But this is probably not the best way to do the problem, if you need to use the calculator to get the answer, because the calculator doesn't have a $\log_3$ button.
Purely out of curiosity, I remember around 7-10 years ago Chinese students were complaining about how we don't have $\log_{b}(a)$ keys and we always had to use either $\log$ (for base 10) or $\ln$ (for base $e$). Have they made such a thing in the U.S. yet?
I have considered buying a TI-Nspire CAS to keep up with current times (still doing tutoring and have met some people with them). Not that I'd want to, but I would like to get to know the calculator...
@BalarkaSen: How do you calculate the homology $S^2 \vee S^1$? Usually you use Mayer-Vietoris. You might write something about how you can use the same relative argument as above to do this calcuation.
maybe i should add an answer here converting my comments into a well-organized answer, but i am ashamed as it might look like hand-waving compared to John's explicit map :P
@KarimMansour Yes, but his compositions are just pop compositions, essentially. vi - IV - I - V is way used too often, especially in that piece you posted
Can anyone explain the Hausdorff space in simple terms? I know only the definition that it's a topological space in which 2 distinct points have disjoint neighborhoods. Why do we need to define such spaces, how do we recognize them?
At least you aren't a Rachmaninoff fanatic, @Clarinetist. One of my brilliant math students this year is a violist/violinist and he was annoyed that I am not fond of the Russians (Rach and Tchaikovsky). My dad was a 20th century composer, btw, Clarinetist.
@MikeMiller seeing his last question, he seems to like to think about everything rigorously (like thinking about very boring, albeit important, point-set topology behind the proof of CW-pairs having HEP), so I am hesitating on posting an answer
@Balarka: I think I've tried to stress this a hundred times, but the kind of geometry you're gearing up to study now and that kind of geometry are completely different.
My initial motivation for learning altop was to know about this (galois theory) <--> (covering spaces) analogy. and now that I have read some altop, I don't think my curiosity has died out at all.
@Paradox101 I don't know, to be honest with you (since I haven't really done a deep study into both texts), but I can tell you that Tao is by far more readable.
@r9m well, like him, I strongly believe that I was blessed by God with the wisdom I have in the area of integrals, series and limits. Just think that I have no background in mathematics, just self-educated. :-)
@KarimMansour Another recommendation. I highly recommend listening to all 16.5 minutes sometime, but this is my favorite section of this beautiful piece.
@Chris'ssis oo!! okay!! I'll put my solution in my blog in a few days:D .. there are too many series and integral posts in my blog ,.. maybe I'll try and write sth about number theory in a post :-)
Write down the definition of surjective, @Vrouvrou, and use finite dimensionality. You shouldn't be studying the math you're studying if you can't do this without my telling you.
oh, I wanted to reply to "who cares about smash product" message of @Mike but I forgot all about it. anyway, the reply was supposed to be "all of my intuition on hopf fibration depends on $S^1 * S^1$, so I do care :P"
@Chris'ssis I thought about sharing a few problems from matrix based inequalities and such ,, but that'll take a long time and effort from my part .. so I have postponed my plans till the day I feel like moving my lazy ass :P
@r9m some people here believe that all I did in terms of mathematics so far was integrals, series and limits, but I did a lot of stuff from various branches.
Smash products are essential when doing later algebraic topology. It's how you do anything with spectra. But you don't need to know that until then, so when people ask me, I generally tell them to not bother with those either.
@r9m The thing that annoys most is that if I consider all these guys that talk about me at a blackboard and ask them to solve, say 10 problems, to solve in group I mean, I'm sure they solve no problem (in one year).
@TedShifrin "After holding brief teaching positions at Columbia and at City College, CUNY, Shifrin received a Fulbright for study abroad, and in 1951–52 he was a student of Darius Milhaud in Paris—another whose influence is felt in Shifrin's music, particularly in his scherzando style, which has something of the fleeting “bounce” of French composers of the neoclassicist tradition."
@TedShifrin You know in complex analysis, we have a decomposition $F(z)=(z-z_0)^pF_1(z)$ where $z_0$ is an isolated zero and $F_1(z_0)\ne 0$, does the power $p$ is unique ?
