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General Q&A about all branches of theoretical and applied mathematics, including closely-adjacent sciences where the central question is about the math.

334 posts   RSS
Activity Age Score Random
Filters (None)
66%
+2 −0
$\sum_{k=0}^{n} \binom{n}{k}=2^{n} \overset{?}{\iff} \sum_{k=0}^{n} \binom{2n+1}{k}=2^{2n}$

1 answer  ·  posted 3y ago by DNB‭  ·  edited 3y ago by DNB‭

combinatorics
60%
+1 −0
Find the intervals on which it is increasing and those on which it is decreasing of the following function.

1 answer  ·  posted 3y ago by deleted user  ·  last activity 3y ago by deleted user

calculus derivatives real-analysis functions maxima-minima
33%
+0 −2
Why isn't the probability of being void in 3 specifi c suits $\frac{1/13}{\dbinom{52}{13}}$?

0 answers  ·  posted 3y ago by DNB‭

probability
50%
+0 −0
How does the change of variable $\color{red}{r↦n−r}$ transmogrify $\sum\limits_{r=0}^n2^{n-r}\binom{n+r}{n}=2^{2n}$ into $\sum\limits_{k=0}^{n} \frac{\binom{2n-k}{n}}{2^{2n-k}}=1$?

1 answer  ·  posted 3y ago by DNB‭  ·  edited 3y ago by Moshi‭

summation
57%
+2 −1
Why rational to be indifferent between two urns, when urn A has 50-50 red and white balls, but you don't know urn B's ratio?

2 answers  ·  posted 3y ago by Chgg Clou‭  ·  last activity 3y ago by celtschk‭

probability
50%
+0 −0
Differentiating a series expansion of an arbitrary function

1 answer  ·  posted 3y ago by deleted user  ·  edited 3y ago by Mithrandir24601‭

calculus derivatives differentiation
50%
+0 −0
A formal-logic formula for decimal to binary conversion

3 answers  ·  posted 3y ago by deleted user  ·  last activity 3y ago by r~~‭

bases conversion
50%
+1 −1
Rules of checking differentiability for Rolle's theorem

0 answers  ·  posted 3y ago by deleted user  ·  edited 3y ago by deleted user

calculus real-analysis limits differentiability rolle's-theorem
50%
+0 −0
Second mean value theorem proof (differentiation)

0 answers  ·  posted 3y ago by deleted user  ·  edited 3y ago by deleted user

calculus real-analysis differentiation
33%
+0 −2
If k = 1, why $n(n-1) \dots \color{red}{(n-k+1)} = n$?

1 answer  ·  posted 3y ago by DNB‭  ·  edited 3y ago by DNB‭

probability
28%
+0 −3
Why shouldn't the Bose-Einstein value be used to calculate birthday probabilities?

0 answers  ·  posted 3y ago by DNB‭

probability
33%
+0 −2
You're sampling k people from a population of size n one at a time, with replacement and with equal probabilities. Order or not?

0 answers  ·  posted 3y ago by DNB‭

probability
33%
+0 −2
What's the bijection between Stars and Bars and Integer Solutions to an Equality?

0 answers  ·  posted 3y ago by DNB‭

combinatorics
50%
+0 −0
"A occurred" vs. "something must happen"

1 answer  ·  posted 3y ago by DNB‭  ·  edited 3y ago by DNB‭

probability
28%
+0 −3
Are Stars and Bars in Combinatorics related to the Fence Post Error?

0 answers  ·  posted 3y ago by DNB‭

combinatorics
28%
+0 −3
Explain to a 9 year old — To count each possibility c times, why divide by c? Why not subtract by c?

0 answers  ·  posted 3y ago by DNB‭

probability
66%
+2 −0
How can I deduce which operation removes redundacies?

3 answers  ·  posted 3y ago by DNB‭  ·  edited 3y ago by DNB‭

probability
33%
+0 −2
What story and two-digit Natural Numbers best fit Bayes' Theorem chart?

0 answers  ·  posted 3y ago by DNB‭  ·  reopened 3y ago by Monica Cellio‭

probability
50%
+1 −1
How can Abraham Wald's approach lead you to ignore crucial features of a problem?

1 answer  ·  posted 3y ago by Chgg Clou‭  ·  last activity 3y ago by JRN‭

intuition
62%
+3 −1
Why are you permitted to define $1 − 1 + 1 − 1 + . . .$?

1 answer  ·  posted 3y ago by Chgg Clou‭  ·  last activity 3y ago by JRN‭

number-theory
66%
+2 −0
How to visualize division as splitting Dividend into B equal “partial groups”, then rounding up A partial groups to get a full group?

1 answer  ·  posted 3y ago by Chgg Clou‭  ·  last activity 3y ago by leovt‭

visualization
60%
+1 −0
How does Pr(an event next year) $= 1/100$ imply Pr(at least one of these events occurring in the next 25 years) $> 1/5$?

1 answer  ·  posted 3y ago by Chgg Clou‭  ·  last activity 3y ago by Nat‭

probability
50%
+0 −0
How's the outcome of airplane crashes almost always certain, but the probability is not? [closed]

0 answers  ·  posted 3y ago by Chgg Clou‭  ·  edited 3y ago by Chgg Clou‭

probability
50%
+0 −0
Why isn't $\Pr(diseased|+ test) = \dfrac{\text{number of true positives}}{\text{number of false positives}}$?

0 answers  ·  posted 3y ago by Chgg Clou‭  ·  edited 3y ago by Chgg Clou‭

probability
50%
+0 −0
Why paradoxical to accept \$3, and avoid betting on Dushanbe's temperature for a prize of \$10?

0 answers  ·  posted 3y ago by Chgg Clou‭  ·  edited 3y ago by thelast19digitsofpi‭

probability
40%
+0 −1
What does "individuals discount the future in a constant manner" mean?

0 answers  ·  posted 3y ago by Chgg Clou‭

probability
37%
+1 −3
If money's less valuable in the two-bullet case of the Russian Roulette problem, then ought you pay more to remove a bullet when the gun has $\ge 2$ bullets?

0 answers  ·  posted 3y ago by Chgg Clou‭

probability
33%
+0 −2
Why should the near-zero prior probability, of 9/11/2001 attacks on the World Trade Centre, overwhelm any subsequent response that may have lowered the objective risk?

0 answers  ·  posted 3y ago by Chgg Clou‭  ·  edited 3y ago by Chgg Clou‭

probability
33%
+0 −2
Why's the unique sub-game perfect equilibrium, that the first player should offer around $1.25 to player 2?

0 answers  ·  posted 3y ago by Chgg Clou‭

game-theory
33%
+0 −2
De-mystifying tricks – If $\{x_n\}$ converges, then Cesaro Mean converges.

1 answer  ·  posted 3y ago by TextKit‭  ·  last activity 3y ago by thelast19digitsofpi‭

analysis
42%
+1 −2
How can I visualize $\lim\limits_{x \rightarrow \pm \infty} f(x) = \lim\limits_{t \rightarrow 0^{\pm}} f(1/t)$?

1 answer  ·  posted 3y ago by TextKit‭  ·  last activity 3y ago by thelast19digitsofpi‭

visualization
50%
+0 −0
How to quantify "married people are less likely than the average person to smoke", "smokers are less likely than the average person to be married"?

1 answer  ·  posted 3y ago by Chgg Clou‭  ·  last activity 3y ago by thelast19digitsofpi‭

probability
50%
+0 −0
What was Justice Scalia's mathematical mistake in Penry v. Lynaugh (1989)?

1 answer  ·  posted 3y ago by Chgg Clou‭  ·  last activity 3y ago by Derek Elkins‭

probability
50%
+0 −0
Why mustn't the proportion of smokers among married people be the same as the proportion of smokers in the whole population?

1 answer  ·  posted 3y ago by Chgg Clou‭  ·  last activity 3y ago by r~~‭

probability
50%
+0 −0
How to intuit : married smokers × all people < all smokers × all married people ?

0 answers  ·  posted 3y ago by Chgg Clou‭

probability
40%
+0 −1
Why do 3D mental pictures usually suffice for high-dimensional geometry?

0 answers  ·  posted 3y ago by Chgg Clou‭  ·  edited 3y ago by Chgg Clou‭

geometry
33%
+0 −2
How can you foretell if a problem is one whose solution admits a simple mathematical description?

0 answers  ·  posted 3y ago by Chgg Clou‭

geometry
50%
+1 −1
Why can an easily graphable definite integral, be labyrinthine to evaluate?

0 answers  ·  posted 3y ago by TextKit‭  ·  edited 3y ago by TextKit‭

calculus
40%
+0 −1
Notation for Euclidean Norm

1 answer  ·  posted 3y ago by Guilherme Costa‭  ·  last activity 3y ago by tommi‭

notation
80%
+6 −0
How to show if a set is simply connected?

1 answer  ·  posted 3y ago by kreijstal‭  ·  last activity 3y ago by Derek Elkins‭

complex-analysis
60%
+1 −0
proving relative lengths on a secant

1 answer  ·  posted 3y ago by msh210‭  ·  last activity 3y ago by Peter Taylor‭

euclidean-geometry
57%
+2 −1
difference between quotient rule and product rule

3 answers  ·  posted 3y ago by deleted user  ·  last activity 3y ago by msh210‭

calculus quotient-rule product-rule
18%
+0 −7
Why is -1 needed to get 65,535 from a 2^16 binary power calculation?

1 answer  ·  posted 3y ago by deleted user  ·  last activity 3y ago by Canina‭

computability power binary
75%
+4 −0
Is this topology basis dependent?

1 answer  ·  posted 3y ago by celtschk‭  ·  last activity 3y ago by Incnis Mrsi‭

topology linear-algebra topological-vector-spaces
75%
+4 −0
Intuitively, why's X% of Y = Y% of X?

1 answer  ·  posted 3y ago by Chgg Clou‭  ·  last activity 3y ago by celtschk‭

percentage
66%
+2 −0
Why aren't $z_1=f(xy)$ and $z_2=f(x/y)$ functions of 2 variables?

1 answer  ·  posted 3y ago by TextKit‭  ·  last activity 3y ago by celtschk‭

calculus
50%
+2 −2
What kind of logic does “Logic in the Theory and Practice of Lawmaking” employ?

0 answers  ·  posted 3y ago by Chgg Clou‭

logic
44%
+2 −3
Approximation of an elliptic integral

0 answers  ·  posted 3y ago by theabbie‭

calculus
57%
+2 −1
If $n = xm$ and $n \rightarrow \infty$, then $m \rightarrow \infty$?

1 answer  ·  posted 3y ago by TextKit‭  ·  last activity 3y ago by The Amplitwist‭

calculus
80%
+6 −0
Does every divergence-free vector field arise as the curl of some vector field?

1 answer  ·  posted 3y ago by The Amplitwist‭  ·  last activity 3y ago by Derek Elkins‭

geometry multivariable-calculus derivatives
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