandDODOM

05:20

@AkivaWeinberger Perhaps you can answer this: How do you prove that, for an integer $n$, $z^n$ is the same $e^{n\log(z)}$ ? $z^n$ is iterated multiplication of $z$, while $e^{n\log(z)}$ resorts to the definition of the principal branch of the logarithm. For real numbers, the equality follows from the functional equality $\ln(ab)=\ln(a)+\ln(b)$ which yields $\ln(a^n)=n\ln(a)$, hence $a^n=e^{n\ln a}$.

Neev Parikh

05:54

@Daminark was HL useful. Did it help prepare you for uni in any way? Or was it's level too simplistic

Daminark

06:11

@Neev So I'll say that I'm coming to UChicago, and in this particular case IB almost/sorta was better for me than AP

I was able to absorb the idea of a proof somewhat faster since IB is marginally more proof-ish than AP in some respects

And while I was behind in terms of content because I just didn't learn integration well

In Chicago, they kinda restart everyone to Spivak, so prior calc background wasn't terribly influential unless you had way more than AP/IB anyway

If you are to go somewhere that does math in a more, computational calc 1 + 2 + multi + linalg, you'll be slightly behind the AP kids, since they get immediate credit while IB often doesn't

The reason is because if you do well in IB, thanks to the topic mixup this doesn't specify, you might've done the algebra option, did gloriously well on a number theory IA, and got every non-calc question correct, then did the worst you possibly could've on the calc questions while still maintaining a 7

On the flip side, you might've understood calculus and anything you need to know to understand it perfectly, and screwed up on stuff like stats and vectors to bring you down

They can't really map it onto individual courses nicely, so they tend not to give credit. Then you really want to supplement so that you can try to place out of things

Sorry for the rant, tl;dr, meh

skull petrol

meh :-)

Daminark

Hey @skull!

skull petrol

Hi pal. If you throw physics into that mix you're gonna get a lot of overlap.

Daminark

Oh yeah IB Physics is ultra merp

I thought I was a hotshot in physics in high school since I did well in IB

n o p e

Cows

hi

stupid question

skull petrol

06:22

np askaway

Cows

are reflexive vs self-dual same . . . please don't tell anyone I asked this

skull petrol

What's self-dual

self-dual

Adjective: self-dual

(mathematics, in projective geometry) Of a proposition that is equivalent to its dual.
(mathematics) Of a graph or polyhedron that is the dual of itself....

Daminark

Reflexive is a property I usually hear applied to Banach spaces

Or well

Vector spaces more generally

Cows

yeah

Reflexive space

In the area of mathematics known as functional analysis, a reflexive space is a Banach space (or more generally a locally convex topological vector space) that coincides with the continuous dual of its continuous dual space, both as linear space and as topological space. Reflexive Banach spaces are often characterized by their geometric properties. == Reflexive Banach spaces == Suppose X {\displaystyle X} is a normed vector space over the number field F = R ...

Daminark

The answer to that is no

Cows

06:24

When Physicists say self-dual, what do they mean

Daminark

If something is isometrically isomorphic to its dual space, then it's automatically reflexive

But consider $L^p$

Where $1 < p < \infty$ and $p\ne 2$

Those spaces are reflexive but not isometrically isomorphic to their dual

If you haven't seen Lebesgue stuff yet (I haven't), then consider $\ell^p$

skull petrol

Recall the reflexive property of equality: if a is a real number, then a = a. @Cows

Cows

@skullpetrol lol ok

skull petrol

sorry, I didn't mean to sound condescending :-)

Cows

@Daminark just so I can be confident can you elaborate more on "isometrically isomorphic" are you saying length preserving isomorphisms, can you paint the picture a bit more? again, just want to be sure I am not painting the wrong picture in my head lol

or same length

Daminark

06:31

So say you have normed spaces $X$ and $Y$

Cows

ok I am thinking L^2

L2

Daminark

$f:X\to Y$ is an isometry if $\|f(x)\|_Y = \|x\|_X$

So isometric isomorphism is that + linear bijection

(Isometry guarantees injection so you only need to explicitly show surjectivity)

Cows

perfect! got it

skull petrol

are reflexive vs self-dual same . . . please don't tell anyone I asked this

Daminark

pings everyone to tell them you asked this

skull petrol

06:38

Don't worry pal your secret is safe us :-)

Cows

hehehe thank god

:D

Neev Parikh

@Daminark aahhhh crap. Knew I should've done Calc BC while I had the time. Well junior year now and no time for APs. Thanks anyway. Guess just work harder

skull petrol

Does AP mean advanced placement?

John P

Guys does anyone have some advice on how to find a curve with curvature (1/s) at every s>0 ?

Daminark

A circle of that radius @John

At least I think

And yeah @skull

John P

06:51

A circle has a constatnt curvature

Daminark

Oh you mean like, a single curve

John P

Yeah.

Daminark

Maybe a spiral?

John P

I tried a spiral of multiplying the circle by (1/s)

but it doesn't work.

Daminark

What?

skull petrol

06:53

A helix?

Daminark

"A spiral of multiplying the circle"

John P

(t cos t, t sin t)

Daminark

Maybe some space filling curve

Like a limit of spirals or I dunno

Also what's $s$ in this context?

Integer?

John P

real number >0

Daminark

Oh, so you don't need to say $\frac{1}{s}$, just for any $s$

John P

06:58

Well thinking about it I'm not sure, maybe I'm looking a bit too much into it.

It says find a planar curve that's arclength parametrized, and it's curvature is $\frac{1}{s}$ for $s>0$.

I was presuming I'm supposed to find a specific parametrization from $(0,\mathbb{R}) \rightarrow \mathbb{R}^2$, such that it's arc-length parametrized and it's curvature is always (1\s)$

skull petrol

07:23

curvature

Noun: curvature (plural curvatures)

The shape of something curved.
(mathematics) The extent to which a subspace is curved within a metric space.
(differential geometry) The extent to which a Riemannian manifold is intrinsically curved.
curvature f
plural of curvatura

(2 more not shown…)

John P

Nevermind I figured it out, just have to solve a differential equation.

Cows

some more silly questions

lattice vs moduli space

ok scratch what i asked, got super confused reading something

It was a super dumb question.

Fawad

08:31

$〈m_1,m_2,m_3 \cdots m_t〉$

Which notion is this and what it means?

Hi everyone : )

Tim The Enchanter

I would suppose the G.C.D but then the statement is trivial.

So perhaps its the L.C.M.

To clarify, I'm talking about the greatest common divisor and the least common multiple respectively

Fawad

@TimTheEnchanter thanks

Will Njundong

anyone active to help me with calculus?

Mateen Ulhaq

08:47

Hit me

Will Njundong

Find the greatest volume that a right circular cylinder can have if it is inscribed in a sphere of radius 20 cm.

Mateen Ulhaq

The volume of a right circular cylinder is given by

$V = \pi r^2 h$

Thus, you can only vary the parameters r and h.

This sounds like a Lagrange multiplier problem.

Will Njundong

I have no idea what that is, but maybe it has been mentioned in class. I havent been attending

Mateen Ulhaq

Is this Calc 1?

Will Njundong

yup

SteamyRoot

08:53

Oooh, that question

I give that one in my calc course too :O

Will Njundong

lol

do you have a solution sheet stored that you could share, perhaps?

SteamyRoot

I only have handwritten solutions

Will Njundong

i have a hearing loss and sitting in class does nothing for me, so i have to figure this stuff out myself ;)

perfect

SteamyRoot

Anyway, the idea is: you'll want the center of the cylinder to be the center of the sphere

Will Njundong

Thats what works best

SteamyRoot

08:54

and you want the cylinder to touch the sphere

Mateen Ulhaq

(OK, then it's probably even easier to just assume a certain symmetry...)

Center your cylinder.

The radius of the sphere can bound the edges of your cylinder. Try to find a relationship between h and r.

Will Njundong

yup, drew a diagram for that

SteamyRoot

Draw a line from the center to where the cylinder touches the sphere

and draw a radius of the cylinder starting from the center

Will Njundong

from that i ended up with $V = \pi r^2 \sqrt {4R^2 - 4r^2} $ where R is radius of sphere and r is radius of cylinder

i rewrote h, and then ended up stuck with that

equating to zero leaves me with two variables still :(

SteamyRoot

You only have one variable anymore, since $R$ is fixed

Will Njundong

08:58

OH WOW

i completely forgot lol

omg i kick myself for dumb mistakes like this :)

Mateen Ulhaq

That should say "Find dV / dh"

Sha Vuklia

hey guys. are Gilbert Strang's online lectures the best for learning the basics of linear algebra?

i want to revise linear algebra, but my book sucks, so I was thinking of just following lectures online

Will Njundong

Thank you for your helps guys! at least i can sleep in peace now

SteamyRoot

@Sha No idea if they're good or not (I never followed any online lectures), but whether they're the best is something very subjective and probably varies from person to person :P

Out of curiosity: what book are you using?

Sha Vuklia

@SteamyRoot oh shit, you're from Belgium aren't ya?

SteamyRoot

09:08

yup

Sha Vuklia

because... the book I don't like, is Belgian XD

Paul Igodt & Wim Veys

SteamyRoot

ahahahahahahaha

Sha Vuklia

XDXD

I think I'm just biased because it isn't in English

SteamyRoot

The first author is like, pretty much my boss.

Sha Vuklia

I just like to read my math in English :P

OMG really

cool!

did you have that book as well?

oh wait

of course XD

sorry I'm slow today

SteamyRoot

09:09

Actually, I didn't

Sha Vuklia

oh, that's interesting

SteamyRoot

The book was only published the year after I did linalg

Sha Vuklia

ahh alright

I usually don't like online lectures if it's for new material, but I do like it if it's for revising old material

SteamyRoot

Well, one thing I can say about the book is that it might not be the greatest book for self-study; or if you have a bad lecturer

We tend to consider books as "supplementary material" for lectures

Sha Vuklia

you mean my book? because yea, it was horrible to learn from

it's rather a nice book once you've already learned most of it

oh and that's funny, because I consider lectures supplementary material for books :P

SteamyRoot

09:15

I can imagine the book doesn't lend itself well to that approach, sadly :/

Well, sadly, this also means I don't have any first-hand experience with other introductory linear algebra books, so I'm afraid I can't help here

You could try Ted's book, but it's probably very geometric in nature

Sha Vuklia

is it available online?

i think Gilbert Strang's lectures will be fine tho

SteamyRoot

Pretty sure Ted mentioned it was "available online if you know where to look"

Sha Vuklia

hahahah! omg :P

that sounds very much like sth he would say XD

I'm not interested in books though. I think I'm just going to stick with Gilbert Strang's lectures for now, because that seems to be my best bet

Alucard

09:54

We got an heretic here, Neo, show him what's up

Yashas Samaga

10:16

someone justifies that 2 + 2 is not equal to 4 by saying "2 inches + 2 feet is neither 4 inches nor 4 feet.....mic drop!"

What do I reply?

SteamyRoot

"learn a proper system of units" ?

Yashas Samaga

I replied "When you add two quanties, they need to have the same units to be added numerically. If they are not, you need to convert them to the same units. 2 inches + 2 feet is not the same as 2 + 2. I feel so bad for you."

He replied "2 in + 2 feet is 14 inches. Still not 4"

what do I say next?

SteamyRoot

To me, this sounds like an argument so childish it's not worth replying to

Alucard

i would say "on your bike"

Yashas Samaga

Yea, I am going to stop.

Alucard

10:20

@Secret glad you could join us :)

oh yes, partytime :D

Secret

I just literally arrive on chat when I open my mac

so be prepared I have absolutely no idea what just happened until I read the trasncript

Will Njundong

Help...Johnny is designing a rectangular poster to contain $12 in^2$ of printing with a 2 in margin at the top and bottom and a 6-in margin at each side. What overall dimensions will minimize the amount of paper used?

Alucard

not bad i'd say

@WillNjundong did you try to actually cut real paper and try it out by brute force?

Will Njundong

10:39

yes i did @Alucard somehow i still ended up with the wrong answer. i know this is supposed to be one of the easy ones, but i've been up all night, im exhausted, and this is due in 2 hours

Alucard

this is a function

take thew deriviative and find the minimum

Will Njundong

$wh = 12$
$(w+6)(h+8)$

$(12/h + 6)(h+8)$

$12+ 96/h +6h + 48$

simplified that, took derivative

Alucard

now equalling that with 0, to find the minimum :)

or to be precise, to find the place of the minimum

Will Njundong

solved for zeroes, ended up with $h = \sqrt\frac{96}{6}$

which is 4

Alucard

then insert that into the function

f(4)=?

Will Njundong

10:44

OHHHH THAT'S THE PART I OMMITTED

*sighhh

so annoyed at this course rn

Alucard

make a ":D" smiley under your work

in red

your teacher will understand

Will Njundong

lmao this is in MyMathLab, a shitty online interface

Akiva Weinberger

@LeGrandDODOM Polar form maybe

Will Njundong

and our professor isnt cool like that lol

Alucard

then i'd suggest you visit him personally

let's see what he got to say

Will Njundong

10:48

well i sent him an email a couple of hours ago asking to see him during office hours to see if there's anything i can do to save my grade

only courses I care about and give attention to are my CS courses. I find everything else uninteresting :(

Alucard

that sounds like you need some music, maybe get unplugged?

i wish you a very wonderful day :D

Will Njundong

heh, no time to chill like that. I play choral music while studying and it helps me focus somewhat. Got a history midterm tomorrow, and I'll have to go rereading a bunch of boring books :(

i had promised myself yesterday that i would sleep early, but here i am lol. and thank you :D you too!

John Doe

11:26

Quick question, does anyone know how to simplify this product of binomial coefficients?

$$\sum_{m = -\frac{N}{2}}^{\frac{N}{2}} \binom{N}{\frac{N}{2} + m}^{\frac{1}{2}} \sum_{m = - \frac{N}{2}}^{\frac{N}{2}}\binom{N}{\frac{N}{2} + m +2}^{\frac{1}{2}}$$

Thanks for any assistance.

Alucard

holy sh...

descendant factorials would be my idea, but honestly i got no idea

Will Njundong

The manufacturer of Zbars estimates that 500 units per month can be sold if the unit price is $225 and that sales will increase by 10 units for each $5 decrease in price. Write an expression for the price p(n) and the revenue R(n) if n units are sold in one month, n≥ 500.

thats the last one and i've got about 15 minutes left. Im not sure what is being asked of me

Alucard

11:42

Trinity, i'll need your help

ok, what you got @WillNjundong anything, have you wrote anything?

Will Njundong

no, i am looking for instructions online lol\

im to tired now to come up with something for this

Alucard

:D

i better run now

Will Njundong

could p(n) possibly be .5n + 225?

turns out answer was 475 - n/2

wonder where the 475 came from

ill attemt another for that point

lol @Alucard I ended up figuring out how they were getting their answers by experimenting (dividing and multiplying) with numbers involved in the problem and working my way backwards to their answer. I saved the steps, and just did the same thing with my last attempt and it got me the right answer. I still don't understand the question. RIP me, i have a ways to go.

John Doe

12:05

Does anyone know how to simplify this $$\sum_{m = 0}^{N} \binom{N}{m}^{\frac{1}{2}} \sum_{m = 0}^{N}\binom{N}{m+2}^{\frac{1}{2}}$$

BAYMAX

12:40

Hi all hallelooyah!

skill patrol

Hey there.

Will Njundong

yo :D

how's everyone's day going so far

BAYMAX

Pretty hard and sometimes sleepy

Will Njundong

Tell me about it. This is the 11th night in a row Im breaking my promise to sleep like a normal person lol

BAYMAX

nah you should take rest.

@zhoraster Thank you for the answer.

Alucard

13:13

Hellsing - Primo Victoria

►

again :D

dipper

13:34

Does this room discuss predicate logic questions?

SteamyRoot

Oooh, Sabaton :3

Daminark

Hey everyone!

BAYMAX

14:01

yo @Daminark

user193319

14:27

Here is the question I am working on: If g is a function defined on the open interval (a,b) such that a < g(x) < x for all x in (a,b), then g is nonconstant. Would the following proof work? Suppose that g(x) = c for all x in (a,b). Then a < c < x < b for every x in (a,b), implying that c in (a,b). Hence, x= c yields a contradiction.

SoumyoB

So I'm making a new song, does anyone here want to listen to its preview?

Vedant Chandra

0

Q: Prove that the maximum total resistance of two parallel resistors is when the resistors are equal

Taking the two resistors as $x$ and $y$, I have to prove that resistance is maximum when $x = y$. The total resistance is given by $$\frac{xy}{x+y}\ $$ Differentiating and equating for zero, I get $$ \frac{y^{2}}{(x+y)^{2}}=0\ $$ which has no sensible solutions that help me. What am I doing wron...

I'm teaching a friend differential calculus, but this question on a problem sheet has stumped both of us. The answer seems obvious, but I've tried everything from Wolfram Alpha to sleeping on it, to no avail.

I feel like I'm missing something very simple.

SoumyoB

@VedantChandra there must be a condition on $x$ and $y$?

as in their sum might be constant?

Vedant Chandra

@SoumyoB That's exactly what I was expecting from the question, since then it gives a relation between X and Y that I can use. But it doesn't

Am I right in assuming the question is unsolvable without some constant relation between the two?

SoumyoB

yes

otherwise you could just take both of them to be infinite

and the total resistance would then be infinite too

Vedant Chandra

14:35

Yes exactly, I found that if the limit of one tends to infinity, the total resistance is the resistance of the other one.

Alright, thank you so much

Shall delete the question

user193319

So, would someone mind critiquing my proof typed above?

Vedant Chandra

14:47

I have left my question up with an edit

Because I'm curious as to how a solution may be found in the general case

With no constant relation between x and y

Vedant Chandra

15:04

The answer's logic for partial differentiation makes sense to me, I just read up on partial derivatives as well

But it implies x = y = 0

The =0 part is the issue

It also seems to imply x+y=xy but I don't see how that helps. That's not true even when x = y

Tim The Enchanter

15:16

The zero part is due to the fact that x or y being zero corresponds to the minima.

But its no use because we are looking for the maxima

Which we know to be unbounded

Alucard

16:12

mmh, dipping sounds like a good idea

dipping into absolutely everything

and therefore into math

Mary Star

A plane A goes up 500m and starts its flight from the point A(1, 2, 0.5).
It is flying on a straight line with constant speed and after one hour it is at the point B(31, 42, 0.5).

A plane B is when plane A starts on the point C(12, 25, 0.3).
Its path is described by x= (12, 25 , 0.3) +s* (-80 , 60, -4), where s is in hours.

Is the flight path of the plane A x= (1, 2 ,0.5)+t* (30, 40 ,0) ?

Now I want to find where and when the planes will meet each other.

So, (12, 25 , 0.3) +s* (-80 , 60, -4) = (1, 2 ,0.5)+t* (30, 40 ,0).

Hello @TimTheEnchanter !! Do you have an idea about my question?

BAYMAX

16:41

Hi@TedShifrin

Ted Shifrin

Hi @BAYMAX.

BAYMAX

I am still struggling with important theorems of differential equations

like existence uniqueness

Danu

Hi @Ted! :-)

BAYMAX

Picards Lindelof

Ted Shifrin

Hi @Danu

Danu

16:42

I have a short exact sequence $0\to \Bbb Z \to H^k(X;\Bbb Z) \to \Bbb Z_2 \to 0$. What do I conclude about $H^k(X;\Bbb Z)$?

BAYMAX

Any reference where I can appreciate the theorem andd proof

Ted Shifrin

@BAYMAX: What is your math background?

Tim The Enchanter

Hi @TedShifrin

BAYMAX

I am now in masters but have never used these theorems in practice

@TedShifrin

used in numerical analysis

Ted Shifrin

I am very fond of Hirsch-Smale's book on differential equations, dynamical systems, @BAYMAX.

Tim The Enchanter

16:43

@MaryStar Your method is correct, so either the question is unrealistic or your calculations are incorrect.

Ted Shifrin

Hi @TimTheEnchanter.

@Danu: What do you think?

Danu

@TedShifrin I want it to be $\Bbb Z$---ohhhh wait a second

BAYMAX

Ok@TedShifrin , thanks

Danu

It has to be $\Bbb Z$, doesn't it... I was afraid that $\Bbb Z\oplus \Bbb Z_2$ would be possible

but of course it isn't

great

Ted Shifrin

Wait.

Danu

16:45

I'm wrong? :P

Ted Shifrin

Yup.

Danu

Nooooo

multiplication by 2 for the map Z into it works

and I don't see any other options

Ted Shifrin

But if you tensor with $\Bbb Z_2$ the dimension of the middle vector space has to be the sum of the dimensions.

Danu

So...?

Ted Shifrin

So, $1\ne 1+1$.

Danu

16:47

I'm confused by this

Ted Shifrin

Yeah, me too.

Danu

So you're saying it embeds onto the first factor of Z+Z_2?

Ted Shifrin

I'm sick, so my brain is mush. Let me think.

Danu

(the result HAS to be Z, according to Kotschick; I'm just trying to understand)

If I take it to be $\Bbb Z\oplus \Bbb Z_2$, I think the map $1\mapsto (1,0)\mapsto 0$ works, if I send $(0,1)\mapsto 1$

Ted Shifrin

Yeah, so tensoring with $\Bbb Z_2$, the sequence is no longer exact if the map is multiplication by $2$. ...

So there are two options. $\Bbb Z$, $\Bbb Z\oplus\Bbb Z_2$. You need more info to decide.

Danu

16:51

damnit

Ted Shifrin

Sometimes you know that cohomology can't have torsion in it.

The expert is here.

Danu

o/ Hi mike

Ted Shifrin

@MikeM: Rafe Mazzeo asked about you again last night.

Danu

Also, I didn't realize before today that having an injective homomorphism into $\Bbb Z$ forces the group to be $\Bbb Z$ (or trivial)

Mike Miller

That's nice. I don't think I made much of an impression. I think I told him I liked his uniformization paper.

Ted Shifrin

16:53

There are no nontrivial homomorphisms from finite groups to $\Bbb Z$.

Mike Miller

(I love his uniformization paper.)

Ted Shifrin

Hi @PVAL

PVAL-inactive

Hi @Ted

Mike Miller

@Ted Should I read Hirsch-Smale?

Ted Shifrin

That was not directed at you, @MikeM.

PVAL-inactive

16:55

I told my adviser I wanted to finish the writing I am doing near to the end of this year (meaning the school year).

Ted Shifrin

That's not very long.

PVAL-inactive

instantly "you mean calendar year right?"

Ted Shifrin

How much writing is there to do?

PVAL-inactive

I mean

Mike Miller

I know. Nonetheless, I don't know much ynamical systems and have been looking to learn some.

PVAL-inactive

16:56

For the work I am doing now

BAYMAX

ha @MikeMiller actually the book was directed to me by @TedShifrin

PVAL-inactive

@Ted Well I'm rewriting something about 15 pages

Ted Shifrin

You might find the level of Nitecki's book more appropriate, @MikeM.

Well, unless there's a giant chasm in there, @PVAL, your goal seems possible. But Bob has knowledge that I don't :P

Mike Miller

Thanks for the pointer.

PVAL-inactive

He's talked about how he spent a lot of time writing certain papers

like 3-4 years after he felt he completely understood all the work.

Mike Miller

16:58

@PVAL I've been telling myself I was going to be done with this in the next three months for a year.

BAYMAX

Actually I am interested in finding resources in mathematics interactive , animations ,lectures ,notes ,books , manga , sites ,MSE

Ted Shifrin

Well, that philosophy is great, @PVAL, but it doesn't help you getting a Ph.D. written.

@BAYMAX: I am not acquainted with what is available on-line.

BAYMAX

it is ok@TedShifrin

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$Mathematics$ Mathematics