oh, @ted, i was just realizing something (which in retrospect could've been obvious to me)

you'd mentioned a colleague a while back (M. Adams) who knows quite a bit about kp equation stuff

@user1667423: In particular, the Hessian as a quadratic form is only intrinsically meaningful at a critical point of the function. Otherwise it is not tensorial.

and I mentioned him again a few days ago, @Semiclassic

yeah

just now i went back and looked at his publication list, and i noticed a certain name (aside from yours, i mean)

Oh, he's done work with some of the guys you're reading, I think.

yeah, J. Harnad. just the other day I had stumbled upon a lecture of his on KP equations and tau-functions which was actually understandable :)

Harnad visited here back in the 80s, but I haven't seen him in ages.

ah, interesting

@TedShifrin So before I was working with f subject to the constraint g = c. I was trying to use TMOLM. Now with the parameterization, I am working on the $n-1$-hypersurface $g(x)=c$ and this allows me to do standard calculus without needing TMOLM?

it's really all of this tau-function business i'm trying to grapple with

which i'm starting to appreciate the spirit of, if not the details yet.

Right, @Stan. This is effectively the method you used in Calc I (and in multivariable, first) when you used the constraint equation to get rid of one of the variables and do "regular calculus." But LM is computationally more efficient !

Yeah, @Semiclassic, I honestly don't know any of that stuff.

it's not obvious, no. though it does link up with something seemingly unrelated i was talking about a while back

i was talking about a certain integral, and the motion of the poles of its integrand as a parameter was varied

Right.

and what i'm hoping to get out of the tau-function business is to be able to view those poles (which are roots of a characteristic polynomial) as the 'coordinates' of some hamiltonian system

i.e. to find an underlying dynamical system for them.

Somehow they should embody conserved quantities?

something like that.

hopefully it's not too quixotic

but having read a bit of Gehktman-Kasman's work on KP tau functions, i think the logic is right.

@TedShifrin Will real analysis help me have a more solid mathematics education foundation? I'm trying to figure out what gaps I have and fill them (I know there are a lot :) but I'm in college! time to learn)

Well, I can't make any intelligent comments, @Semiclassic, other than to urge you onward :)

heh, okay

Most likely, the real analysis course will assume a lot of background and proof experience, @Stan. That's another reason to think through an introductory book such as the one I mentioned earlier.

one thing i wish i did have, for practical purposes, was some go-to geometric notion of what a grassmannian is in order to have the right intuition

i kind've understand it, but not in a sufficiently stable way

What can be more intuitive than a space that parametrizes the $k$-dimensional subspaces of your vector space? Much the way the unit sphere parametrizes oriented $1$-dimensional subspaces.

hmm, that's a good point

@Hippalectryon salut

@TedShifrin Hi

@Gato o/

I find differential forms the most intuitive way to understand the calculus on Grassmannians, @Semiclassic, but that's my innate bias :)

Salut, @Gato @Hippa

hah

i'd probably appreciate that, tbh, given my physics background

though, 1D subspaces? i'd have expected 2D, since i can think of each ray through the sphere as defining the normal direction of a plane through the origin.

though i guess in 3D there's a duality between 1- and 2-forms

In a few words, @Semiclassic, you work with adapted orthonormal (or unitary) frames $e_1,\dots,e_k;e_{k+1},\dots,e_n$. The basis for the $1$-forms comes from looking at $\omega_{\alpha\mu} = de_\alpha\cdot e_\mu$, where $1\le \alpha\le k$ and $k+1\le \mu\le n$.

These visibly tell you how the frame is twisting out of the subspace you're in.

hmm, i think i see what you're getting at

Right, you're confusing subspace and perp with that last comment.

$e_1,\dots,e_k$ span your $k$-dimensional subspace, and the $e_\mu$ span the perp.

hmm

@Hippalectryon j'ai un petit exo marrant :soit $\alpha_n$ une suite de réels positifs telle que $\lim_{n\rightarrow +\infty }n\alpha_n=0$ alors $\lim_{n\rightarrow +\infty } (1+\alpha_n)^n=1$

:D

Très intéressant, @Gato. Néanmoins $(1+k/n)^n \to e^k$.

well, i guess my question then is: if the 1D subspaces of $\mathbb{R}^3$ are parametrized by the unit sphere, what are the 2D subspaces parametrized by?

By something that is abstractly different, but just the same as the sphere, @Semiclassic (assuming orientations, of course).

This is an appearance of the hodge star operator which is the isomorphism between $k$-vectors and $(n-k)$-vectors, given by perp.

nod

@TedShifrin What's the difference between mathematics and statistics departments in terms of courses taught? Why do they have separate departments (at least they do at U of C)? Is it just for research purposes or are there differences in how the two groups teach mathematics?

$\star dx = dy\wedge dz$ and all that

Stat really doesn't teach mathematics. Statistics and probability (and on the theoretical level, measure theory) overlap, of course, but the statisticians have a very much more applied viewpoint. They emphasize when you can meaningfully interpret data. Probably more important in the real world than a lot of math.

sounds right. i was starting from "what is the unit sphere parametrizing" rather than "what parametrizes the 1D subspaces"

@TedShifrin Oui je n'ai pas utilisé l'exponentiel ici, cependant je ne sais pas si elle aide pour la solution.

Right, @Semiclassic. That's an instance of your associating a $2$-plane with its normal vector.

@Gato Comme Cesaro. $\displaystyle1\le(1+a_n)^n\le1+\sum_{1}^{N-1}\binom{n}{k}a_k+\frac{n-N}n \epsilon$

Moi, je regarde un peu de la série de Taylor, @Gato.

right. which is fine in 3D, but in higher dimensions that's not the duality given by the hodge star

@Semiclassic, but it's always the correspondence $V\leftrightarrow V^\perp$.

right

though if memory serves it all gets a bit more subtle when you're doing, for instance, electromagnetism in spacetime rather than just space

@Hippalectryon@TedShifrin plusieurs méthodes possible comme d'hab :)

though i'm forgetting the right terminology, ugh

Mais, tout simplement, $\log (1+a_n)^n = n\log (1+a_n) = n(a_n + o(1/n^2)) \to 0$.

minkowski v. euclidean space

@Semiclassic: I've never learned that.

@TedShifrin $a_n=n\alpha_n$ ?

Oops. $a_n = \alpha_n$.

Wikipedia has a brief discussion

mais on ne peut faire comme comme cela donc

@Semiclassic: I've always been particularly fond of "Classical electrodynamics as the curvature of a line bundle."

Pourquoi pas, @Gato?

also here re: the hodge star link

@TedShifrin pour fare avec log il faut que $\alpha_n$ tende vers $0$

Mais tu nous as dit que $\alpha_n = o(1/n)$.

my point being that the association of hodge duality with $V\to V^{\perp}$ gets more subtle in that case due to the metric not being positive-definite

well, right, because there are light cones.

i'm vaguely remembering some comments in one of Penrose's texts to that effect, though i'm not a relativist

you're only relatively unsure?

yep

Boooooooooooooo.

glarees @Fargle

@TedShifrin Je ne vois pas pourquoi $\alpha_n$ tend vers 0 avec cet argument..

:D

@Gato, tu nous as donné le fait que $n\alpha_n\to 0$, n'est-ce pas?

oui

Donc, ça veut dire que $a_n\to 0$, en particulier.

Je ne comprends pas ton problème là ...

@TedShifrin Non rien, je pensais à autre chose en même temps ^^

on a less esoteric note, i've also seen the hodge star operator used in the context of electromagnetism in $\mathbb{R}^3$ to represent the difference between electric displacement and electric field

@Fargle: I'll have more to say to you when you're less ghostly.

@TedShifrin Well, say it now, as long as you're done with puns!

I'm never done.

No, I figured you might have something more to say. I hope your police issue is long past and resolved.

BTW, I'm sure Ken subjected you to our poor mathematician humor, as well.

It is. Refunded and all. My father didn't want to pursue any action as long as they gave him the money back.

ugh, finally found the paper i was looking for

And yes, I really enjoyed Dr. Knox's sense of humor. I could tell that I seemed a bit, er, "posery", as I laughed at a lot of jokes that the typical math undergrad doesn't understand yet.

"What's an anagram of Banach-Tarski? Banach-Tarski Banach-Tarski." "HAHAHAHAHAHAHA...hahaha...oh."

no

@Fargle reddit ?

Can someone tell me which book is better out of those two?

I mean, that's where I first saw the joke, @Hippa. But he told that one--or one in the same vein (maybe the Mandelbrot joke) in class.

bah, i hate it when my html links don't work and i can't tell why

@TedShifin if you had the option of designing an ideal undergrad mathematics education, how would you design it?

@Semiclassical That's a good read. A bit over my head as yet, but still, neat stuff.

it's interesting, yeah

It blows my mind sometimes how well-suited mathematics is to physics. But that's an old-hat discussion.

heh, yeah

It provides a really good answer to the question of "why even study pure math", though, besides the usual answer I give of "knowledge for knowledge's sake is never a mistake". Look at how useful linear algebra has turned out to be ~150 years later. Applications often follow long after the groundwork.

@Hippalectryon ^^^

Yep I know this one too :D

group theory is another big instance of that. the fact that clebsch-gordon coefficients are essential in certain quantum mechanics calculations is sort've hilarious

@Hippalectryon Too short unfortunately.

@Fargle yes, that's a cool one.

then there's the "what does the B stand for in Benoit B. Mandelbrot?" "Benoit B. Mandelbort".

Yeah, that one's among my favorites as well.

Or the more silly and surreal ones. "What's purple and commutes?" "An abelian grape."

There's a worse one involving an abelian poop

alternate answer: Barney the Dinosaur on his way to work?

"What's purple, commutes, and is worshipped by a small number of people?" "A finitely-venerated abelian grape."

yeah, haha.

but nothing beats the ffee joke.

YES.

It took me a few years to get that one fully. (I still have yet to read/be taught a good treatment of category theory.)

yes, it's a bit sophisticated.

hey i need help with law of cosines, i keep getting the wrong answer (at least according to google)

Speaking of. Do you know of any good resources regarding such? I find myself bored today, and I'd like to put my energy toward learning.

resource on category theory?

Yeah.

There are multiple books solely devoted to category theory. MacLane's being the standard text.

can some one tell me if you get 49.65182845 degrees for unknown angle here:

But I wouldn't prefer actually going ahead and learning category theory

because google says 65

Picking the stuff up as you go along learning other things is the best way to learn general nonsense, in my opinion.

A lot of general nonsense won't make sense unless provided the appropriate context.

(thus the adjective "nonsense"!)

@Dave This should just require law of sines, not the law of cosines, right?

oh, speaking of, I recalled an even better one : 'a coconut is nut, whenever the nut is finite dimensional'

@Fargle i dont know =/ i thought it would be cosine

@Fargle what gives away that it should be law of sine?

@Dave The big hint here is that theta is opposite a given side, and you're given another angle opposite another given side.

theta being the angle 0?

$\theta$, yeah.

@Hippalectryon ^^^

Hey @BalarkaSen

ah thats what that symbol is called !

:D

And @Hippalectryon

ok ill try law of sines and see what i get! thanks!

hoy @KajHansen

@Dave No problem!

We're using Hungerford in my Algebra course this coming semester @BalarkaSen. I'm impressed with it so far. Lots of rigor, and fairly readable at the same time.

I've never read it.

Sounds like fun

@Balarka: I have a copy kicking around here somewhere. It's good, but I still prefer D-F. (Bias is bias.)

I like Artin.

Lots of intuition.

But D-F has strong exercises

Yeah, it's not too bad. I'm just going through it slowly, in order. The first chapter introduces Neumann-Bernays-Godel set theory so that he can talk about categories in the next.

I used Artin a good bit when I was taking my first algebra course. I'm a pretty big fan. And I've used D&F as a reference...also a fan but less familiar.

I'm just glad the professor didn't choose Lang. I've heard some negative things about it.

@BalarkaSen Thanks for both the book recommendation and the insight--you're probably right. I'll try to broaden myself a bit before I step up to gen. abs. nonsense.

@KajHansen That was used when I had algebra over 35 years ago.

@robjohn, Hungerford you mean?

@Dave I get $56.1791665189724^\circ$

@KajHansen yep

Em hello?

Hi.

Hey @VermillionAzure

I'm looking for a good bioinformatics/stats place to talk about

I'm at work and I'm trying to try out a differential expression tool but there's just soo many concepts I don't get sooo...

Is this the place?

@VermillionAzure It depends on the question and who's here.

Uhhh :(

well I'll try anyways

I need to figure out how this tool uses Bayesian probability to map count data of samples vs. features and why it maps to xy-plane or something and derives differentiation from a variable named Z

Do any of these concepts sound familiar?

@VermillionAzure the terms are familiar, but if someone is to answer, they'd need more information.

@robjohn Right uhhhh

I have a matrix of data, rows and columns

Rows represent features (genes)

Columns represent samples

Each sample is assigned to one of two groups or sets

Each data point in the table represents how many times a gene appears in a sample

We are performing differential analysis on this table--I want to find out which features are different or differ the most between the two

The tool states they use Bayesian probability or something; the status messages do indicate they use both posterior and prior probability but...

I don't understand how they go from that to...

A table of something like:

conc.b conc.a fail.r corr.b corr.a corr.theta

This sounds like it would be more apropos on the stats site. There might be someone here, but I don't hear anyone piping up.

@robjohn mmm, yes I think I agree. Thanks for the suggestion

Does the tool come with any documentation?

@KajHansen Yes, but it's for statisians who know what these things are, not a sophomore intern from EE

pklab.med.harvard.edu/scde/Tutorials

@VermillionAzure I think that this is the stats room.

@robjohn No one is there :(

I'll just post a question

haha, I don't know anything about statistics

@VermillionAzure That sounds reasonable.

@KajHansen Lang is... ugh

@BalarkaSen, that's what I hear from pretty much everyone :)

so, what have you been thinking about, lately?

been doing much math?

@BalarkaSen, I recently finished my REU where I was doing math 7 hours a day. We were studying rational dynamics in a special kind of space that included a complete, algebraically closed extension of the p-adic numbers as a subset.

I don't know whether to call that ugly or beautiful, @Chris'ssis

@Fargle simply amazing

Now I'm studying for the GRE, which really means that I'm reviewing calculus, differential equations, and linear algebra. And I'm starting studying Hungerford.

That works, too. Clearly I need to brush up on my calculus.

@Fargle :D

@KajHansen sounds cool

what is rational dynamics?

@Kaj: Was this at Georgia? Who does arithmetic dynamics at UGA?

@MikeMiller hello.

@MikeMiller, it was, with Robert Rumely

OK.

I learned algebra out of Hungerford. Whether or not that's a recommendation is up to you to decide.

@BalarkaSen, so in certain spaces mathematicians are interested in studying what happens when functions act on the space over and over again....meaning what does the image of $f \circ f \circ f \circ \cdots$ look like?

@Mike I found an analogy for neighborhood of a point in field theory. It's a commutative diagram consisting of a pt $k \hookrightarrow k^{alg}$, a map $k \to A$ and a pt $A \to k^{alg}$. Trying to analogize the notion of a covering map formally using this.

$A$ should be some special kind of $k$-algebra, but haven't figured out what.

The "rational" is referring to the functions being rational functions.

@KajHansen hm, ok. can we use this somewhere?

I think Mike told me about it while talking about Vojta's dictionary, but I hardly know anything about it, so forgive my ignorance

@BalarkaSen, well this sort of thing is how fractals are generated

For example, read the first sentence here: en.wikipedia.org/wiki/Mandelbrot_set

ok, right. so what do we study about these?

You see how that sequence is generated by composing a function with itself over and over again?

@SaalHardali translate it so it contains the origin, scale it down, then translate it back

Goodnight, @Balarka.

hi @Kaj

@anon Ah right! so obvious i missed it... thanks!

well, @Ted, I'll be asleep soon enough.

Chat guidelines | $\LaTeX$ in chat

@anon: I noted this morning someone needed to put that back up!

Oh, and hi :)

hi

@BalarkaSen, so when a function acts on a space in this way, the points of the set fall into one of two complementary subsets - either a given point is part of the "Fatou set" or it is part of the "Julia set". You can read about these here, since the Wiki article does about as good of a job explaining them as I could: en.wikipedia.org/wiki/Julia_set

Got exciting plans for this fall, anon?

I am not currently thinking that far ahead

oh, sorry ... I assume you'll be doing the GRE and applying?

And one interesting question to ask is, given a function, can actually find the Julia and Fatou sets.

Hey @TedShifrin

(not to be too much of an annoyance)

interesting.

What's wrong with Lang, @Kaj?

I figured he'd use Hungerford. Lang isn't that bad with a good teacher who doesn't just read the book in class, but not quite enough exercises.

He likes plain vanilla books.

Well, I don't have any personal experience with Lang @KhallilBenyattou. I've just heard a ton of horror stories.

His exercises are good, though, @Ted.

How do you type the font used for a category?

Like Set

There's a lot of interesting stuff in the later editions of Lang, Kaj. Did you take my Lang or did someone else?

\math***

?

@MikeM ... Better than Dummit/Foote's?

@dREaM, $\textbf{Set}$ ?

thanks

(Also, so I don't seem like a stalker, r9m added me on Facebook and I saw a picture of you that he liked. I liked it too but only realised that it was you until afterwards, @Kaj!) :-P

Automatically, since it's not packed into a book that has twice as many pages as it should.

That doesn't evaluate the exercises, @MikeM.

\textbf{...} in case you didn't see the code, @dREaM ^_^

D-F's exercises are good.

yeah, thanks.

@MikeMiller I really, really like D-F's exercises, as I've discussed with @Balarka on here recently.

@TedShifrin, someone else did. I'm pretty happy with Hungerford so far though. There's a lot of rigor, but at the same time I've been able to pick it up and read it without too much trouble.

yeah, it's a perfectly ok book, Kaj ...

The way he refers to everything by lemma number instead of words annoys me. Lee does this too.

Like proposition 2.34 etc. @Mike?

I probably do that too much, too, @MikeM ... It's an effect of LaTeX. Some things I call by name, as well.

That's a fair nitpick. It's all a matter of taste in the end anyway, as long as they both describe the material sufficiently.

@KhallilBenyattou, that's hilarious. People who I presume are from MSE like my Facebook stuff all the time, but I usually don't know who they are on here.

You know who I am, @Kaj. Oh wait ... I never like you.

I just ridicule you occasionally :D

:P

Off-topic, but I started reading Regular Polytopes by Coxeter. I literally started applauding when I saw von Staudt's proof of Euler's formula for polyhedra.

Haha! :-)

Not sure I know what that is, @Fargle. I don't know the name.

The book, or the proof, @Ted?

easiest proof of Euler's formula is to delete a face, project to the plane, and do systematic deletion of edges, faces and vertices

I'm trying to multiply a bunch of 2x2 matrices in Sage, and as far as I can tell, it's outputting something of the form [[formula],[formula,formula]]

Which is sort of, you know, missing a block.

I've seen the book, but long ago. I meant the proof, @Fargle.

I've never Saged, @MikeM, can't help you.

I thought it was based on Maple syntax.

but the shortest proof is, of course, by realizing euler char as an alternating sum of rank of homology groups

@TedShifrin Ah. It's pretty easy to put into words. Let $v$ be the number of vertices, $e$ the number of edges, and $f$ the faces. Then construct a tree out of the graph of edges and vertices--by necessity, it has $v-1$ edges.

@Balarka: That is killing a fly with an atom bomb.

It spits out its matrices like: [formula(space)formula] [formula(space)formula]. But for some reason it's not showing me the desired space in the first bit.

@Ted I agree :P

So it's probably got my two blocks smashed together. I actually asked it to factor the first entire block and it parsed correctly, which is obnoxious.

@DanielFischer The op hasn't replied anything to my response .. does this make sense or did I make some mistake? :| please take a look when you have time ..

Take the dual of this tree--it has $f$ nodes. Assuming the polyhedron is simply connected, the only way for some of these nodes to be isolated from the rest of the dual graph is for there to be a circuit around some of the faces in the original graph, which is impossible, because that graph is a tree.

How do you graph-theoretically describe a polyhedron as convex, or as having the type of a sphere, as opposed to something heinous, @Fargle?

@anon I think $K \otimes_k k^{alg}$ contains all the information of the fibers, one has to learn to read it (I haven't!). since $K \otimes_k k^{alg}$ is isom to a direct product of $k^{alg}$, a map $K \otimes_k k^{alg} \to K$ is an algebraic version of the map $* \sqcup * \sqcup \cdots \sqcup * \to X$. so I can believe that it's a "concise" way to write down the fibers, although extracting the homs $K \to k^{alg}$ from that seems pretty impossible.

hmm

Likewise, if the dual graph had a circuit, it would cause the original tree to fail to be connected. Thus, the dual graph is also a tree, and has $f - 1$ edges. Since the edges of the polyhedron are counted in full by the tree and its dual, we have $(v-1) + (f-1) = e$, from which Euler's formula follows immediately.

fun fact: $K/k$ is separable $\iff K\otimes_k k^{\rm sep}$ is reduced

I wish I had a chance to take graph theory. Seems cool, but all sorts of other cool math is always in the way.

"reduced"?

@TedShifrin Convexity is not required, only simple connectedness--that is, every circuit of edges bounds at least one face.

Or physics was in the way, @Kaj.

haha, indeed @Ted

Ah ... so that is used essentially, @Fargle, good.

I think that's why you got stuck in my diff geo class, @Kaj :P

@TedShifrin It's a very pretty proof, in my opinion. Easily described in words, and there are no outrageous leaps of logic.

Oh, differential geometry would've taken precedence over graph theory any day @Ted

I like the cool counting arguments that go into the Gauss-Bonnet Theorem. Book-keeping with vertices, edges, faces, too.

Just because you did too much discrete math anyhow, @Kaj?

I didn't know about this proof @Fargle. Interesting.

@BalarkaSen It's very elegant. I think Armstrong's Basic Topology also starts with this proof as motivation.

Graph theory seems like one of those subjects I can pick up as I need it, which is why it's low on the totem pole in my mind. But nevertheless, it would've been nice to have it at some point @Ted

I don't recall.

And it's true that we did a reasonable amount in combinatorics, and I picked up some more in the 4950/Ramsey theory stuff.

You could easily pick up a graph theory book and plow through it quickly, @Kaj.

Ok, I guess just extracting it entry by entry works fine. Painful.

@MikeM ... Your Canadian sojourn is almost over?

Exactly my thoughts @Ted. That might be what I'd be doing right now if it wasn't for preparing for the GRE and algebra :P

BTW, @Kaj, Clarinetist posted on here that the GRE folks have put up a new sample exam. You should download it and share it with our friends. I was shocked at how much of it is now single variable calculus/analysis. Sort of disappointing.

Yes. Ciprian talks in 47 minutes about work he did recently with one of his postdocs. It went on the arXiv on Monday. Friday is off, Saturday is coming home, Sunday is assembling my home, Monday - retirement is work.

LOL ... well, perhaps one day in the next weeks will be to reassemble my home :P

Thanks for the heads-up @TedShifrin. Also, there are two subject GREs being offered between now and when I'm sending my applications off. Is there any downside to taking both? I ask because I know sometimes taking a test multiple times dilutes the value of your scores. (e.g. taking the SAT 20 times to get a perfect score is less impressive than the same feat accomplished after one time).

Your home is bigger. Will probably take multiple days.

@BalarkaSen I mean, it's basically identical to von Staudt's proof. It's graph-theoretic, but it boils down to combinatorics.

Unfortunately, unless you do the spring one, you don't have time to find out how you do on the first one in the fall before the registration date for the second has passed. They aren't cheap, though, @Kaj.

@Kaj: Just take one and study. You'll do well.

Practice doing lots of calculations and basic proof thinking quickly.

ok, I gotta go sleep.

Ok, that's good to know. I haven't taken one yet myself. I'll go ahead and register for one of them and really study my butt off over the next 6 weeks before the beginning of the semester.

I saw a bunch of problems on the test last night which I could do in 5 seconds, but will take most of you guys minutes because you don't approach them right.

'night everyone.

You can save a lot of time by making rudimentary approximations. eg some trig integral was like 1/(sin^2 + sin - 2) from 0 to pi/8 or something silly like that; take the dumbest possible upper and lower bounds for the integrand; suddenly only one answer works

'Night @Balarka!

saved me minutes on at least 5 problems

I only saw one integral problem where symmetry was a good thing, @MikeM. Very few integrals.

I noticed that as well @Ted in working practice problems. Oftentimes I'll start on a slower approach and be like "wait a sec! Trivial!"

The practice tests I took had half the number of integrals as the test I took.

@r9m A mis-spelled Möbius, a few forgotten "the", misplaced commas. But no mistake where it matters.

guten Abend @DanielF

Bon soir @Ted.

@DanielFischer :-) Thanks a lot!!!

I make that claim particularly on linear algebra things, @Kaj.

Morning @Mike.

Morning.

@MikeMiller, reminds me of when I was preparing for the calculus AP exam. The practice exams hit polar functions hard, and then the actual AP exam didn't have any at all.

Saw King Lear last night. It was a good performance, but their Cordelia was angry all the time. Which doesn't fit. Other than that I was happy.

I've actually never read Lear :( But Shakespeare is being taken with me.

Not the bard's best but that doesn't say much about its quality.

i remember similar things re: eliminating wrong answers with the Physics GRE

making sure the units make sense, for example

and checking limiting cases to see if they reproduce the right thing, yadda yadda

well, those are just logical things to do, @Semiclassic ... even mathematicians should do those :P

true. though i'm not sure a mathematician remembers, say, the expected far-field form of an electric dipole :)

I just meant the techniques/methods you were advising. Mathematicians find things with parameters.

yeah, the problem-solving is the same. just different applications

though for the physics gre it also helps to know certain combinations of fundamental constants from memory, since you don't get access to a calculator if memory serves

I'm outta here for now. Time for dinner. Take care.

later

See ya later, @Ted!

Which format do you leave your answers in, @Semiclassical?

Fractions of already known constants?

the physics gre is all multiple choice questions

Hello, can you tel me if it is right : $<A'(0)w,v>=\int_0^1\left[\int_0^1 G(t,s) f_u(s,u(s)) w(s) ds\right]' v'(t) dt=\int_0^1 [G(t,1)f_u(1,0) w(1)-G(t,0)f_{u}(0,0) w(0)]v'(t) dt$

Ah, gotcha.

so if you want to know the wavelength of light in a certain problem, say, you'd better know the constants

knowing things like $hc=1240\text{ nm}\cdot\text{eV}$ is really handy for those kinds of things

$hc$? Planck's constant by the speed of light?

yeah

Where would that be useful?

many, many places

(I haven't done much physics recently so I'm out of touch!)

Haha, I felt that'd be the answer!

Do you know if GRE papers can be found online?

one obvious example is that the energy of a photon is given by $hc/\lambda$

Oh, of course!

but it also comes in handy for the bohr atom

there's a whole (unofficial) site for the physics GRE

including the four available practice tests

or, at least there was when i took it. haven't looked in years.

@TedShifrin Hello, can you tel me if it is right : $<A'(0)w,v>=\int_0^1\left[\int_0^1 G(t,s) f_u(s,u(s)) w(s) ds\right]' v'(t) dt=\int_0^1 [G(t,1)f_u(1,0) w(1)-G(t,0)f_{u}(0,0) w(0)]v'(t) dt$

please

thank you

though my favorite thing like that isn't a fundamental constant. it's a way of remembering how to derive the bohr atom

May I ask which area of math that formula is from, @Vrouvrou?