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 Curious
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Feb
3
comment Are binary bit-strings the most efficient representation of integers?
No because the entropy of an integet is captured precisely by its binary bits, so it's impossible to be more efficient in representing it. Moreover, the hardware that handles them is built of transistors that are basically binary switches. So other low level representation requires either emulated or completely different hardware. You can maybe try to think about the cpu architecture that perform arithmetic on integers, see if you can be clever. Keep in mind, Intel has been thinking about this for decades.
Jan
15
awarded  Curious
Jan
14
comment Solve $a^x + b^x = c$ for $x$.
Numerical methods don't interest me much since we have wolfram alpha for that. But thanks anyways.
Jan
14
accepted Solve $a^x + b^x = c$ for $x$.
Jan
14
comment Solve $a^x + b^x = c$ for $x$.
Well the original question was to solve $6^x - 2^x = 32$. Re-arranging, $3^x - 2^{(5 - x)} = 1$ implies $1 \leq x \leq 5$, so I assumed integer solution and found $x=2$. The solution is probably unique.
Jan
14
comment Solve $a^x + b^x = c$ for $x$.
Okay, a bit of pity. I was hoping for a clever approach. I'll delete this question in a day or so since it adds nothing for the rest of the community.
Jan
14
asked Solve $a^x + b^x = c$ for $x$.
Sep
8
accepted Expected number of flips until kth head
Sep
8
asked Expected number of flips until kth head
Aug
13
comment Find $\int\frac{x^2+x}{(e^x+x+1)^2}dx$
$a^2 (b + c + d)^2 \neq (ab + ac + ad)^2$. The expression for the second integral is incorrect.
Aug
13
comment Jobs in industry for pure mathematicians
@Vectornaut Let's be clear about what is pure math and what is not. Computational complexity theory (of which quantum computation is a part) is a branch of computer science. Computation theory is an application of math. Also in one of your very example papers, did you notice the word x box 360 live in the title? Think that's a coincidence? I think not. It's another marketing strategy to promote their products.
Aug
13
awarded  Teacher
Aug
13
answered Jobs in industry for pure mathematicians
Mar
13
revised product of different order Bessel function integral
changed picture formula to latex
Mar
13
suggested approved edit on product of different order Bessel function integral
Jan
30
accepted In a 4-card hand consisting of only numbered cards (2 - 10), what is the probability that the sum of red cards is twice the sum of black cards?
Jan
30
comment In a 4-card hand consisting of only numbered cards (2 - 10), what is the probability that the sum of red cards is twice the sum of black cards?
Thank you. Your count matches what I have from my program which solved it by brute-force, so it has to be correct.
Jan
30
revised In a 4-card hand consisting of only numbered cards (2 - 10), what is the probability that the sum of red cards is twice the sum of black cards?
edited body
Jan
30
comment In a 4-card hand consisting of only numbered cards (2 - 10), what is the probability that the sum of red cards is twice the sum of black cards?
No. You do not replace the cards. You draw cards in the traditional sense of drawing cards from a deck, meaning once card A is drawn, it cannot be drawn again. Independent means the current set of drawn cards doesn't affect the result of drawing the next card. And yes, you are essentially only drawing from 36 cards.
Jan
30
asked In a 4-card hand consisting of only numbered cards (2 - 10), what is the probability that the sum of red cards is twice the sum of black cards?