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http://mathoverflow.net/questions/77728?sort=oldest | ## Can local duality for elliptic curves be proven with “big rings”?
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From Exercise 5.14, Ch. V of Silverman's "Advanced Topics in the Arithmetic of Elliptic Curves", I learned that the local duality for elliptic ... | {"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": 50, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/17800/how-to-implement-heuns-method-to-solve-a-2nd-order-ode?answertab=active | # How to implement Heun's method to solve a 2nd order ODE? [closed]
I am trying to simulate a soft body object by having a collection of points connected by springs. I also want to have the object bounce on a plane. I have been able to implement Euler's method to make this simulation work, but it is not satisfactory 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": 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/77558/area-of-distance-sphere-in-manifold-with-ricci-ge-0 | Area of distance sphere in manifold with Ricci $\ge 0$.
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Let $M$ be a open complete manifold with Ricci curvature $\ge 0$. By a theorem of Calabi and Yau, the volume growth of $M$ is at least of linear. I am wondering... | {"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": 28, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/advanced-algebra/204024-solving-equations-groups-print.html | # Solving equations in groups
Printable View
• September 24th 2012, 08:24 PM
jzellt
Solving equations in groups
I will denote x-inverse as x' and the identity as e.
I'm asked to solve the two equations below simultaneously:
(1) ax^2 = b and (2) x^3 = e
Here's what i did:
ax^3 = bx (by multiplying (1) on the right... | {"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/54020/list | ## Return to Answer
5 deleted 3 characters in body
That link reveals that a certain heuristic but extremely plausible assymptotic formula is highly accurate at least up to $10^{10}$. That information tells us what a graph over a larger range would look like. So one knows certain patterns are there even if the graph 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": 35, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/algebra/107060-lost-some-basic-skills-working-square-root.html | # Thread:
1. ## Lost some basic skills, working with a square root
Okay, so I'm doing a TON of identities in trig, and have come to a point where I'm working on problems such as:
$\sqrt(1+cos(30))/2$
cos of 30 is $\sqrt3/2$
I've forgotten what it's called but I need a step by step guide to simplifying this! (it si... | {"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": 14, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/72931/list | ## Return to Question
2 added 590 characters in body; deleted 14 characters in body
The first definition of the category of Poisson algebras that comes to mind is that a morphism between Poisson algebras is an algebra homomorphism that is also a Lie algebra homomorphism with respect to the Poisson bracket. This 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": 8, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://en.wikipedia.org/wiki/Splitting_field | # Splitting field
In abstract algebra, a splitting field of a polynomial with coefficients in a field is a smallest field extension of that field over which the polynomial splits or decomposes into linear factors.
## Definition
A splitting field of a polynomial p(X) over a field K is a field extension L of K over wh... | {"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": 27, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/number-theory/122809-rsa-algorithm-why-impossible-useful-rsa-code.html | # Thread:
1. ## RSA algorithm why is this impossible for a useful RSA code?
e = 3
n = 10
M = 7
phi(n) = (5-1) * (2-1) = 4
ed = 1 mod 4
3d = 1 mod 4
d = 3
why is this impossible for a useful RSA code?
2. I don't know what you mean, it is a correct key generation mathematically speaking. Now, you can see that $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": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://nrich.maths.org/1947/index?nomenu=1 | $ABCD$ is a square of side 1 unit. Arc of circles with centres at $A, B, C, D$ are drawn in. Prove that the area of the central region bounded by the four arcs is: $(1 + \pi/3 + \sqrt{3})$ square units. | {"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/204494/quadratic-equations/205423 | Quadratic equations
Does anyone know how to find integer solutions of the quadratic equation
$$y^2+y+z=f$$
where $z$ is a fixed odd prime or $1$ and $f$ is a fixed odd prime greater than $3$?
This problem arose from the Diophantine equation $A+B=C$ where $A,B,C$ are natural numbers with no common factor.
-
3
Hmmm... | {"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": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/79189-integral-expression-bessel-functions.html | # Thread:
1. ## integral expression for bessel functions...
Can someone give me a hand with this problem? I cant figure out how to integrate things once I have y y' and y'' plugged into the bessel function.
problem in a .png linked below
I only need help with the integration on part A. Thanks in advance!
-Canopy
... | {"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://complexzeta.wordpress.com/2007/08/13/tschirnhaus-transformations/ | An Idelic Life
Algebraic number theory and anything else I feel like telling the world about
# Tschirnhaus Transformations
Monday, August 13, 2007 in Galois theory
This is based on a talk by Zinovy Reichstein from the PIMS Algebra Summer School in Edmonton.
The motivation comes from looking at ways to simplify pol... | {"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": 40, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/92344/unconditional-bases-for-sum-infty-n1-oplus-elln-2-ell-1 | ## unconditional bases for $(\sum^\infty_{n=1} \oplus \ell^n_2 )_{\ell_1}$ [closed]
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are there unconditional bases for $(\sum^\infty_{n=1} \oplus \ell^n_2 )_{\ell_1}$ ?
-
Actually, if I understand it correctly, 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://math.stackexchange.com/questions/121562/confusion-about-partial-differentiation-and-cauchy-riemann-equations | # Confusion about partial differentiation and Cauchy-Riemann equations
In complex analysis class (using Stein's Complex Analysis), we learned about the derivation of the Cauchy-Riemann equations, and that made sense. We take a holomorphic $f : O \rightarrow \mathbb{C}$, where $O \subset \mathbb{C}$ is open, and split ... | {"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": 35, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/algebra/107840-simplify.html | # Thread:
1. ## Simplify
This Question came up in a test i did today
(X+3)(X+2)(X+1)
What i did was multiply out the first two brackets
X² + 5x + 6
then i tried
(X²+5x+6)(X+1)
X³ + 5x then i get confused since i dont know what to multiply 6 by
X² + 5x² i can also work this bit out but i have no idea whats next.... | {"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": 4, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/122539/the-unreasonable-effectiveness-of-pade-approximation/122542 | ## The unreasonable effectiveness of Pade approximation
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I am trying to get an intuitive feel for why the Pade approximation works so well. Given a truncated Taylor/Maclaurin series it "extrapolates" it beyond 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": 54, "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-applied-math/96332-proof-problem.html | # Thread:
1. ## Proof problem
Hi everyone, I have trouble proving this problem:
the question is:
Show that if a zero-sum game has a (pure) Nash equilibrium (i∗ , j∗ ), then the van
Neumann value of the game is $a_i^*j^*$
Hint. Show that $max_P min E_j (P) >= a_i^*j^*$ and that $min_Q max F_i (Q) <= a_i^*j^*$
, 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": 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/calculus/37714-double-integration-limits.html | # Thread:
1. ## Double integration: limits
I am given the following probability density function:
$f (x,y) = \frac{2x + 2 - y}{4}$ for 0<x<1 and 0<y<2
$f (x,y) = 0$ otherwise
I am to find P[X + Y > 1].
My attempts at the double integration failed.
The answer begins:
$\int_0^1 \int_{1-x}^2 \frac{2x + 2 - y}{4} dydx... | {"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/questions/81842?sort=oldest | ## Heat equation bounds
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I am interested in the following damped heat equation on $\mathbf{R}$, $u_t = u_{xx} - 1_{x \in [-1,1]} u$ with initial data $u(0,x) = \delta(x-x_0)$ for some $x_0 \in \mathbf{R}$.
In par... | {"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": 9, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://liuxiaochuan.wordpress.com/2009/02/11/%E5%80%A1%E8%AE%AE/ | # Xiaochuan Liu's Weblog
mathematics and other aspects of life
## 倡议
（参考我的帖子：经验一二三，给学数学的你，中国的学生差在哪，哦大学，等等）
Tao在数学研究中的经验以及给年轻人的建议
Let X be a topological space. Show that X is compact if and only if every net has a convergent subnet. (Hint: equate both properties of X with the finite intersection property, and revie... | {"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": 22, "mimetex.cgi": 0, "/images/ma... |
http://crypto.stackexchange.com/tags/one-way-function/hot | # Tag Info
## Hot answers tagged one-way-function
9
### Are there hash algorithms with variable length output?
Sure. If you want a $b$-bit hash of the message $m$, then use the first $b$ bits of AES-CTR(SHA256($m$)). That'll do the trick. In other words, compute SHA256($m$) and treat the resulting 256-bit string 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": 35, "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/41628/examples-of-faithfully-flat-modules/42499 | # examples of faithfully flat modules
I'm studying some results about flatness and faithful flatness and I'd like to keep in my mind some examples about faithfully flat modules. In general, free modules are the typical example. Another (unusual) example of faithfully flat module is the "Zariski Covering" (Let $R$ be 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": 78, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?p=2877517 | Physics Forums
## Solving for a Surjective Matrix
I saw this in a book as a Proposition but I think it's an error:
Assume that the (n-by-k) matrix, $$A$$, is surjective as a mapping,
$$A:\mathbb{R}^{k}\rightarrow \mathbb{R}^{n}$$.
For any $$y \in \mathbb{R}^{n}$$, consider the optimization problem
$$min_{x \in \m... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 9, "mathjax_display_tex": 38, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/94371-maximum-area-triangle-print.html | # Maximum area of a Triangle
Printable View
• July 4th 2009, 07:08 AM
JoAdams5000
Maximum area of a Triangle
Suppose a triangle has perimeter 2. Let
x and y be the lengths of two of its sides and A its area. Show that A^2 = (x + y − 1)(1 − x)(1 − y). Use this formula to find the maximum area of a triangle with perime... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 14, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/1019/common-false-beliefs-in-physics/1935 | # Common false beliefs in Physics [closed]
Well, in Mathematics there are somethings, which appear true but they aren't true. Naive students often get fooled by these results.
Let me consider a very simple example. As a child one learns this formula $$(a+b)^{2} =a^{2}+ 2 \cdot a \cdot b + b^{2}$$ But as one mature's ... | {"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": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/discrete-math/144268-infinite-collections.html | # Thread:
1. ## Infinite collections???
Does there exist an infinite collection of sets such that the intersection of every two sets in the collection is nonempty, but the intersection of every three distinct sets in the collection is empty???
Could you also explain what sets are???
Thanks
2. Originally Posted 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": 6, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/16621/what-do-you-lose-when-passing-to-the-motive | ## What do you lose when passing to the motive?
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I contemplated about what information about a scheme we lose when passing to its motive. I came up with the following examples:
1. The projective bundle of a vecto... | {"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": 53, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/pre-calculus/213044-epsilon-2.html | 1Thanks
# Thread:
1. ## Re: Epsilon
Originally Posted by Petrus
Defination 7 says me what im doing idk, but the problem says i shall use defination 7.
I agree with the definition, of course. As I described in post #11, the inequality from the definition is translated into two inequalities. One of them holds 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": 18, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/9961/list | ## Return to Question
5 deleted 1 characters in body; edited title
# colimitsColimits of schemes
this
This is related to another question.
I've found many remarks that the category of schemes is not cocomplete. the The category of locally ringed spaces is cocomplete, and in some special cases this turns out to be ... | {"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://mathhelpforum.com/advanced-algebra/144977-how-determine-sigma-sgn-sigma-matrices.html | # Thread:
1. ## how to determine sigma and sgn(sigma) for matrices
As the topic says, I don't know how to determine $sgn(\sigma)$ or $\sigma$ for any n x m matrix
I know this section falls under determinants but I am kind of having a hard time finding online resources for this section
2. I thought I new matrices pr... | {"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": 7, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://terrytao.wordpress.com/tag/margin-of-error/ | What’s new
Updates on my research and expository papers, discussion of open problems, and other maths-related topics. By Terence Tao
# Tag Archive
You are currently browsing the tag archive for the ‘margin of error’ tag.
## Small samples, and the margin of error
10 October, 2008 in expository, math.ST, non-technic... | {"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": 10, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/93136/enumerative-meaning-of-natural-q-catalan-numbers | ## enumerative meaning of natural q-Catalan numbers
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Define $[n]=(1-q^n)/(1-q)$ and $[n]!=[1][2][3] \cdots [n]$, so that $[2n]!/[n]![n+1]!$ is a polynomial in $q$ (the most algebraically natural $q$-analogue of 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": 57, "mathjax_display_tex": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.sciforums.com/showthread.php?111942-The-Problem-of-Time-leads-to-a-Problem-of-Energy-for-the-Universe | • Forum
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1. If this is your first visit, be sure to check out the FAQ by clicking the link above. You need to register and post an introductory thread before you can post to all subforums: click the register li... | {"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": 0, "mimetex.cgi": 106, "/images/m... |
http://math.stackexchange.com/questions/175452/how-to-simplify-an-expression-like-this-x2x-2-21-2/175459 | # How to simplify an expression like this: $(x^2+x^{-2}-2)^{1/2}$
Sorry, I am not sure how to do the maths mark-up on this site but hopefully the question will make sense. I should know how to do this, but I have got myself stuck! Can anyone help?
$(x^2+x^{-2}-2)^{1/2}$
-
## 4 Answers
$$\left(x-\frac{1}{x}\right)^... | {"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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/7824/factorization-of-elements-vs-of-ideals-and-is-being-a-ufd-equivalent-to-any-pro | ## Factorization of elements vs. of ideals, and is being a UFD equivalent to any property which can be stated entirely without reference to ring elements?
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Why exactly is the unique factorization of elements into ... | {"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://mathoverflow.net/questions/61498/units-in-quaternionic-algebras/61512 | ## Units in quaternionic algebras
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Let $H$ be a quaternionic algebra over ${\bf Q}$, and let $R$ denote a maximal ${\bf Z}$-order in $H$. Is there a theorem on the structure of the units in $R$ analogous to the Di... | {"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": 30, "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/23515?sort=oldest | ## Cofinal inclusions of Waldhausen categories
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Let $\mathcal{C}$ be a Waldhausen category. Suppose that $\mathcal{B}$ is a subcategory of $\mathcal{C}$, and that $\mathcal{B}$ is closed under extensions. If $\mat... | {"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": 39, "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/176260/convergence-of-the-sequence-f-1-leftx-right-sqrtx-and-f-n1-leftx | Convergence of the sequence $f_{1}\left(x\right)=\sqrt{x}$ and $f_{n+1}\left(x\right)=\sqrt{x+f_{n}\left(x\right)}$
Let $\left\{ f_{n}\right\}$ denote the set of functions on $[0,\infty)$ given by $f_{1}\left(x\right)=\sqrt{x}$ and $f_{n+1}\left(x\right)=\sqrt{x+f_{n}\left(x\right)}$ for $n\ge1$. Prove that this sequ... | {"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": 88, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/144641/variational-formulation-for-bilaplacian-problem | # Variational formulation for bilaplacian problem
I am trying to derive a variational formulation for the following problem $$\left\{ \begin{array}{ll} \Delta^2u=f, & \Omega \\ \Delta u+\rho \partial_{\nu}u=0, & \partial \Omega \end{array}\right.$$
where $\rho>0$ is constant. I intend to show that the right functiona... | {"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": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathematica.stackexchange.com/tags/linear-algebra/hot?filter=year | # Tag Info
## Hot answers tagged linear-algebra
21
### Computing polynomial eigenvalues in Mathematica
(I've been waiting for somebody to ask this question for months... :D ) Here's the Mathematica implementation of the Frobenius companion matrix approach discussed by Jim Wilkinson in his venerable book (for comple... | {"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... |
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Home ▸ Science ▸ Mathematics » what is the probability that if 5 fair 6-sided dice are rolled the pro... | {"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": 0, "mimetex.cgi": 2, "/images/mat... |
http://mathhelpforum.com/number-theory/151779-number-1-2-b-1-2-always-irrational-following-conditions.html | # Thread:
1. ## Is the number a^(1/2) + b^(1/2) always irrational with the following conditions?
Is the following number (with the added conditions taken into account) always irrational? And how would one go about proving this? Heres the number and the conditions:
Is the number $\sqrt{a} + \sqrt{b}$ always irrationa... | {"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": 20, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://xianblog.wordpress.com/2010/06/05/on-particle-learning/ | # Xi'an's Og
an attempt at bloggin, from scratch…
## On particle learning
In connection with the Valencia 9 meeting that started yesterday, and with Hedie‘s talk there, we have posted on arXiv a set of comments on particle learning. The arXiv paper contains several discussions but they mostly focus on the inevitable... | {"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://www.citizendia.org/Homomorphism | Not to be confused with homeomorphism. Topological equivalence redirects here see also Topological equivalence (dynamical systems.
In abstract algebra, a homomorphism is a structure-preserving map between two algebraic structures (such as groups, rings, or vector spaces). Abstract algebra is the subject area of Mathem... | {"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": 16, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/6927/list | ## Return to Answer
2 deleted 46 characters in body
Let me say first that Engelbrekt's last point is not true - in fact a Dedekind zeta function is always a product of Artin L-functions. It is the structure of the Galois closure which is relevant here. Let me give a nice example which is indicative of the general cas... | {"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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/225621/a-nonlinear-version-of-the-riesz-isomorphism | # A nonlinear version of the Riesz isomorphism
The present question regards the proof of the following theorem which is found in Adams' Sobolev spaces, §2.30 - 2.33. Here $(\Omega, \mathcal{M}, \mu)$ denotes some arbitrary measure space and $L^p$ always stands for $L^p(\Omega)$.
Riesz Representation Theorem Let $1<p<... | {"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": 12, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://www.reference.com/browse/gluon | Definitions
Nearby Words
# gluon
[gloo-on] /ˈgluɒn/
gluon, an elementary particle that mediates, or carries, the strong, or nuclear, force. In quantum chromodynamics (QCD), the quantum field theory of strong interactions, the interaction of quarks (to form protons, neutrons, and other elementary particles) is describ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 13, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.emathematics.net/sistres.php?ejercicio=simple | User:
Documento sin título
Pre-algebra Arithmetics Integers Divisibility Decimals Fractions Exp... | {"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": 0, "mimetex.cgi": 1, "/images/mat... |
http://mathoverflow.net/questions/98609?sort=votes | ## Algorithmically unsolvable problems in topology
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This question is inspired by a paper by B. Poonen that appeared on the arxiv some time ago: http://arxiv.org/abs/1204.0299. The paper gives a sample of algorithm... | {"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": 52, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/statistics/4812-mutually-exclusive-events-need-help-sure.html | # Thread:
1. ## Mutually exclusive events? need help for sure
P(E_1)=0.25, P(E_2)=0.75, P(FlE_1)=0.05. P(FlE_2)=0.12. P(E_2lF). Ok I'm looking for an area or space between both. As for the text book no good example is close to this one. Ok so 0.25*0.75=.1875, and 0.05*0.12=.006. Now is the hard part what do I do next... | {"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": 16, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/advanced-algebra/193513-hilbert-symbol-when-k-p-adic-numbers.html | # Thread:
1. ## Hilbert symbol when K = the p-adic numbers
How can I show that the Hilbert Symbol is bimiltuplicative, when the local field is the p-adic numbers? Everything I can find just sort of asserts bimultiplicativity without much proof, so I'm guessing it's pretty straight forward, but I haven't done much wor... | {"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": 9, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/55778/renormalization-group-and-ising-with-d-1-and-d-1 | # Renormalization Group and Ising with d=1 and D=1
I have a question about the results of RG on Ising model. I know it's possible to obtain two couple of relations
1. $K'(K)$, $q(K')$
2. $K(K')$, $q(K)$
between the coupling costants. My problem arise when i try to draw the flow diagram of the coupling constants. I 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": 12, "mathjax_display_tex": 7, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?p=1828423 | Physics Forums
## Is this inequality true and provable?
1. The problem statement, all variables and given/known data
My question is whether the following inequality can be proven.
2. Relevant equations
[tex]
\left|\int_a^bg\left(x\right)dx-\int_a^bh\left(x\right)dx\right|\leq\int_a^b\left|g\left(x\right)-h\left(x\ri... | {"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": 13, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/13444?sort=votes | ## Prime divisors of numbers 2^n + 3
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I'm interested in the following problem: do there exist infinitely many prime numbers $p$ such that $p^2|2^{n}+3$ for some natural number $n$?
Some motivation:
If we replace... | {"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": 56, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://anhngq.wordpress.com/2009/11/10/a-trivial-identity-of-probability-measures/ | # Ngô Quốc Anh
## November 10, 2009
### A trivial identity of probability measures
Filed under: Các Bài Tập Nhỏ, Giải Tích 6 (MA5205) — Ngô Quốc Anh @ 14:36
Let us consider a probability space $(X,\mathcal B,\mu)$, i.e., $(X,\mathcal B,\mu)$ is a measurable space together with $\mu(X)=1$. We assume further that $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": 0, "wp_latex": 14, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/advanced-algebra/177142-question-about-separability.html | # Thread:
1. ## Question about separability
I have this kind of exercise:
Let $f \in F[X]$ be an irreducible polynomial where F has characteristic $p > 0$. Express $f(X) = g(X^{p^m})$ where $m \in N$ is a large as possible. Show that g is irreducible and separable.
I know how to show that g is irreducible, but how ... | {"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": 4, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://crypto.stackexchange.com/questions/1534/families-of-public-private-keys-in-elliptic-curve-cryptography | # Families of public/private keys in elliptic curve cryptography
I'm looking for a related key scheme for elliptic curve cryptography. The basic idea would be that there would be a master public key and a master private key. From the master public key, you could generate a series of public keys. From the master privat... | {"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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://terrytao.wordpress.com/2009/09/ | What’s new
Updates on my research and expository papers, discussion of open problems, and other maths-related topics. By Terence Tao
# Monthly Archive
You are currently browsing the monthly archive for September 2009.
## Two quick updates
30 September, 2009 in non-technical, update | Tags: google wave, mathematica... | {"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": 100, "mimetex.cgi": 0, "/images/m... |
http://en.wikipedia.org/wiki/Quantum_mechanics | # Quantum mechanics
This is the latest accepted revision, accepted on 14 May 2013.
For a generally accessible and less technical introduction to the topic, see Introduction to quantum mechanics.
Quantum mechanics
Introduction
Glossary · History
Background
Fundamental concepts
Experiments
Formulations
Equations
Interpr... | {"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": 24, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.aps.org/synopsis-for/print/10.1103/PhysRevLett.104.120601 | # Synopsis:
In thin air
#### Thermodynamically Admissible 13 Moment Equations from the Boltzmann Equation
Hans Christian Öttinger
Published March 22, 2010
In a sufficiently rarefied gas, the tools of standard hydrodynamics, namely, the Navier-Stokes-Fourier equations (based on Newton’s second law applied to... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 1, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://programmingpraxis.com/2012/01/13/ | # Programming Praxis
A collection of etudes, updated weekly, for the education and enjoyment of the savvy programmer
## Excel’s XIRR Function
### January 13, 2012
We studied numerical integration in a previous exercise. In today’s exercise we will look at the inverse operation of numerically calculating a derivativ... | {"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": 3, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/284002/let-g-v-x-cup-y-e-be-a-bipartite-graph-show-that-g-has-a-matching-which-mat | # Let $G=(V=X \cup Y,E)$ be a bipartite graph.Show that G has a matching which matches every vertex of X.
I have a similar question to this on my test tomorrow. Any help towards this question will help
Let $G=(V=X \cup Y,E)$ be a bipartite graph. Suppose that the degree of each vertex d(v)≥1. Assume also that for eac... | {"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": 30, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/5001/notions-of-degree-for-maps-sn-to-sn/5007 | ## Notions of degree for maps $S^n \to S^n$?
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In algebraic topology, we define a degree for a map $f: S^n \to S^n$ as where the induced map $f_*$ on the $n$-th homology group of $S^n$ sends $1$.
In differential 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": 46, "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/9836/how-many-boats-does-it-take-to-find-an-acoustic-buoy-by-doppler-shift?answertab=oldest | # How many boats does it take to find an acoustic buoy by Doppler shift?
Inspired by this question on the Doppler shift, suppose there is buoy somewhere on the surface of the ocean emitting a pure frequency.
You get to place some boats wherever you want on the surface of the ocean, moving whatever direction you want ... | {"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://unapologetic.wordpress.com/2007/11/16/continuity-redux/?like=1&source=post_flair&_wpnonce=9a71b83933 | # The Unapologetic Mathematician
## Continuity redux
So now we have two new ways to talk about topologies: neighborhoods, and closure operators. We can turn around and talk about continuity directly in our new languages, rather than translating them into the open set definition we started with.
First let’s tackle ne... | {"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": 59, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/trigonometry/139025-pythagorean-theorem-triangles-question.html | # Thread:
1. ## Pythagorean theorem and triangles Question
I need help with c) and d) and also e).
For c) they are asking for 2θ however I don't know what they did to get 1 - 2y^2.
d) Can you please explain to me what we do with the (pi - θ)?
e) Cos is adjacent over hypotenuse. However what do we do with the inverse... | {"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": 15, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/115689/can-the-cardinality-of-continuum-exceed-all-aleph-numbers-in-zf/115701 | # Can the cardinality of continuum exceed all aleph numbers in ZF?
More precisely, is either of the following two statements consistent with ZF:
1. $2^{\aleph_0}\geq\aleph_{\alpha}$ for every ordinal number $\alpha$,
2. $2^{\aleph_0}\leq\aleph_{\alpha}\implies 2^{\aleph_0}=\aleph_{\alpha}$ for every ordinal number $... | {"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": 92, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://topologicalmusings.wordpress.com/2009/07/09/a-relation-is-an-equivalence-iff-it-is-reflexive-and-euclidean/ | Todd and Vishal’s blog
Topological Musings
A relation is an equivalence iff it is reflexive and euclidean
July 9, 2009 in Elementary Math Problem Solving | Tags: equivalence relation, euclidean, reflexive
High-school students and undergraduates are (almost) always taught the following definition of an equivalence r... | {"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": 67, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/607?sort=votes | ## Non-conjugate words with the same trace
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Let n>=2, p a large prime, G = SL_n(Z/pZ).
If n=2, there are words that, while not conjugate in the free group, do have identical trace in G. For example, tr(g h^2 g^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": 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/tagged/gravity?sort=unanswered&pagesize=30 | # Tagged Questions
Gravity is an attractive force that affects and is effected by all mass and - in general relativity - energy, pressure and stress. Prefer newtonian-gravity or general-relativity if sensible.
learn more… | top users | synonyms
2answers
459 views
### Ski Jumper's vertical velocity after 246.5m reco... | {"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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://www.physicsforums.com/showthread.php?t=548513 | Physics Forums
## Induced current in conductor moving circularly in constant B-field
1. The problem statement, all variables and given/known data
A light bulb with resistance R is attached on a metal rod which is rotating around the point O on the figure. The metal rod is in contact with an electrical conductor whic... | {"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://mathoverflow.net/questions/tagged/computer-science | ## Tagged Questions
1answer
140 views
### What structure has been found for functions with this relationship.
Given $f$ and $g$ $\forall x y. f(x) = f(y) \Longrightarrow f(g(x)) = f(g(y))$ Or equivalently $ker\ f \subseteq ker\ (f \circ g)$. Note: if $f$ is injective then this holds fo …
0answers
92 views
### An in... | {"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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?t=124550 | Physics Forums
## Millennium Problems
This mainly goes out to the professional mathematicians, but what would be your assessment of the Millennium Problems?
In the sense of which would be the most difficult, which might be solved first, the current status of the problems within the community itself.
Not necessarily ... | {"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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/tagged/distribution-theory+probability-theory | # Tagged Questions
1answer
56 views
### expectation of a function of two dependent random variables
I have a formula that I believe it's right but I do not know how to prove it. Could you please give me some arguments or references to show that. Let $\{X_t,t\geq0\}$ be a gamma process. Let $\tau_M$ ...
1answer
63 vi... | {"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/37912/what-is-the-easiest-way-to-stop-a-star/37962 | # What is the easiest way to stop a star?
On long enough cosmological time scales, hydrogen and helium nucleii will become scarce in the Universe. It seems to me that any advanced civilisations that might exist in that epoch would have the motivation to try and prevent the stars from using them up, in order to burn 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": 16, "mathjax_display_tex": 14, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathoverflow.net/revisions/5250/list | ## Return to Answer
4 typesetting
In short, I'd tell your friend: "If you believe a ring can be understood geometrically as functions on a its spectrum, then modules help you by providing more functions with which to measure and characterize these spectra.its spectrum."
Elements of a module over a ring $R$ are like ... | {"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://torus.math.uiuc.edu/cal/math/cal?year=2012&month=08&day=07&interval=year®exp=Group+Theory+Seminar&use=Find | Seminar Calendar
for Group Theory Seminar events the year of Tuesday, August 7, 2012.
.
events for the
events containing
Questions regarding events or the calendar should be directed to Tori Corkery.
``` July 2012 August 2012 September 2012
Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa ... | {"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": 2, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://psychology.wikia.com/wiki/Income_inequality_metrics?oldid=142357 | # Income inequality metrics
Talk0
31,726pages on
this wiki
Revision as of 12:10, December 25, 2011 by Dr Joe Kiff (Talk | contribs)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Assessment | Biopsychology | Comparative | Cognitive | Developmental | Language | Individual differences | Per... | {"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": 3, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://gilkalai.wordpress.com/2008/11/04/a-diameter-problem-6-abstract-objective-functions/?like=1&source=post_flair&_wpnonce=0619346065 | Gil Kalai’s blog
## A Diameter Problem (6): Abstract Objective Functions
Posted on November 4, 2008 by
George Dantzig and Leonid Khachyan
In this part we will not progress on the diameter problem that we discussed in the earlier posts but will rather describe a closely related problem for directed graphs associated... | {"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": 107, "mimetex.cgi": 0, "/images/m... |
http://nrich.maths.org/319/solution | ### There's a Limit
Explore the continued fraction: 2+3/(2+3/(2+3/2+...)) What do you notice when successive terms are taken? What happens to the terms if the fraction goes on indefinitely?
### Not Continued Fractions
Which rational numbers cannot be written in the form x + 1/(y + 1/z) where x, y and z are integers?... | {"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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/169879/circular-random-walk | # Circular random walk
Suppose we have a circumference divided in N arcs of the same length. A particle can move on the circumference jumping from an arc to the adjacent, with probability $P_{k \to k-1}=P_{k\to k+1}=\frac{1}{2}$. I have some difficulty to find the probability that the particle fulfilled at least one 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": 14, "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/118169/is-there-a-relationship-between-entropy-of-a-fininte-distrete-probability-distrib | ## Is there a relationship between Entropy of a fininte distrete probability distribution and the squre sum of the values of probability mass function of that distribution?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Sorry for the long title. What I mean 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": 25, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showpost.php?p=2947325&postcount=2 | View Single Post
Mentor
Quote by bob1182006 1. The problem statement, all variables and given/known data Find the roots of: $$x^5-1=0$$ 2. Relevant equations Polynomial long division. 3. The attempt at a solution $$x^5-1 = (x-1)(x^4+x^3+x^2+x+1) = 0$$ $$x^4+x^3+x^2+x+1 = (x^2+1)^2+x^3+x-x^2$$ $$(x^2+... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/advanced-statistics/28341-probability-distribution.html | # Thread:
1. ## Probability distribution
A rental agency, which leases heavy equipment by the day, has found that one expensive piece of equipment is leased, on the average only one day in five. If rental on one day is independent on rental on any other day, find the probability distribution of Y, the number of days ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 3, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://crypto.stackexchange.com/questions/tagged/zero-knowledge-proofs+prime-numbers | # Tagged Questions
1answer
166 views
### How to construct a zero-knowledge proof of a number of the form $n=p^a q^b$
Let $n = p^a$$q^b$ where p and q are distinct primes and a and b are positive integers. How to construct a zero knowledge proof that n is of such form? This is actually a homework problem with 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": 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/revisions/58010/list | ## Return to Question
2 typo-b-gone
In Mitchell's book "Theory of Categories", Corollary I.16.8 (page 24) states that the following holds in any exact category:
Let $$0 \to A \to B \to C \to 0$$ $$0 \to B^' \to B \to B^{''} \to 0$$ be short exact sequences. Then $B^' \to B \to C$ is epi iff $A \to B \to B^{''}$ is 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": 4, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/165097/does-the-specification-of-a-general-sequence-require-the-axiom-of-choice/165103 | # Does the specification of a general sequence require the Axiom of Choice?
Many results in elementary analysis require some form of the Axiom of Choice (often weaker forms, such as countable or dependent). My question is a bit more specific, regarding sequences.
For example, consider a standard proof of the boundedn... | {"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": 37, "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/32667/numerical-mathemtics-how-to-solve-hexagonal-central-differences | ## [Numerical Mathemtics] How to solve hexagonal central differences
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
I want to simulate a 2d linear wave equation on a circle ($\displaystyle\frac{\partial^2 z(x,y,t)}{\partial t^2}=v^2\cdot\left(\displaystyle\fr... | {"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://mathoverflow.net/questions/66727/bound-of-polynomial-on-product-space-in-terms-of-values-on-the-diagonal | ## Bound of polynomial on product space in terms of values on the diagonal
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
We work in the multivariate case so that $x$ stands for $(x_1,\ldots, x_n)$. Let $q(x,y)$ be a symmetric matrix representation of a homog... | {"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": 27, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/106544/list | Return to Question
4 added 17 characters in body
Given a polynomial $p(x_1,x_2,\ldots,x_d)$ in $d$ variables, with maximum degree $k$, what is the maximum number of components of $\mathbb{R}^d$ minus $p(\ldots)=0$? In other words, into how many pieces can an implicit polynomial equation partition $\mathbb{R}^d$?
For... | {"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": 65, "mathjax_display_tex": 12, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathhelpforum.com/discrete-math/90716-number-ways-7-distinct-objects-can-put.html | # Thread:
1. ## Number of ways in which 7 distinct objects can be put..?
Find the number of ways in which 7 distinct objects can be put in three identical boxes so that no box remains empty.
2. This is similar to a problem i had in an old course where you had to find integers x,y,z s.t. x + y + z = some +ve integer.... | {"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": 25, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/251567/parametric-curve-on-cylinder-surface/251900 | # Parametric curve on cylinder surface
Let $r(t)=(x(t),y(t),z(t)),t\geq0$ be a parametric curve with $r(0)$ lies on cylinder surface $x^2+2y^2=C$. Let the tangent vector of $r$ is $r'(t)=\left( 2y(t)(z(t)-1), -x(t)(z(t)-1), x(t)y(t)\right)$. Would you help me to show that :
(a) The curve always lies on ylinder surfac... | {"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": 54, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://crypto.stackexchange.com/questions/2414/is-this-authenticated-one-way-communication-protocol-secure?answertab=active | # Is this authenticated one-way communication protocol secure?
I am looking to see if this one-way communication protocol is secure. Assume Alice wants to send Bob a message (and doesn't need Bob to reply in the same session/channel - think email). Bob knows Alice's public key $A_{public}$, and Alice knows Bob's publi... | {"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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://en.wikipedia.org/wiki/Ideal_norm | # Ideal norm
In commutative algebra, the norm of an ideal is a generalization of a norm of an element in the field extension. It is particularly important in number theory since it measures the size of an ideal of a complicated number ring in terms of an ideal in a less complicated ring. When the less complicated numb... | {"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": 40, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/218791/an-intuitive-vision-of-fiber-bundles?answertab=votes | # An intuitive vision of fiber bundles
In my mind it is clear the formal definition of a fiber bundle but I can not have a geometric image of it. Roughly speaking, given three topological spaces $X, B, F$ with a continuous surjection $\pi: X\rightarrow B$, we "attach" to every point $b$ of $B$ a closed set $\pi^{-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": 34, "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/206414/faces-of-a-non-planar-graph | “faces” of a non-planar graph
Good afternoon,
I have a question concerning concepts in graph theory. Graph theory is a field quite strange to my knowledge, so my question is maybe stupid.
For a planar graph, we can define its faces as follows : we delete all its edges and its vertices from the plane. Then the remain... | {"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": 28, "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/201276/sigma-question-is-it-legal-to-write-something-like-this/201287 | # Sigma question: is it legal to write something like this?
Is this mathematical syntax correct?
$$\sum_{n+1}^m\sin(n-2)$$
As you see, the starting value is $n+1$ instead of being just purely one variable.
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5
It may even be legal, depends on the judge. But it is a really bad idea to use $n$ as the (presumed) summ... | {"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": 8, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/291921/proving-that-two-equations-are-the-same | # Proving that two equations are the same
Where am I doing it wrong? Both of them should be simplified to $A \cup (B \cap C)$
1$$A \cup (B \cap (A \cup C) ) = A \cup (A \cup B^c)^c) \cap (A\cup C)$$ 2$$A \cup ((B \cap A)\cup(B \cap C)) = A \cup (A^c \cup B)\cap (A\cup C)$$ 3$$(A \cup (B \cap A )) \cup (A \cup (B \cap... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 4, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/142041/how-to-prove-q-wedge-p-vee-q-wedge-p-q/142043 | # How to prove $((Q \wedge ¬P) \vee (Q \wedge P)) = Q$
I cannot see any steps to this problem! Surely the answer is obvious? Is there a particular law which is used to make this statement?
$$((Q \wedge ¬P) \vee (Q \wedge P)) = Q$$
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Shouldn't it be $$((Q \wedge ¬P) \vee (Q \wedge P)) = Q$$? – Peter Tamaroff May 7 '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": 6, "mathjax_display_tex": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
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