Mathematics - 2016-11-19 (page 1 of 10)

Fargle

00:00

@TedShifrin :I

Ted Shifrin

@Fargle: I seem to have found the issue. Change in syntax with changing footnote symbols.

Fargle

@TedShifrin I'll pretend to know what that means. ;) Good you found it, though!

Ted Shifrin

Well, when they do away with Medicare, maybe I should go back to work as a private detective :P

Fargle

Ted Shifrin: LaTeX detective.

...goodness, that sounds lewd if you mispronounce LaTeX.

trilolil

00:21

Hello

I am reading the following document but it is not entirely clear how to get equation "(17)" on page 7/8.

Could anybody give some information on how to get $H_{\Phi}$ ?

Semiclassical

Absent a document, that's fairly hard.

trilolil

oops sorry @Semiclassical

whites.sdsmt.edu/classes/ee382/notes/382Lecture32.pdf

Semiclassical

oh hey, radiation

I probably saw this stuff back when I did graduate level electrodynamics. (was not a fan of it)

meow-mix

should i use a times-like font to typeset my document

trilolil

@Semiclassical It is just that one thing, which is the last thing I need, that is unclear to me.

Semiclassical

00:29

@trilolil Well, eq (17) seems pretty straightforward by itself; E-bar can be written in spherical coordinates with certain components

what those components are (eq 18) is a good deal more involved, of course.

meow-mix

oh boy

this looks like vector calculus all over again

trilolil

@Semiclassical well yes. This is what I am trying to find out. How to get to those components, i.e. the angle and magnitude.

heather

does anyone know a good place to find some practice calculus problems that are physics oriented?

trilolil

Does it really involve that much?

heather

preferably easier ones, as I just taught myself the basics of calculus

meow-mix

00:31

@trilolil for magnitude you can just use distance formula, no?

Semiclassical

Do you mean, how you get those particular E_r, E_theta?

trilolil

@Semiclassical yes.

I am pretty new to that subject.

Semiclassical

yeah, that seems pretty tedious/painful.

trilolil

hmm... that maybe explains why I can't find any paper explaining ow to get E_r and E_theta.

Semiclassical

I mean, I don't think this is particularly -complicated-

It's straightforward, just painful/tedious

i.e. plug equation (15) into eq. (16) and grind through the derivatives/simplification

There's nothing interesting there, but nothing mysterious either.

trilolil

00:34

mhm

oh yes now I see where the painfull part is: correctly calculating that partial derivative and then (if the previous step was done correctly) simplify everything.

Semiclassical

Right.

I mean, it's not -so- bad---I've seen worse

trilolil

I am not a matematician or physician unfortunately, I am into EE. :/

Jacksoja

what is EE

Semiclassical

eh, EE can have its painful computations

Jacksoja

Hello semi

:)

Semiclassical

00:39

hello

trilolil

yes I noticed it when I came accross this equation...

Jacksoja

You helped me other day

Semiclassical

@trilolil Essentially, you're solving a time-dependent PDE with particular boundary conditions and certain approximations

and that can get in the realm of tractable-but-painful calculations pretty easily

ah, did I? glad to hear I was useful :)

heather

@Jacksoja, electrical engineering

Jacksoja

@heather thanks :)

trilolil

00:41

I think it is OK actually I can see through the derivation process.

heather

10 mins ago, by heather

does anyone know a good place to find some practice calculus problems that are physics oriented?

anyone? =)

Semiclassical

Glad to hear it @trilolil

Jacksoja

@heather i think any calculus course is based on physics , what do you really want ?

heather

@Jacksoja, some problems that are, instead of something like "Evaluate: $\int x^2 dx$" more physics oriented, that's all.

But that are also a little easier (most of the problems I've found go over my head).

Jacksoja

Well you can skip the proofs on any calculus course and the rest is really physics

Do you need a book or video lectures?

heather

00:46

either would be good, just something that has problems. extra points for it being free =)

Jacksoja

there are TTC video on pure physics that helped me years ago

meow-mix

hey, does anyone know of a good book which has information on ring theory, field theory, and galois theory, assuming only basic group and ring theory?

Jacksoja

@heather anselm.edu/internet/physics/cbphysics something like this maybe ?

Ramanujan

@heather you are doing differentiations…?

heather

@Ramanujan, derivatives/integrals, yes

@Jacksoja, hmm, perhaps, let me give a few a try

Ramanujan

00:49

You asked question on d/dx (cos2x-sin2x)

Did you understand that?

@heather Tell what will be d/dx (sin3x)?

heather

@Ramanujan, sort of, I'm reading more about the chain rule on my own and then I'll come back to the problem and try again. the derivative of sin(3x) would be cos(3x) * 3

Ramanujan

Yes

Frankly saying,my math teacher never used word "chain rule"

meow-mix

chain rule is perfectly ok, ramanujan

there's nothing wrong with it

@heather hm, i might be able to give you some problems. can i see some examples of the problems youre having trouble with?

@heather also, heres an example problem. Derive ln(1/x)

you can use the chain rule for that :)

Ramanujan

I was teached like : we need to find d/dx(sin(F(x))) so first sin derivative then F(x) derivative

heather

$1/(1/x)*1/x$, right? @meow-mix

Ramanujan

00:56

No

heather

do I need to do the chain rule with the division too?

Ramanujan

Chain rule key is to multiply the derivative of F(x) which is F(x)=1/x

heather

man, i'm not very good at this at all

okay, let me see: derivative of ln(x) is 1/x

trilolil

@Semiclassical I think I may have totally misunderstood you. This is what I tried, but is totally not going in the expected direction...

imgur.com/nTUrZqF

Did I misunderstand you?

Ramanujan

@heather yes

heather

01:02

1/x can be rewritten as $x^{-1}$

so then you'd get $-1x^{-2}$, right?

as the derivative, I mean

so then you can do $1/(1/x) * -1x^{-2}$

arctic tern

yes

heather

which the first part turns into x, right, because 1/1/x = 1*x

so x*-1x^-2

and then x^-2 can be rewritten as 1/x^2, that times negative 1, so -1/x^2

and then that times x, so -x/x^2

meow-mix

correct

1/1/x = x

Ramanujan

-x/√x

trilolil

@Semiclassical Did you leave?

Ramanujan

01:04

Or simply -√x

meow-mix

uhh no ramanujan

Ramanujan

??

meow-mix

where did you get the square root

heather

fractional exponents are square roots

negative exponents are fractions

meow-mix

im confused let me do this problem on my own

Ramanujan

01:06

Ohhh,it was square,sorry

meow-mix

@heather yeah i know theres just no fractional exponents lol

Ted Shifrin

@meow: I've got the chapter all nicely typeset now, with figures, if you want to send me an email.

trilolil

a square root means exponential 1/2, so that doesn t make much sense I think.

meow-mix

so f(x) = ln x, right @heather

and g(x) = 1/x

f(g(x)) = ln(1/x)

so d/dx f(g(x)) = f ' (g(x)) * g'(x) by chain rule

f'(x) is 1/x

g'(x) is -x^{-2} or -1/x^2

Ted Shifrin

Even better, ln(1/x) = -ln(x) :)

meow-mix

01:08

so f'(g(x)) is 1/1/x or x

@TedShifrin i just realized that lmao

Ted Shifrin

ooooh, you need parentheses, meow

meow-mix

because 1/x = x^{-1}

so you really dont need chain rule in this problem, if youre smart like ted ;)

Ted Shifrin

no, dumb like ted :)

meow-mix

alright ted, ill send an e-mail :]

Ted Shifrin

using least possible

heather

01:09

-1/x would be the final result if you simplified again, right?

meow-mix

yes

Ted Shifrin

yes, @heather :)

heather

=)

meow-mix

@TedShifrin do you have any ring/field/galois theory books you'd recommend to me?

I have the basics of group theory (isomorphisms and homomorphism, group actions) and a miniscule amount of ring theory

Ted Shifrin

Go ahead and email me, @meow ...

meow-mix

01:11

im going

ok ok

i sent it

Ted Shifrin

LOL ... no need to get snappy :)

meow-mix

i want to do dual enrollment next year but i dont know if my parents will let me

heather

college and middle school?

Ted Shifrin

ROFL

heather

if so, best of luck =)

Ted Shifrin

01:16

We had a 12- or 13-year old who took our Calculus with Theory course many years ago. He loved it and excelled. Taking my differential topology the next year was a bit much for him, though. :P

heather

I'm in middle school as well =)

meow-mix

@TedShifrin i assume calculus with theory is a rigorous calculus course?

Ted Shifrin

yup, Spivak's book (which I recommend to everyone)

meow-mix

i don't know why, but analysis is so tedious for me

Ted Shifrin

I should open a math school for meow and heather ...

Fargle

01:22

Maybe this is just the egotist in me but I kinda wish I had been doing theoretical math earlier on.

Ted Shifrin

it's beautiful stuff, meow, but it'll take a few years for you to appreciate it

heather

@TedShifrin, that'd be fabulous lol =D

Fargle

@TedShifrin Lemme in. >_>

meow-mix

@Fargle i started having an interest in math when in 3rd grade i looked up what "sin, cos, tan" meant on my new "scientific" calculator

Ted Shifrin

I'm volunteering at the library helping 2nd to 7th graders every week, and most of them can't add 3+8 without using their fingers

meow-mix

01:23

@heather how old are you?

Ted Shifrin

sigh

heather

14 @meow-mix

you?

Ted Shifrin

@meow: I answered your email

meow-mix

13

Fargle

@meow-mix I've been interested in mathematics for a long time as well. I just didn't have the resources for it, haha.

arctic tern

01:24

if @Ted leaves the average age in the chatroom might be at an all-time lowest

meow-mix

@TedShifrin im much more interested in stuff like algebraic number theory

Fargle

The world could use more young people interested in math.

Ted Shifrin

Was that a hint, tern? :D

arctic tern

nah (:

heather

@meow-mix, and from the sound of it you're way ahead of me in math =)

meow-mix

01:25

Ted, be my tutor for now on >:)

@heather just looked on your page, looks like youre WAY ahead of me in physics

all i know is F=ma and an object in motion stays in motion

@TedShifrin yeah, and i answered your answer

Ted Shifrin

I got it. I'm retypesetting ... technical issues. Be back to you soon.

Physics is cool ... For people who know calculus, I highly recommend the book by Kleppner and Kolenkow on mechanics. It was fascinating, great exercises.

heather

@meow-mix, not really...I have a halfway decent intuitive understanding of some stuff, but I can't really use it, mathematically I mean.

@TedShifrin, oh, I might try that book =) you're not the first person to have recommended it.

Ted Shifrin

I took that course my first year at MIT ... it almost turned me into a physicist.

meow-mix

i want to be a professor when i grow up.

Ted Shifrin

So you can torture students too :P

heather

01:31

@meow-mix, cool, best of luck

I dunno what I want to be

Currently I'm very interested in quantum computing

@TedShifrin, preface to the 2nd edition of Spivak's calculus: "Most of the new problems are the work of Ted Shifrin." =D

Ted Shifrin

Yes, @heather ... I know ... but it's a great book despite that :)

heather

@TedShifrin, I'm sure, I just thought it was cool =)

sometimes I forget the people on the internet are real

Ted Shifrin

@heather: When you get to multivariable calculus and linear algebra, you can watch 112 of my YouTube lectures :P

heather

@TedShifrin, wow, could you give a link?

Ted Shifrin

it's in my profile

heather

01:37

okay

112 lectures, wow.

meow-mix

@TedShifrin is your book enough to supplement me with the knowledge for both algebraic geometry and commutative algebra?

Ted Shifrin

Be patient, @meow. You have lots to learn before you get there. But it's a great start.

heather

love this "proof" (read: I love driving people nuts with this proof)

meow-mix

you divide by (x-y)

which is 0

division by 0 is not allowed in fields

heather

exactly

Semiclassical

01:41

@trilolil here now

Ted Shifrin

Not allowed in anything :)

Semiclassical

and yeah, that's pretty far off :/

Fargle

@Ted, I feel like Rudin is throwing me trick questions. Not hard ones, just ones that are maybe designed to look harder than they are.

meow-mix

@TedShifrin what would you recommend i study after ring/field/galois theory and projective geometry?

Ted Shifrin

@meow: Ask me after you've learned all of this ... :P

Semiclassical

01:43

in particular, when they write $\sin\theta H_\phi$, they mean $(\sin \theta)(H_\phi)$ not $\sin(\theta H_\phi)$

meow-mix

ok >,<

im going to read some of your papers, ted

Fargle

@meow-mix Yeah, he won't even let me ask that. >_>

Semiclassical

also, $H_\phi$ is the component of a vector, it's not a vector itself

meow-mix

> For each g-dimensional principally polarized abelian variety (A,Θ) together with a marked odd theta characteristic ξ, consider the theta function θ[ξ](z,Ω) and its Taylor expansion with respect to z about the origin,

it just happened when i copied from it

Semiclassical

gotcha

Theta functions are weird

meow-mix

01:45

@TedShifrin papers on arxiv are usually preferred to be written in english.

not, whatever that is

Fargle

Sick burn.

Ted Shifrin

LOL, what the heck are you talking about, @meow?

Fargle

I actually can't stop laughing.

meow-mix

dude, I hate when you're driving home, and all the sudden, this stuck-up g-dimensional principally polarized abelian variety (A,Θ) together with a marked odd theta characteristic ξ comes up and cuts you off.

Ted Shifrin

Oh ...

There's a long way from middle school to advanced differential/algebraic geometry :)

meow-mix

01:47

well

Semiclassical

"this stuck up θ[ξ](z,Ω) comes and cuts you off"

almost looks like an expletive :P

meow-mix

there exists middle school differential/algebraic geometry?

Ted Shifrin

um, no

meow-mix

i kid you

it was the fault of the English language

Ted Shifrin

you're wasting my time when I'm trying to typeset this darned thing

Semiclassical

01:48

high school algebraic geometry = analytic geometry. (i kid, mostly)

meow-mix

every day at lunch i get this kid who asks me to teach him trigonometry

Ted Shifrin

not so much

that's quite cool, @meow

meow-mix

and when i do decide im in a good enough mood to teach, he doesn't listen

Semiclassical

not so cool

meow-mix

at least he remembers SOHCAHTOA :D

Ted Shifrin

01:49

He's ahead of some high school kids I worked with last year.

meow-mix

Professor Shifrin's class: "Middle School Algebraic Geometry 450"

Ted Shifrin

smacks @meow

Balarka will be glad that you're the one getting smacked now.

meow-mix

that was my first time being handed a Ted-smack

Semiclassical

It's interesting how the perspective changes

From "equations represent curves" to "these equations -are- the curves"

meow-mix

in what instance would the equations be the curveS?

Semiclassical

01:52

I'm probably putting the point too strongly

Fargle

I think @Ted's smacked me once or twice. It's a true badge of "honor", if by "honor" you mean something totally other than honor.

Semiclassical

Badge of infamy?

Fargle

Like chagrin.

Ted Shifrin

glares @Fargle

heather

shame, perhaps?

Fargle

01:53

Those work too.

@TedShifrin I only bug you because you're fun.

...and you've helped me a good number of times.

Semiclassical

I got Ted-smacked a few days ago. I forget why, but I probably both deserved it and wasn't ashamed :P

Ted Shifrin

You guys would get along with all my long-suffering former students. :)

Fargle

Heck, I feel like I practically am a long-suffering former student at this point.

Ted Shifrin

No, you're infinitesimal-suffering.

Semiclassical

you're in an epsilon-neighborhood of suffering

Fargle

01:55

@TedShifrin So it'd take Cauchy and Weierstrass to formalize how I'm suffering?

Ted Shifrin

Précisément.

meow-mix

@ted hey, i finally found a word that i understand in your document

"Holomorphic" :D

Ted Shifrin

LOL, @meow. That's about the worst paper to have picked, btw.

Brody

Like a hologram that morphs rite?

Ted Shifrin

Look for the one on Polar Varieties and INtegral Geometry. Much more cool.

meow-mix

01:57

no, its like a transformer

but hollow

Brody

oh

Ted Shifrin

howdy @Browdy

guess that won't ping

Brody

uh-uh

I'm quite okay, @Theodore

Transcript for

$Mathematics$ Mathematics