@TedShifrin I have played it a few times. I like it as a game to play with people who don't regularly play board games, since it is fairly simple and not too deep strategically (so people don't end up spending too much time trying to optimize their play)
I have considered getting it myself, since it is also of an appropriate level of difficulty to play with my daughter without having to alter the rules to make them easier
That reminds me. Got the preliminary plan for re-exams today. 6 people eligible for the algebra re-exam. Should not be too tough to grade those, though it feels like a shame to have to make an entire exam set just for 6 people
@TedShifrin These programs do feel a bit slow at times, since I already know the rules and a bit about bidding. But on the other hand, they do teach some fundamentals I did not know. Just went through a chapter on finessing, which is not something I had really considered before.
Yeah, and if you have a choice of finessing either way, do you have information from which to infer which way is more likely? (Bidding/counting points that have shown up in the respective hands, signals, etc.)
@TedShifrin This is before anything about bidding. But it did make a point of having you play as many cards as you could safely do before choosing which finess to take.
I am new to Math.SE. I have seen an accepted answer to some question that contains a fundamental mistake. Can you tell me what to do? If this is not the right location to ask this question, please excuse me and tell me ahere to look.
So far I have things on it like Tao's Analysis vol 1, Spivak's Calculus 3rd edition, Munkres' Topology Vol 2, Probability Theory (Jaynes), Principles of Mathematical Analysis (Rudin), etc
@TobiasKildetoft I was wondering if the dual question I had you help me with earlier was at all connected to using the $f_i := e_{i+1,i}$ to define the highest weight vectors (that is, f_i kill the highest weights).
@anakhronizein It should be to some extend, since the way we "fix" the duality is essentially to transpose the matrices (except we don't do this when we do things abstractly)
@orbit-stabilizer there seems to be (at least in my experience) a lot with functional analysis and non-commutative geometry. So I think that is one of the many branches that branch out.
my other answer was a joke but i would say that after you know the basics of functional analysis there's no direct next thing you can do, but you can apply the things you learned in like half of all math lol
So, my analysis prof said that there's two main directions you can go with functional analysis. One is geometry of Banach spaces, the other is PDE. It has applications elsewhere (e.g. Ergodic theory) but those are probably what someone who's principally interested in functional analysis will end up doing
Jesus , when I say analysis on metric space , am talking about the subject of generalizing analysis from eucledian spaces to metric measure spaces , see the book by Ambrosio for example
@orbit-stabilizer Are Hahn-Banach, Banach-Steinhaus and the open mapping theorem in Rudin? Those are the "big three" in an intro to functional analysis, then you get the weak and weak* topology, Banach-alaoglu and stuff, then you have the basics and you can see what you're more interesting in to go from there. That's also where I decided I had enough functional analysis and moved on to something else :P
You can take it down an interesting avenue for sure, we talked about Sobolev spaces and Hille-Yosida, but yeah it wasn't quite my favorite part of the class.
@BalarkaSen people like you are the reason nobody in math is comfortable asking trivial questions, you immediately put them in a low catagory even if they have decent knowledge
If you already know what a Banach space is (and maybe have seen the $L^p$ spaces, but just to have some examples to keep in mind) I suggest Brezis as a functional analysis book. It assumes a bit of knowledge, but not a lot (it starts with Hahn-Banach on page 1)
Chain homotopies are an abstract way to define homotopy in the category $\mathsf{Ch}_\bullet$ of chain complexes. But indeed, there is a geometric interpretation of this.
$f, g : X \to Y$ be two homotopic maps, with homotopy given by $F : X \times [0, 1] \to Y$. $f_{\#}, g_{\#}$ be the induced m...
oh ok. $(f_{n})$ converges to $f$ almost everywhere if there exists a set $M \in$ X with $\mu(M)=0$ such that for all $\epsilon>0$ and $x \in$ X $-M$, there exists a natural number $N(\epsilon, x)$ such that if $n \ge N$ then $|f_{n}(x)-f(x)| < \epsilon$ @0celo7
@LeakyNun Then $P$ is literally the map $C_n(X) \to C_{n+1}(Y)$ sending a singular $n$-cuboid $\square$ in $X$ to the $(n+1)$-cuboid $f(\square \times I)$ in $Y$
so if i say that let $M \ne \phi$ belong in $\sigma$ algebra on $X$ s.t $\mu(M)=0$. then by pointwise convergence on X $-M$, we have what we want. Now if such an $M$ exist, we are done, if there does exist such an $M$, then what does that mean? or will there always exist such an $M$? @0celo7