@TedShifrin Thanks for the answer ! BTW, I have a book of almost the same name (40 Challenging problems in probability) from Springer too ! Does the book by Pitman addresses the issues commonly faced be beginning learners (and also understandable by beginners) ?
I don't know the Springer one, @Alex. The texts I named are written for college students, but they don't use a huge amount of baggage (although eventually they get to using calculus). I think Pitman has lots of interesting stuff in it; he's more of a statistician, so it's a bit more concrete than some math texts.
@Meow: So do you see the end?
@Alex: A few years ago I decided to teach probability for the one and only time before I retired. I truly enjoyed it and wished I had done so many years ago. It can be confusing, but it's very important (things like false positives/negatives on tests) and interesting.
@TedShifrin Ah very nice ! BTW, do you know similar books for linear algebra (because I need linear algebra to understand the very nice stuff here math.cmu.edu/~ploh/docs/math/mop2011/alg-comb.pdf , but they're way over my head)
@Alex: It's a matter of taste. My coauthor and I emphasize dot products and vector geometry from the beginning, whereas a lot of linear algebra texts delay dot product until Chapter 8 or later ...
@Phase: The issue is not the range but that the domain should be a space of functions, rather than a finite-dimensional $\Bbb R^n$ (in that case, $n=3$).
@TedShifrin Having $k_1 = 1$ and $k_2 = -1$ at every point would mean $K = -1$ everywhere, would it not? But there's no compact everywhere nonpositively curved dude out there in R^3
@TedShifrin I actually don't know how to prove there's no complete everywhere nonpositively curved surface in $\Bbb R^3$, I don't think. But I see what he's asking; I know everywhere -1 curved surfaces in $\Bbb R^3$ but none that I can construct off the top of my head with $k_1 = 1$ and $k_2 = -1$, nope.
@Daminark I have to look for some newer hipster music.
@Studentmath Me neither unfortunately, your $\theta$ doesn't seem to depend on anything except the value of $X_1$, but you're given the distribution of $X_1$
I asked a while ago, but how can I render mathjax in the chat rooms? I'm using chrome on Android. The solution (tinyurl.com/cfqcvpc) in the description doesn't work for me.
@MatheiBoulomenos It's a soft question unfortunately ;( In Germany, when you say "take a seminar" what do you mean? I feel like the word is used differently over there. Is it just like a reading course?
I see; the structure of the BMS programme requires you to take at least one seminar I think, so that just involves giving talks and listening to talks?
Yeah we call it a defence too, but it's not really a defence because the lecturers don't really care. You just show you did some work and pass. hahahah
Great! I love algebraic number theory and I'm really glad that I can finally take a lecture on it. I'm a little nervous about my seminar talk this tuesday, though
@Mike I'm not sure what I think of it, though I'm finding that the class in general just seems to going poorly. Between the pace, the problems, all that business, I'm finding that a number of people are just starting to really dislike the subject
Some people are just predisposed to dislike it but given that the rate is much higher now than what I think the class last year had, I do think part of it is just that the presentation is iffy
This most recent pset had Burnside's Lemma, one about relating a certain action of S_n to matrices (quite long to state so I'll do it when I'm not on my phone), a few that used Burnside, etc
But I've found many people didn't like the problems about rotation groups, and some were just like "List out the number of elements in each conjugacy class of S_6" which were long and dull
@Daminark Oh yeah, that sounds dull. We had to classify all subgroups of S_4 at one point, which involved a lot of casework, but it's useful for computing Galois groups of degree 4 polynomials to have that result, so there's that
For certain courses, I couldn't improve on the books much — Munkres, Guillemin & Pollack. Graduate complex I was never happy. I didn't love Ahlfors or Stein/Stakarchi.
Even when I wrote the book, I never just read out of the book to the class, but I know some profs who literally put the book up on the board every time.
My analysis professor taught and assigned all his problems from these 4 books, and aside from a few tangents even the theorem order was mostly the same
Another was like "I'm just kinda doing stuff, this material is all in finitely many books so I can give you that"
@TedShifrin I don't think I'm terribly fond of that style
@TedShifrin I'm sorry for bringing this up (again) but I still haven't understood why is that the number of rational numbers above the line $y=\epsilon$ being finite matters, I talking about that proof we discussed perhaps 2 days ago, thanks in advance.
@Mathei: I'm doing a high-school-ish course that they want to be universal no matter who teaches it. But of course the discussion and what we write down on each slide is up to me, more or less. But still ... A white board for little discussions, Demonark.
@Fuzzy: Take $\delta = \min(|a-x_1|,\dots,|a-x_s|)$. What can you say about $f(x)$ if $|x-a|<\delta$?
@Demonark @Mathei: I am writing a few extra problems that are my favorites or ones I'm thinking up that are a bit different, but interesting.
@Demonark: I am getting better at writing on computer screens with pens that show up on the wall :P
He seems to know an awful lot, Demonark. He knows esoteric stuff I've never thought about, too. And the few times I've asked him to derive/explain, he does it, and well. When he writes exercises in class that ask for explanations, he writes full sentences. Pretty impressive 9th grader.
I've been trying to give him some harder stuff to challenge him. We'll see if he does this week's homework before tomorrow morning.
We're getting to harder stuff now ... trig addition formulas and applications. The proof we'll do in class together is one I've never seen (although I'm kicking myself for not having thought of it).
