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http://unapologetic.wordpress.com/2011/01/13/standard-polytabloids-are-independent/?like=1&source=post_flair&_wpnonce=c1c9c39881 | # The Unapologetic Mathematician
## Standard Polytabloids are Independent
Now we’re all set to show that the polytabloids that come from standard tableaux are linearly independent. This is half of showing that they form a basis of our Specht modules. We’ll actually use a lemma that applies to any vector space $V$ wit... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 39, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/tagged/real-analysis?sort=faq&pagesize=30 | # Tagged Questions
Theoretical foundations of calculus: limits, convergence of sequences, construction of the real numbers, least upper bound property, and related analysis topics such as continuity, differentiation, integration through the fundamental theorem of calculus...
6answers
4k views
### How can you prove t... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 161, "mathjax_display_tex": 14, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/... |
http://mathhelpforum.com/calculus/83966-find-unit-vector-angel.html | # Thread:
1. ## Find Unit Vector and Angel
Suppose that you are climbing a hill whose shape is given by , and that you are at the point (90, 50, 300).
In which direction (unit vector) should you proceed initially in order to reach the top of the hill fastest?
,
If you climb in that direction, at what angle above the... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://www.math.uah.edu/stat/poisson/Poisson.html | $$\newcommand{\P}{\mathbb{P}}$$ $$\newcommand{\E}{\mathbb{E}}$$ $$\newcommand{\R}{\mathbb{R}}$$ $$\newcommand{\N}{\mathbb{N}}$$ $$\newcommand{\bs}{\boldsymbol}$$ $$\newcommand{\var}{\text{var}}$$ $$\newcommand{\sd}{\text{sd}}$$ $$\newcommand{\skew}{\text{skew}}$$ $$\newcommand{\kurt}{\text{kurt}}$$
## 4. The Poisson D... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 17, "mathjax_display_tex": 220, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/... |
http://mathoverflow.net/questions/109868?sort=newest | ## Finding linearly independent columns of a large sparse rectangular matrix
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
I have a problem that necessitates solving a large non-negative least-squares problem. My matrix A is large, sparse, highly rectangular... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 6, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/advanced-algebra/176353-center-sl-n-f.html | Thread:
1. center of SL(n,F)
Show that Z(SL(n,F)) $\cong$ {a $\in$ F* | a^n = 1}.
I know that if X $\in$ Z(SL(n,F)) then det(X) = det(aI) = a^n which has to equal 1 since it is in SL(n,F).
Any Help greatly appreciated.
2. Hi!
You write X=aI, so i suppose you know that a matrix commutes with any other matrix iff i... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 10, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/advanced-applied-math/20836-fourier-series.html | # Thread:
1. ## Fourier series
i,
I have a question about Fourier Series(FS) in my textbook which is persentted like this:
The uniqueness of a FS means that if we can find the FS of a waveform, we are assured that there is no other waveform with that FS, except for waveforms differing from the waveform under conside... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 5, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://snikolov.wordpress.com/2012/11/14/early-detection-of-twitter-trends/ | Early detection of Twitter trends explained
/
Next »
A couple of weeks ago on Halloween night, I was out with some friends when my advisor sent me a message to check web.mit.edu, right now. It took me a few seconds of staring to realize that an article about my masters thesis work on a nonparametric approach to detec... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 17, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/241583/computing-a-derivative-using-logarithmic-differentiation?answertab=active | Computing a derivative using logarithmic differentiation
Using the Logarithmic Differentiation find the derivative of $y=\sqrt{x(x-1)/(x-2)}$...so I tried,but the result is not correct..can you show me a hint?
so $\ln y= 0.5\ln[x(x-1)/(x-2)]$
$$\ln y=0.5[\ln x+\ln(x-1)-\ln(x-2)]$$
$$\ln y=0.5\ln x+0.5\ln(x-1)+0.5\l... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 14, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/124123/number-of-divisions-using-trial-division-to-factorize-the-product-of-two-k-digit | # Number of divisions using trial division to factorize the product of two k-digit primes
I'm more of a programmer than a Mathematician so please bear with me if my question is too trivial.
I am looking up RSA specifically the key generation bit. Using Trial division, I know that it would take roughly `(2*(n^0.5))/ln... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 5, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/pre-calculus/126338-graphing-function-window-print.html | # Graphing a function in the window?
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Show 40 post(s) from this thread on one page
• January 30th 2010, 05:14 PM
krzyrice
Graphing a function in the window?
I need help with this problem. So do I start out with plugging in random values for x? Such as -2, -1, 0, 1, 2 and so on. And what do they mean by ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 13, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/288319/what-is-a-tangent-bundle-aubin/288334 | # What is a tangent bundle? (Aubin)
Here's what I read in A Course in Differential Geometry by Thierry Aubin.
2.5. Definition. The tangent bundle $T(M)$ is $\bigcup_{P\in M} T_P(M).$
And then
2.6. Definition. Let $\Phi$ be a differentiable map of $M_n$ into $W_p$ (two differentiable manifolds). Let $P\in M_n,$ and ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 58, "mathjax_display_tex": 3, "mathjax_asciimath": 3, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/tagged/modular-arithmetic?page=1&sort=votes&pagesize=50 | # Tagged Questions
Modular arithmetic (clock arithmetic) is a system of arithmetic of integers. The basic ingredient is the congruence relation $a \equiv b \bmod n$ which means that $n$ divides $b-a$. In modular arithmetic one can add, subtract, multiply and exponentiate but not divide in general. The Euclidean ...
1... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 147, "mathjax_display_tex": 15, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/... |
http://mathematica.stackexchange.com/questions/tagged/functions+manipulate | Tagged Questions
6answers
258 views
Manipulate and Turning Expressions into Functions
I've been trying to use Manipulate to do interactive plotting, but I've been running into a few problems with saved expressions. I have an expression saved as "func" and I want to work with it and ...
1answer
217 views
Cournot Equ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/10349?sort=oldest | ## Smoothness of Symmetric Powers
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Here's something that's been bothering me, and that's come up again for me recently while reading some stuff about Hilbert schemes of points (Nakajima's lectures, specifically):
... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 93, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/8149/collision-time-of-brownian-particles/9552 | # Collision time of Brownian particles
Let's assume two spherical particles $p_1$ and $p_2$ of finite radius $r_1$ and $r_2$, which are at locations $(\pm\frac{d}{2},0,0)$ a distance $d$ apart at initial time $t$. These particles diffuse with coefficients $D_1$ and $D_2$, respectively. How can I obtain the probability... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 101, "mathjax_display_tex": 14, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/... |
http://mathhelpforum.com/calculus/28254-need-help-here-derivatives.html | # Thread:
1. ## Need help here with derivatives
Hey guys. I'm having trouble with derivatives and I need someone's help with my homework. Could you guys please explain to me how to solve these problems?
1.
Given $y = f(x) = \frac{1}{x^2} - \sqrt[3]{x}$
Find the second derivative
$f"(x)=\frac{d^2y}{dx^2}$
2.
Given $... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 11, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/76687/list | ## Return to Answer
2 added 120 characters in body
I had a minor thought. Did you ever look the paper Multiplicity of the special fiber of blowups by Corso,Polini, Vasconcelos.
In particular, they give an upper bound on the number (I realize that you are interested in lower bounds, but maybe some of the ideas are re... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 4, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/52028/radiation-pressure-on-a-dyson-sphere | # Radiation pressure on a Dyson sphere
To find the outward pressure from the sun's light on an enveloping spherical shell (Dyson sphere), one can simply divide the insolation by $c^2$. Using the entire system, we can specify the power of the sun in watts, $W$, leading to a pressure of $P=W/(4 \pi R^2 c^2)$.
The probl... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 57, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/14683/can-the-quantum-torus-be-realized-as-a-hall-algebra/14744 | ## Background
### The Quantum Torus
Let $q$ be an arbitrary complex number, and define (the algebra of) the quantum torus to be $$T_q:=\mathbb{C}\langle x^{\pm 1},y^{\pm 1}\rangle/xy-qyx$$ For $q=1$, this is the commutative ring of functions on the torus $\mathbb{C}^\times\times \mathbb{C}^\times$; hence, for general... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 48, "mathjax_display_tex": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?p=4024320 | Physics Forums
## How did "v" come out of this derivative?
1. The problem statement, all variables and given/known data
3. The attempt at a solution
I basically understood how to attack the problem and my answer was very close to the key. The only thing bothering me is that v on the top. I cannot see how that could... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 25, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://stats.stackexchange.com/questions/tagged/regularization?sort=active&pagesize=15 | # Tagged Questions
The regularization tag has no wiki summary.
1answer
215 views
### matlab gmdistribution.fit 'Regularize' - what regularization method?
I am wondering what is behind matlab 'Regularize' option for method gmdistribution.fit. If it is simply adding a 'little' value to diagonal elements of covariance... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 46, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/47777/list | ## Return to Answer
3 added 66 characters in body
The "correct" abstract definition of a derived functor involves the theory of "homotopical categories". An abelian category $\cal A$ does not have enough structure alone to consider homotopical properties. To this end, we usually look at $Ch^+(\cal A)$ or $s\cal A$ of... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 23, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://stats.stackexchange.com/questions/21997/odds-ratio-for-continuous-variable | # Odds ratio for continuous variable
I have a question
How would you interpret the odds ratios for a continuous variable?
-
1
– Macro Feb 1 '12 at 2:27
## 1 Answer
It's not completely clear from your question, but I'm assuming you're talking about the situation where you have a single binary response $Y$ and a co... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 11, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/23829/solutions-to-the-continuum-hypothesis/50654 | ## Solutions to the Continuum Hypothesis
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
(A related MO question: http://mathoverflow.net/questions/14338/what-is-the-general-opinion-on-the-generalized-continuum-hypothesis )
## Background
The Continuum Hypothe... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 136, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathoverflow.net/questions/44833?sort=newest | ## If $k[S]$ is noetherian, is S finitely generated?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Let $S$ be a semigroup. If $S$ is abelian, then it follows that the semigroup algebra $k[S]$ is finitely generated if and only if $S$ is.
What if we relax the... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 38, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.haskell.org/haskellwiki/index.php?title=User:Michiexile/MATH198/Lecture_3&diff=30605&oldid=30322 | # User:Michiexile/MATH198/Lecture 3
### From HaskellWiki
(Difference between revisions)
| | ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 38, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/162781/possible-subgroups-of-mathbbz-36-mathbbz-oplus-mathbbz-35-mathbbz-o?answertab=oldest | # Possible subgroups of $\mathbb{Z}/3^6\mathbb{Z} \oplus\mathbb{Z}/3^5\mathbb{Z}\oplus\mathbb{Z}/3^2\mathbb{Z}$
$G \cong \mathbb{Z}/3^6\mathbb{Z} \oplus\mathbb{Z}/3^5\mathbb{Z}\oplus\mathbb{Z}/3^2\mathbb{Z}$
$H\leq G$ so that $G/H \cong \mathbb{Z}/3^2\mathbb{Z}\oplus\mathbb{Z}/3\mathbb{Z}$
Find all possible $H$ up t... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 23, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/21892?sort=oldest | ## Formal deformations of algebras over not necessarily commutative rings
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
In Iain Gordon's survery article "Symplectic reflection algebras" the concept of formal deformations of algebras over semisimple artinian ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 6, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/80759/how-to-prove-that-x4x3x23x3-is-irreducible-over-ring-mathbbz-of-i/80762 | How to prove that $x^4+x^3+x^2+3x+3$ is irreducible over ring $\mathbb{Z}$ of integers?
Which criterion (test) one can use in order to prove that $x^4+x^3+x^2+3x+3$ is irreducible over ring $\mathbb{Z}$ of integers ?
Neither of Eisenstein's criterion and Cohn's criterion cannot be applied on this polynomial. I know t... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 26, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://nrich.maths.org/6416 | ### Lunar Leaper
Gravity on the Moon is about 1/6th that on the Earth. A pole-vaulter 2 metres tall can clear a 5 metres pole on the Earth. How high a pole could he clear on the Moon?
### Which Twin Is Older?
A simplified account of special relativity and the twins paradox.
### Whoosh
A ball whooshes down a slide ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 3, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://cstheory.stackexchange.com/questions/376/using-lambda-calculus-to-derive-time-complexity | # Using lambda calculus to derive time complexity?
Are there any benefits to calculating the time complexity of an algorithm using lambda calculus? Or is there another system designed for this purpose?
Any references would be appreciated.
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## 6 Answers
Ohad is quite right about the problems that the lambda calcul... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/tagged/analytic-geometry+differential-geometry | # Tagged Questions
1answer
42 views
### Willmore energy of an ellipsoid
Given an ellipsoid of equation $$\frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}=1$$ How can I calculate the Willmore energy of this surface knowing that its definition is: ...
1answer
61 views
### The intuition behind the definition of geodesi... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 34, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/56603?sort=newest | Quasi-isometries vs Cayley Graphs
Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
The following questions might be trivial, however, I couldn't solve them:
Let $G$ be generated by a finite symmetric set $S.$ Suppose that $\Gamma(G,S)$ is the corresponding right C... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 38, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/114020/how-to-understand-the-harish-chandra-isomorphism/114029 | ## How to understand the Harish-Chandra isomorphism?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
The Harish-Chandra isomorphism describe the center $Z(\mathfrak{g})$ of $U(\mathfrak{g})$ as invariants of $\text{Sym}^*\mathfrak{h}$ under the action of the W... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 10, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/231848/prove-that-a-function-is-a-total-function-as-opposed-to-a-partial-function/236121 | # Prove that a function is a total function (as opposed to a partial function)
I've got as part of an assignment to determine whether a given function is total, and if so, to say whether it's injective, surjective, or bijective. I can tell the answer by looking at it, but I feel that I need to make some kind of concre... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 18, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/advanced-algebra/150025-why-set-subspace.html | # Thread:
1. ## Why is this set a subspace ??
Why is the following set a subspace of $M_{n \times n}^R, n \geq 2$
$B = \{A \in M_{n \times n}^C | A_\downarrow_1 = (1-2i)A_\downarrow_2 \}$
I immediately said it is not a subspace since complex numbers aren't in real numbers. It's the other way around. But I am wrong... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 6, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/revisions/106579/list | ## Return to Answer
3 added 1 characters in body
Your example of $f(x,y)=\left(y-T_5(x)\right)\left(x-T_5(y)\right)$ is ```$$ 256\,{x}^{5}{y}^{5}-320\,{x}^{5}{y}^{3}-320\,{x}^{3}{y}^{5}-16\,{x}^{6
}+80\,{x}^{5}y+400\,{x}^{3}{y}^{3}+80\, x{y}^{5}\\-16\,{y}^{6}+20\,{x}^{4
}-100\,{x}^{3}y-100\,x{y}^{3}+20\,{y}^{4}-5\,... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 31, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/263101/prove-every-odd-integer-is-the-difference-of-two-squares/263108 | # Prove every odd integer is the difference of two squares
I know that I should use the definition of an odd integer ($2k+1$), but that's about it.
Thanks in advance!
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Hi, papercuts. You might want to start thinking about upvoting answers that are helpful (click on the upward arrow (grey) to the left of the answer... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 23, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/10933/why-do-we-say-that-the-earth-moves-around-the-sun | # Why do we say that the earth moves around the sun?
In history we are taught that the Catholic Church was wrong, because the Sun does not move around the Earth, instead the Earth moves around the Sun.
But then in physics we learn that movement is relative, and it depends on the reference point that we choose.
Wouln... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/186214/computing-an-integral | # Computing an integral.
How to compute $\displaystyle\iint\limits_{\Sigma} z\sqrt{1+z^2}dS$, where $\Sigma=\Big\{(x,y,z)\Big| \cfrac{x^2}{2}+\cfrac{y^2}{2}+z^2=1,z\ge 0\Big\}$?
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## 3 Answers
Since in $\Sigma$, $z>0$ so our domain is $D:\sqrt{1-(1/2)x^2-(1/2)y^2}>0$ or $D: x^2+y^2<1$. Clearly $S: f=x^2+y^2+2z^2=2$... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 23, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/43969/relativistic-momentum | # Relativistic momentum
I have been trying to derive why relativistic momentum is defined as $p=\gamma mv$.
I set up a collision between 2 same balls ($m_1 = m_2 = m$). Before the collision these two balls travel one towards another in $x$ direction with velocities ${v_1}_x = (-{v_2}_x) = v$. After the collision thes... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 73, "mathjax_display_tex": 20, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://math.stackexchange.com/questions/295918/simple-topology-question-about-bases-of-topologies | # simple topology question about bases of topologies
For a topological space $(X,T)$ with a basis $B$, is every basis element of $B$ an open set of $X$ (i.e. in $T$)?
(Forgive me for the dumb question, just trying to learn the basics)
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2
yes, $B$ is a subset of $T$. – Damien L Feb 6 at 0:52
## 2 Answers
By defin... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 29, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://nrich.maths.org/2365/solution | ### Golden Thoughts
Rectangle PQRS has X and Y on the edges. Triangles PQY, YRX and XSP have equal areas. Prove X and Y divide the sides of PQRS in the golden ratio.
### Ladder and Cube
A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 22, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/tagged/ads-cft | # Tagged Questions
The ads-cft tag has no wiki summary.
0answers
37 views
### Construction of the supergravity side explicitly in gauge/gravity dualities
Although the motivation of this question comes from the AdS/CFT correspondence, it actually is related to a more general principle of gauge/gravity duality. We kn... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 23, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/4458/how-do-i-map-a-spherical-triangle-to-a-plane-triangle | # How do I map a spherical triangle to a plane triangle?
My goal here is to make my own custom "polyhedral map" of Earth. If you print out something from the "Map Fold-outs" page, you will have something almost exactly like what I'm trying to make.
I have 2 triangles. One is a spherical triangle drawn on a 3D globe. ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 6, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/3534/dont-heavier-objects-actually-fall-faster-because-they-exert-their-own-gravity/3556 | # Don't heavier objects actually fall faster because they exert their own gravity?
The common understanding is that, setting air resistance aside, all objects dropped to Earth fall at the same rate. This is often demonstrated through the thought experiment of cutting a large object in half, the halves of which clearly... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 44, "mathjax_display_tex": 10, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathhelpforum.com/calculus/92589-limit-rational-expression-above-below.html | Thread:
1. Limit of Rational Expression Above or Below
How can you tell if the limit is from above or below?
2. Originally Posted by Yale
How can you tell if the limit is from above or below?
Do you mean from the left or the right?
Do you mean f(x) tendind to -infinity or +infinity?
I'm having trouble understandi... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 13, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://programmingpraxis.com/2013/02/15/facebook-hacker-cup-2013-round-1-problem-1/2/ | # Programming Praxis
A collection of etudes, updated weekly, for the education and enjoyment of the savvy programmer
## Facebook Hacker Cup 2013, Round 1, Problem 1
### February 15, 2013
The first step is to understand the problem. Consider the example with N = 4, K = 3, and a = [3, 6, 2, 8]. There are four differe... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 1, "mimetex.cgi": 0, "/images/mat... |
http://nrich.maths.org/434/index?nomenu=1 | Let $N$ be a six digit number with distinct digits. Find the number $N$ given that the numbers $N$, $2N$, $3N$, $4N$, $5N$, $6N$, when written underneath each other, form a latin square (that is each row and each column contains all six digits). | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 8, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://nrich.maths.org/481 | ### I'm Eight
Find a great variety of ways of asking questions which make 8.
### Calendar Capers
Choose any three by three square of dates on a calendar page. Circle any number on the top row, put a line through the other numbers that are in the same row and column as your circled number. Repeat this for a number of... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/80955?sort=newest | ## mean value theorem for operators
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
This might be a trivial question but I am not very familiar with the subject matter. I was wondering if some sort of mean value theorem works for operators on function spaces. ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 19, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/293580/do-there-exist-bijections-between-the-following-sets | # Do there exist bijections between the following sets?
Let $A$ be an infinite set.
Do there exist bijections between the following sets?
1. $A$ and $A\setminus B$ where $B$ is a finite subset
2. $A$ and $A\times \{1, 2, \dots, n\}$
3. $A$ and $A\times A$
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Yes to the three of them. What have you tried? Where are yo... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 23, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://en.wikipedia.org/wiki/Pushdown_automaton | # Pushdown automaton
In computer science, a pushdown automaton (PDA) is a type of automaton that employs a stack.
The PDA is used in theories about what can be computed by machines. It is more capable than a finite-state machine but less capable than a Turing machine. Because its input can be described with a formal ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 159, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathhelpforum.com/differential-geometry/123731-uniform-continuity.html | # Thread:
1. ## uniform continuity
Let $f:\mathbb{R}^{2} \to \mathbb{R}$ be defined as $f(x,y)=\text{max}\{|x|,|y|\}$. Prove that f is uniformly continuous
2. Originally Posted by Chandru1
Let $f:\mathbb{R}^{2} \to \mathbb{R}$ be defined as $f(x,y)=\text{max}\{|x|,|y|\}$. Prove that f is uniformly continuous
Okay, w... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 13, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/27383/a-question-on-finding-the-intersecting-line-between-two-planes | A question on finding the intersecting line between two planes
According to my math book, in order to find the intersecting line between two planes we need to:
1. Find the vector product of the direction normals of the two planes
2. Write the equations of the planes in Cartesian form.
3. Assume that $z=0$ since the l... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 14, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/tagged/energy+spring | # Tagged Questions
1answer
74 views
### Simple harmonic oscillator system and changes in its total energy
Suppose I have a body of mass $M$ connected to a spring (which is connected to a vertical wall) with a stiffness coefficient of $k$ on some frictionless surface. The body oscillates from point $C$ to ...
2answer... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 10, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/158168/how-to-show-that-f-is-an-odd-function?answertab=votes | # How to show that $f$ is an odd function?
An entire function $f$ takes real $z$ to real and purely imaginary to purely imaginary. We need to show that $f$ is an odd function. well, $f=\sum_{n=0}^{\infty}a_nz^n$ what I can say is $f(\mathbb{R})\subseteq\mathbb{R}$ and $f(\mathbb{iR})\subseteq\mathbb{iR}$
How to proce... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 17, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://gilkalai.wordpress.com/2008/11/24/sarkarias-proof-of-tverbergs-theorem-1/?like=1&source=post_flair&_wpnonce=1c9f85538d | Gil Kalai’s blog
## Sarkaria’s Proof of Tverberg’s Theorem 1
Posted on November 24, 2008 by
Helge Tverberg
Ladies and gentlemen, this is an excellent time to tell you about the beautiful theorem of Tverberg and the startling proof of Sarkaria to Tverberg’s theorem (two parts). A good place to start is Radon’s theor... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 141, "mimetex.cgi": 0, "/images/m... |
http://nrich.maths.org/6541 | ### F'arc'tion
At the corner of the cube circular arcs are drawn and the area enclosed shaded. What fraction of the surface area of the cube is shaded? Try working out the answer without recourse to pencil and paper.
### Do Unto Caesar
At the beginning of the night three poker players; Alan, Bernie and Craig had mon... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 14, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/141133/how-to-prove-lim-x-y-to0-0-fracxyxy-0 | # How to prove $\lim_{(x,y)\to(0,0)} \frac{xy}{x+y} = 0$
I want to find $\displaystyle\lim_{(x,y)\to(0,0)} \frac{xy}{x+y} = 0$. After trying different ways to approach $(0,0)$, I am fairly convinced the limit is $0$, but I need to prove it by definition, and I seem to be stuck. I want to prove that $\forall \epsilon >... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 29, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://poker.stackexchange.com/questions/1063/the-importance-of-mathematics-in-poker/1074 | # The Importance of Mathematics in Poker
Poker is an awesome and very difficult game. But as a probability/strategy game is a subject of mathematics. However, I found a lot a rounders, even pros, that are completely blind to the power of mathematics in this game. The most evident example is in heads up play, that is c... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/advanced-algebra/23577-proving-function-one-one.html | # Thread:
1. ## Proving a function is one-to-one
Problem:
Prove that the function f: Q ---> R, f(a/b) = (2^a)(3^b) is one to one, assuming that gcd(a,b) = 1, that is the fraction a/b is reduced.
I know f is one to one if it never maps 2 different elements to the same place, i.e. f(a) does not equal f(b) whenever a ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/205273/dense-subset-of-the-cantor-set | # Dense subset of the Cantor set
Prove that the set of endpoints of removed intervals in the Cantor middle thirds set is a dense subset of the Cantor set.
Attempt at proof:
Since each subinterval is of length $(1/3)^n$, any point contained in $K_n$ is at a distance of less than or equal to $(1/3)^n$ from an endpoint... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 29, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/23934/understanding-the-oscillating-part-of-the-gutzwiller-trace?answertab=votes | # understanding the oscillating part of the Gutzwiller trace
given the density of states according to Gutzwiller's trace formula
$g(E)= g_{smooth}(E)+ g_{osc}(E)$
i know that the 'smooth' part comes from $g_{smooth}(E)= \iint dxdp \delta(E-p^{2}-V(x))$ for one dimensional system
however how it is the oscillating pa... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 3, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/216984/finding-the-number-of-subset-pairs-of-a-set/216985 | # Finding the number of subset pairs of a set
If a set $S$ has $n$ elements, how many such pairs $(A,B)$ can be formed where $A$ and $B$ are subsets of $S$ and $A \cap B = \emptyset$?
-
## 2 Answers
Hint: If you don't insist that $A \cup B = S$, each element has three places it can go: into $A$, into $B$ or neither... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 24, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/30929/intersection-of-2-spheres-and-a-cube/30942 | Intersection of 2 spheres and a cube
In the Cartesian coordinate system, given 3 geometrical solid objects (interior plus boundary): spheres S1(x1,y1,z1, R1), S2(x2,y2,z2, R2) and a cube (which is orthogonal with coordinate system) at the center C (x3,y3,z3) with size L x L x L. The question is “Whether the 3 objects ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 8, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/55288/how-to-show-modularity-of-an-elliptic-curve/55292 | ## How to show modularity of an elliptic curve?
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In the days before [W, TW, BCDT], how did people show that specific elliptic curves over $\mathbb{Q}$ were modular? For instance, I was reading through a paper of B... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 33, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/106150?sort=votes | ## Commutator of algebraic subgroups is connected
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Let $G$ be an algebraic group over an algebraically closed field. If $H$ and $K$ are closed subgroups and one of them is connected, then their commutator $[H,K]$ ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 55, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://unapologetic.wordpress.com/2010/06/08/ | # The Unapologetic Mathematician
## Mean Convergence is Complete
I evidently have to avoid saying $L^1$ in post titles because WordPress’ pingbacks can’t handle the unicode character ¹…
Anyhow, today we can show that the $L^1$ norm gives us a complete metric structure on the space of all integrable functions on $X$.... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 48, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/12628/applications-of-euler-cauchy-odes | ## Applications of Euler-Cauchy ODEs
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The Euler-Cauchy ODE (2nd order, homogeneous version) is:
$$x^2 y'' + a x y' + b y = 0$$
Looking in various books on ODEs and a random walk on a web search (i.e. I didn't cl... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 6, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://stats.stackexchange.com/questions/24263/model-stability-in-cross-validation-of-regression-models | # Model stability in cross-validation of regression models
Given multiple cross-validation folds of a logistic regression, and the resulting multiple estimates of each regression coefficient, how should one measure whether or not a predictor (or set of predictors) is/are stable and meaningful based on the regression c... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 3, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/16261/quotient-of-a-reductive-group-by-a-non-smooth-central-finite-subgroup/16273 | ## Quotient of a reductive group by a non-smooth central finite subgroup
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I need a construction in linear algebraic groups which uses taking quotient by a central finite group subscheme. My question is, whether i... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 98, "mathjax_display_tex": 4, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/158281/pattern-of-orders-of-elements-in-a-cyclic-group/158286 | # Pattern of orders of elements in a cyclic group
Doodling as I was contemplating another recent question, I picked out the orders of elements of the cyclic group $Z_{15}$ namely:
1 element of order 1
2 elements of order 3
4 elements of order 5
8 elements of order 15
In a group of order 3 you have 1 element of or... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 61, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://nrich.maths.org/5616/clue | ### Flexi Quads
A quadrilateral changes shape with the edge lengths constant. Show the scalar product of the diagonals is constant. If the diagonals are perpendicular in one position are they always perpendicular?
### Flexi Quad Tan
As a quadrilateral Q is deformed (keeping the edge lengths constnt) the diagonals an... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 20, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/43573/negative-sign-of-acceleration | # Negative sign of acceleration [closed]
This is the problem from our Physics textbook :
A player throws a ball upwards with an initial speed of 29.4 m s–1. (a) Choose the x = 0 m and t = 0 s to be the location and time of the ball at its highest point, vertically downward direction to be the positive direction of x-... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 14, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://unapologetic.wordpress.com/2012/02/16/ohms-law/?like=1&source=post_flair&_wpnonce=671450efa2 | # The Unapologetic Mathematician
## Ohm’s Law
When calculating the potential energy of the magnetic field, we calculated the power needed to run a certain current around a certain circuit. Let’s look into that a little more deeply.
We start with Ohm’s law, which basically says that — as a first approximation — the e... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 23, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/tagged/wave-particle-duality?sort=unanswered&pagesize=50 | # Tagged Questions
The wave-particle-duality tag has no wiki summary.
I am trying to solve a problem that includes a function of the light hitting a certain area. My question is, how would I change a function $G(x)$ of photons hitting a certain area to include just ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/143055/propositional-logic-substitution | propositional logic - substitution
Prove: $\varphi_1 =\!\mathrel|\mathrel|\!= \varphi_2 \implies \varphi_1[\psi/p] =\!\mathrel|\mathrel|\!= \varphi_2[\psi/p]$.
We've proven that $\varphi_1 =\!\mathrel|\mathrel|\!= \varphi_2 \implies \psi[\varphi_1/p] =\!\mathrel|\mathrel|\!= \psi[\varphi_2/p]$.
Maybe you could give ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 34, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://simple.wikipedia.org/wiki/Golden_ratio | # Golden ratio
If a person has one number a and another smaller number b, he can make the ratio of the two numbers by dividing them. Their ratio is a/b. He can make another ratio by adding the two numbers together a+b and dividing this by the larger number a. The new ratio is (a+b)/a. If these two ratios are equal to ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 13, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://cdsmith.wordpress.com/2009/07/20/calculating-multiplicative-inverses-in-modular-arithmetic/?like=1&source=post_flair&_wpnonce=57db9114c5 | software, programming languages, and other ideas
July 20, 2009 / cdsmith
I’m sure plenty of people already know this, but I ran into it today, and it’s interesting… so here it is. A common and very easy result in abstract algebra is that the ring $\mathbb{Z}_q = \mathbb{Z}/q\mathbb{Z}$ (where $q$ is any positive inte... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 38, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/pre-calculus/148538-limits-point.html | # Thread:
1. ## Limits at a point
Hey guys,
I'm trying to understand how to determine the left and right side of this limit:
limit as x -> 2
|x-2|/(x-2)
Do I have to graph it, or is there an algebraic way to do this? Cheers.
2. Originally Posted by Glitch
Hey guys,
I'm trying to understand how to determine the ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 13, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://jlebl.wordpress.com/2012/11/09/numerical-range/ | # The Spectre of Math
## November 9, 2012
### Numerical range
Filed under: Hacking,Mathematics — jlebl @ 12:06 am
I was fiddling with numerical range of two by two matrices so I modified my root testing python program to do this. The numerical range of $A$ is the set of all values
$\frac{v^* A v}{v^* v}$
for all ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 6, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/revisions/84954/list | 2 edited title
1
# Can you make the cotangent bundle to a complex
The cotangent bundle of a manifold has a canonical symplectic form and if we choose a riemannian metric on $M$, we can give it an almost complex structure.
Is this structure integrable, and if it isn't in general, what are the conditions on the manif... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 3, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://lucatrevisan.wordpress.com/2010/04/22/cs254-lecture-1-introduction/ | in theory
"Marge, I agree with you - in theory. In theory, communism works. In theory." -- Homer Simpson
# CS254 Lecture 1 – Introduction
April 22, 2010 in CS254 | Tags: CS254 2010
Last revised 4/29/2010
This course assumes CS154, or an equivalent course on automata, computability and computational complexity, as ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 95, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/120545?sort=newest | Compute roots of sum_i c_i/(a_i + b_i x)^p
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How to compute the (real) roots of
$$\sum_{i=1}^n \frac{c_i}{(a_i + b_i \cdot x)^p}$$
for given reals $a_i, b_i, c_i$, and positive integers $n, p$? The cases $p=1, ..., 5... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 13, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/206376/how-to-plot-n-points-on-the-surface-of-a-d-dimensional-sphere-roughly-equidistan?answertab=votes | # How to plot N points on the surface of a D-dimensional sphere roughly equidistant apart?
Let's say I have a D-dimensional sphere with a radius R. I want to plot N number of points evenly distributed (equidistant apart from each other) on the surface of the sphere. It doesn't matter where those points are exactly, ju... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 9, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://www.physicsforums.com/showthread.php?t=42938 | Physics Forums
## Gravity forces converted to energy
Can anyone help me on this?
If I have a very large ball (ball A) and a tiny ball (ball B) as such that ball B is attracted by the center of ball A, then theorically, if ball A is a perfect sphere I could expect ball B to start spinning on ball A and never stop as ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/57719/algebraic-closure-of-commuting-pairs-of-matrices | ## algebraic closure of commuting pairs of matrices
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Let $F$ be an arbitrary field of characteristic $0$, $K$ its algebraic closure. Define $M=\{ (x,y)\in M_n(F)×M_n(F) \mid [x,y]=0\}$ and let $N$ be the Zariski c... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 23, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/differential-geometry/127612-fort-space-topology.html | # Thread:
1. ## Fort Space Topology
Does anybody know which sets are both open and closed, and which sets are neither open nor closed for the Fort Space Topology?
2. Hello,
Just write down what open and closed sets are in this topology.
Let X be the infinite set. Fix $p\in X$.
Open sets A :
1.a) $p\not\in A$
1.b) ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 8, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/132569/characterizing-open-closed-compact-sets-in-the-metric-space-mathbbzn-d | # Characterizing Open/Closed/compact sets in the metric space $(\mathbb{Z}^n,d)$
What is an open set in the metric space $(\mathbb{Z}^n,d)$, where $d$ is the Euclidean distance in $\mathbb{R}$?
As far as I know, in a metric space an open set $O$ is defined as follows: For each point $x\in O$ it exists an $\varepsilon... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 19, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/12483/uniqueness-of-a-polygon | ## Uniqueness of a polygon
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Suppose I have two $n$-sided polygons A and B. Is there a non-trivial upper bound on the number of parameters (eg. area, perimeter, etc) of the two polygons, that need to be the same, f... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 11, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/tagged/distributions+quantum-mechanics | # Tagged Questions
3answers
135 views
### Hilbert space of harmonic oscillator: Countable vs uncountable?
Hm, this just occurred to me while answering another question: If I write the Hamiltonian for a harmonic oscillator as $$H = \frac{p^2}{2m} + \frac{1}{2} m \omega^2 x^2$$ then wouldn't one set of ...
2answers
72... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 10, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://nrich.maths.org/1131/note | ### Calendar Capers
Choose any three by three square of dates on a calendar page. Circle any number on the top row, put a line through the other numbers that are in the same row and column as your circled number. Repeat this for a number of your choice from the second row. You should now have just one number left on t... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 7, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://psychology.wikia.com/wiki/Natural_number?interlang=all | # Natural number
Talk0
31,725pages on
this wiki
Assessment | Biopsychology | Comparative | Cognitive | Developmental | Language | Individual differences | Personality | Philosophy | Social |
Methods | Statistics | Clinical | Educational | Industrial | Professional items | World psychology |
Statistics: Scientific me... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 9, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/41689?sort=votes | ## Why symmetric spaces?
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In Bar-Natan's "Knots at Lunch" seminar at the University of Toronto, we are currently discussing a talk by Alekseev at Montpellier about Rouvière's expansion of the Duflo isomorphism to ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 21, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/3618/solving-an-equation-with-irrational-exponents | # Solving an equation with irrational exponents
Is there any theory (analogous to Galois theory) for solving equations with irrational exponents like:
$x^{\sqrt{2}}+x^{\sqrt{3}}=1$
?
-
Well, for one thing, this is now a transcendental equation instead of an algebraic one, and the theory of seeing whether a transce... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 12, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/229652/existence-of-a-sequence-which-is-good-for-mean-convergence-but-not-good-for-poin?answertab=oldest | # Existence of a sequence which is good for mean convergence but not good for pointwise convergence
The ergodic theorems talk about the limit behaviour of the ergodic averages. For example, if $(X,\chi,\mu,T)$ is a measure preserving system, where $\mu$ is a probability measure on $X$, then we have the mean ergodic th... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 7, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/calculus/114989-help-trig-limit.html | # Thread:
1. ## Help with trig limit
Can anyone show me how the limit of $\frac{sin 5x}{x}$ as x goes to 0 equals 5?
I'm only supposed to use the fact that $\frac{sin x}{x}$ goes to 1 as x goes to 0.
Any tips?
2. Originally Posted by paupsers
Can anyone show me how the limit of $\frac{sin 5x}{x}$ as x goes to 0 eq... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 6, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://unapologetic.wordpress.com/2011/09/20/pseudo-riemannian-metrics/?like=1&source=post_flair&_wpnonce=a832ba55c5 | # The Unapologetic Mathematician
## (Pseudo-)Riemannian Metrics
Ironically, in order to tie what we’ve been doing back to more familiar material, we actually have to introduce more structure. It’s sort of astonishing in retrospect how much structure comes along with the most basic, intuitive cases, or how much we can... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 27, "mimetex.cgi": 0, "/images/ma... |
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