14,903 reputation
12975
bio website linkedin.com/in/crntaylor
location London, United Kingdom
age 30
visits member for 3 years, 4 months
seen 11 hours ago

I'm broadly interested in very applied math. I try to apply ideas from mathematics, statistics, machine learning, formal systems and computer science to solve real-world problems. Mostly in applied finance/quantitative trading, but in other areas if the mood takes me.


The following is for my own use, but feel free to borrow it -

Hi. It looks like you are new here. We are generally very willing to help, but we like users to show the work that they've done towards solving the problem on their own first. If you can edit your question to show the code you've written so far, and where you are stuck, then you will get a much better response.


Mar
5
comment Game Theory/Bayesian approach to a bluffing game
@DanielR Pretty sure (although open to being proved wrong). Player 1's expectation, if he bluffs with probability $q$, is $E = 0.2(2p + (1-p)) + 0.8(q(-p + (1-p)))$ which simplified to $E=0.2(1+p) + 0.8q(1-2p)$. Therefore if $p>0.5$ the second term is negative, so $q=0$ maximizes the expectation. If $p<0.5$ the second term is positive, so $q=1$ maximizes the expectation. This assumes that player 2 never changes their strategy, of course.
Mar
4
comment What is equivalence of $(p \vee q) \wedge \neg (p \vee q)$?
Let $a = p \vee q$. Then you have $a \wedge ¬ a$.
Feb
21
comment How do you describe your mathematical research in layman's terms?
@Arthur Feynman was speaking about theoretical physics, which deals with quarks, gluons, hadrons, bosons and other things that most people aren't familiar with. His book QED succesfully imparted the flavour of quantum electrodynamics and the path integral formalism to me as a sixteen year old. I don't think we should shrug off our responsibility as mathematicians so easily.
Feb
18
comment Standard Deviation Annualized
@kookster Yes, still true (note that with only 30 data points the confidence intervals on your measured standard dev will be quite wide).
Feb
1
comment integration method
This transformation gives better convergence properties for the algorithm described in your code (which is essentially Gaussian quadrature at random locations) but that's not what I understand by the "hit and miss" method (generating random $(x,y)$ pairs and checking to see if they fall into the region being integrated).
Feb
1
comment integration method
This answer from over two and a half years ago suddenly got a flurry of upvotes - anyone know why?
Jan
31
comment Is this number rational or irrational?
@HagenvonEitzen Thanks. This question was actually inspired by this topic on Hacker News.
Jan
31
comment Coin flipping probability game ; 7 flips vs 8 flips
I would also be perfectly willing to accept the intuitive explanation as a proof. In fact, it's a strictly better proof than the one given, because it immediately generalizes to the case where your friend flips $n$ times and you flip $n+1$ times for $n\geq 0$.
Jan
31
comment Is this number rational or irrational?
@Martín-BlasPérezPinilla How long did it take you to come up with this argument? Did you see it instantly?
Jan
28
comment Few calculus questions
Hi. It looks like you are new here. We are generally very willing to help, but we like users to show the work that they've done towards solving the problem on their own first. If you can edit your question to show what you've done so far, and where you are stuck, then you will get a much better response.
Jan
15
comment Why isn't $\int\sin(ix)~dx$ equal to $i\cos(ix)+C$ ?
@Lucian The law in the land of Mathematics is "unequal until proven equal" ;)
Jan
14
comment Rational probabilities
@Did Oh, I misunderstood! I Assumed you were giving a reason that my example couldn't be a measurable space, and somehow twisted your words to mean something they didn't.
Jan
14
comment Rational probabilities
@Did Interesting - in what way does $2^\mathbb{N}$ fail to be a sigma algebra?
Jan
14
comment Rational probabilities
Interesting. I had initially written "consider only countable sample spaces" but decided to remove it to make the question more general. Any reason not to use a measure taking values on $\mathbb{Q}$ if you have a countable sample space (the sigma algebra could still be uncountable, I think, eg if $\Omega=\mathbb{N}$ and $F=2^\mathbb{N}$)
Jan
10
comment How to compute the output of floating numbers?
No problem - it's good to have you here at Math Stack Exchange!
Jan
10
comment Explain cosmic distances to a child
@Ethan Indeed. Or about 350 blocks in New York City.
Jan
9
comment Are there more even numbers than odd numbers?
@Jordy This next bit, you'll have to imagine me saying in a stage whisper. Here it is: mathematicians have come up with a way of treating $\infty$ as a number! Shh, don't tell anyone. If you want the secrets, you'll have to learn a bit more math, and then go and read about transfinite ordinals. The smallest infinite ordinal is normally written $\omega$. Confusingly, $1+\omega=\omega$, but $\omega+1>\omega$.
Jan
9
comment Are there more even numbers than odd numbers?
@Jordy The mistake was in thinking that $\infty$ is a number, and that $\infty+1$ is an expression that makes sense. It's easy to see that $\infty$ isn't a number, for here is a list of all the numbers: $\{0,1,2,3,4,\dots\}$. Where is $\infty$ in that list? You can't say "at the end", because the list doesn't have an end! (You also can't say "it's the ninth element in the list, but it's fallen over.")
Jan
9
comment There exists a power of 2 such that the last five digits are all 3's or 6's. Find the last 5 digits of this number
Thanks, this was very interesting.
Jan
8
comment There exists a power of 2 such that the last five digits are all 3's or 6's. Find the last 5 digits of this number
In case anyone is interested, the first such powers of 2 are $2^{1196}$, $2^{3696}$, $2^{6196}$ ... and all solutions are of the form $2^{1196 + 2500k}$ for $k=0,1,2,\dots$.