2,039 reputation
1229
bio website benalpert.com
location Mountain View, CA
age
visits member for 4 years, 2 months
seen Sep 13 at 20:29

I'm a software developer originally from Boulder, CO, currently working at Khan Academy in Mountain View, CA. In my spare time, I contribute to React, make music, and cook.


Feb
17
comment Proving the value of a limit using the $\epsilon$-$\delta$ definition
I don't think your sarcastic condescension helps anyone.
Feb
13
comment Finding $\int_0^{\pi/2} \sin x\,dx$
@Arturo: Yes, but why is the derivative of $\cos(x)$ equal to $-\sin(x)$ when $x$ is measured in radians?
Feb
13
comment Finding $\int_0^{\pi/2} \sin x\,dx$
@Isaac, you're right that that does make more sense. I'll change my question (though I'm not sure it was particularly unclear originally).
Feb
13
comment Finding $\int_0^{\pi/2} \sin x\,dx$
So you answered why the integrals give different answers scaled by a the ratio between a degree and a radian, but I already knew this. My question was why radians are special and give the answer of 1 (which you skip entirely when you say, "We know that…"). Sorry if my question was unclear.
Feb
13
comment Coloring points on an n-gon
Perfect, exactly what I was looking for!
Feb
13
comment Coloring points on an n-gon
Thanks; I'm accepting Qiaochu's answer because it's more complete (and also was a few seconds before yours).
Jan
26
comment I want to put my words into a formula/algorithm but I lack the mathematical fortitude
I agree with Yuval here; there's no reason to use any fancy math notation because the words you have currently are already very clear. Adding any symbols would unnecessarily complicate the algorithm. (And anyway, I don't think that there is any standard notation for what you want. Probably the best you can do is just write pseudocode for the algorithm, but that's not particularly mathy.)
Jan
24
comment Algorithm for generating integer partitions
@Will: Are you sure? I think that should work fine; that's what maxval is for.
Jan
22
comment a question related to two competing patterns in coin tossing
@PEV: I can't tell if I'm just being really stupid here, but I'm still unsure how that helps. For example, if with a fair coin you're looking for TH vs HH, it's much more likely ($3/4$ vs. $1/4$) that you'll see TH first because once you see a single T, it's impossible to get HH before seeing TH. How do we get the same answer using your method? (Presumably that would be $pq$ vs $p^2$.)
Jan
22
comment a question related to two competing patterns in coin tossing
@PEV: So if that's a fair coin, you're saying the probability is $1/32$. Of course, that's the probability that a random flip sequence of length 5 is equal to HTHTH but doesn't seem to answer whether HTHTH or HTHH is more likely to appear first.
Jan
22
comment a question related to two competing patterns in coin tossing
Sorry, but does this actually answer either of the part of the problem? I'm (not very familiar with Markov chains and am) confused about what the mean time tells you. (And I'm assuming $q = 1 - p$; is that right?)
Jan
22
comment a question related to two competing patterns in coin tossing
I'm also interested to know how to solve this problem; I've seen variations a few times on contests but never knew how to solve it.
Sep
16
comment Finding $\lim\limits_{n \to \infty} \sum\limits_{k=0}^n { n \choose k}^{-1}$
Why is the text on this so big?
Aug
3
comment How to solve this exponential equation
Besides, that's not a complete answer. x ≈ 1.37129 works as well.
Jul
30
comment Which average to use? (RMS vs. AM vs. GM vs. HM)
Isaac: Thanks, fixed.
Jul
30
comment Which average to use? (RMS vs. AM vs. GM vs. HM)
Qiaochu Yuan: Can you elaborate a little more? I'm not sure you mean by rotational invariance. How are you rotating the values?
Jul
30
comment Which average to use? (RMS vs. AM vs. GM vs. HM)
(Couldn't decide whether or not this is appropriate for this site; vote to close at will.)
Jul
30
comment Proof that $n^3+2n$ is divisible by 3
Indeed. If you do enough problems like this, then at least tricks like this become second nature.
Jul
30
comment Counting how many hands of cards use all four suits
This is a fantastic solution that I hadn't thought of. Thanks!
Jul
30
comment Are the “proofs by contradiction” weaker than other proofs?
Related: math.stackexchange.com/questions/198.