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http://math.stackexchange.com/questions/81145/why-this-limit-cant-be-computed-like-this | # Why this limit can't be computed like this?
This is the limit: $$\lim_{x \to 2} \frac{3x^2-x-10}{x^2-4}$$
The solution manual says it is: $\frac{11}{4}$
I've tried to solve it like a polynomial like this:
$$\frac{(\frac{3x^2}{3x^2}-\frac{x}{3x^2}-\frac{10}{3x^2})*3x^2}{(\frac{x^2}{x^2}-\frac{4}{x^2})*x^2}=$$
$$=... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 43, "mathjax_display_tex": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/9218/probabilistic-proofs-of-analytic-facts/10312 | ## Probabilistic Proofs of Analytic Facts
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What are some interesting examples of probabilistic reasoning to establish results that would traditionally be considered analysis? What I mean by "probabilistic reasonin... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 72, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/147166/does-my-definition-of-double-complex-noncommutative-numbers-make-any-sense/147170 | # Does my definition of double complex noncommutative numbers make any sense?
I wanted to factorize $a^2+b^2+c^2$ into two factors in a similar way to $$a^2+b^2 = (a+ib)(a-ib)$$ This doesn't seem to be possible using real or complex numbers. However I came up with the following idea $$(a + ib + jc) (a -ic -jc) = a^2+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": 36, "mathjax_display_tex": 12, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathoverflow.net/questions/45351/does-pi-1-have-a-right-adjoint/45375 | ## Does $\pi_1$ have a right adjoint?
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Eilenberg and Mac Lane showed that given a group $G$ there exists a pointed topological space $X_G$ such that $\pi(X_G,\bullet)\cong G$. It is obviously a way to "invert dire... | {"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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/80430?sort=oldest | ## General form of Schwarz reflection principle
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Hello all,
It is easy to find results on reflecting holomorphic functions over circles and lines, but I am wondering what there is for reflecting over smooth curve... | {"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/7508?sort=oldest | ## A hypersurface with many points
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Ok, it's time for me to ask my first question on MO.
Consider the affine curve $Y+Y^q=X^{q+1}$ over the finite field `$\mathbf{F}_q$`. It's interesting because it has the large... | {"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": 116, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://math.stackexchange.com/questions/265264/prove-f-n1f-n-1-f-n2-1n-without-induction | # Prove $F_{n+1}F_{n-1}-(F_{n})^2=(-1)^n$ without induction
I am asked to pove the statement about fibonacci sequence. The task is from the passage about series and sequences. But the proof seems to need induction way, doesn't it?
Prove the statement $$F_{n+1}F_{n-1}-(F_{n})^2=(-1)^n$$ for all $n\ge 1$.
How can I 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": 21, "mathjax_display_tex": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.math.uni-bielefeld.de/sfb701/projects/view/22 | Faculty of Mathematics
Collaborative Research Centre 701
Spectral Structures and Topological Methods in Mathematics
# Project C8
## Finiteness Properties of Infinite Discrete Groups
Principal Investigator(s) Other Investigators
## Summary:
The main goal is to establish finiteness properties (finite generation, fin... | {"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/138958/can-i-apply-rolles-theorem-in-reverse | # Can I apply Rolle's theorem in reverse?
I want to prove the following statement:
Let $f$ and $g$ be two real functions continuous in some interval $[a, b]$ and differentiable in $(a, b)$. If $f' = g'$, then $f(x) = g(x) + c$, where $c$ is a constant.
I thought I could argue like this: Consider $h(x) = f(x) - g(x)$... | {"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": 32, "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/68875?sort=oldest | ## How to invert the matrix [n choose 2j - i] ?
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In a certain model of a stat-physics type, one encounters a matrix $$A_n:=\left[\binom{n}{2j-i}\right]_{i,j=1}^{n-1}.$$ The determinant of this matrix (equal to $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": 42, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/67727-gradient-directional-derivative-way-represent-vector-equations.html | Thread:
1. Gradient and directional derivative way of represent the vector equations
I have question about presentation of directional derivative.
Sometimes I see directional derivates and gradient to be represented as a function but I think that it is convenient to use "vector presentation" instead.
My question is ... | {"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": 27, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/94645/expected-smallest-prime-factor | # Expected smallest prime factor
For a random integer $x$ chosen uniformly between 2 and $n$, what is the expected value of the smallest prime factor of $x$ as a function of $n$?
What is the behavior of the function as $n$ tends to infinity?
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## 3 Answers
A quick and dirty answer... (I began before Will answered.... | {"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": 9, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/advanced-algebra/39099-matrix-inverse.html | Thread:
1. matrix inverse
Find the inverse of the given matrix
[2 4 3]
[3 -4 -4]
[5 0 -1]
Can you please teach me the steps of sloving the inverse of this matrix? Thank you very much.
2. Which methods have you learned in class? You can perform row operations on your matrix until you get it into row echelon form 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 7, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/73553?sort=newest | ## When may Function (meromorphic) be expanded as power series with coefficients of integers
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Let F be meromorphic function,with what properties may it expanded as power series with coefficients of integers in suc... | {"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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://harrisonbrown.wordpress.com/tag/math-nt/ | # Portrait of the Mathematician
Mathematics, statistics, philosophy, and way too much pop culture
## Posts Tagged ‘math.NT’
### The importance of choosing the right model
December 13, 2009
I’ve had the idea for this post bouncing around in my head for several months now, but now that I don’t have classes to worry ... | {"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://en.wikibooks.org/wiki/Pictures_of_Julia_and_Mandelbrot_Sets/The_Mandelbrot_set | # Pictures of Julia and Mandelbrot Sets/The Mandelbrot set
Interesting Julia set
Ugly Julia set
In appearance a Julia set can go from one extreme to the other. And if we have a family of functions containing a complex parameter c, we will observe that by far the majority of c-values the Julia set is completely withou... | {"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": 122, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://physics.stackexchange.com/questions/tagged/error-analysis | # Tagged Questions
The error-analysis tag has no wiki summary.
1answer
38 views
### How many measurements should be done? [closed]
I am measuring time of a computer operation. The operation should run roughly same time each time I measure it. How many times should I measure it to get good average and standard devia... | {"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://gilkalai.wordpress.com/2008/07/06/from-helly-to-cayley-iv-probability-questions/?like=1&source=post_flair&_wpnonce=8cb43e0c56 | Gil Kalai’s blog
## From Helly to Cayley IV: Probability
Posted on July 6, 2008 by
I decided to split long part III into two parts. This (truly) last part of this series deals with probabilistic problems and with combinatorial questions regarding higher Laplacians.
### 21. Higher Laplacians and their meanings
Our ... | {"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": 11, "mimetex.cgi": 0, "/images/ma... |
http://researchinpractice.wordpress.com/tag/galois/ | # Research in Practice
## The History of Algebra, part II: Unsophisticated vs. Sophisticated Tools
Friday, Jul 9 2010
Ben Blum-Smith 6:11 pm
Math ed bloggers love Star Wars. This post is extremely long, and involves a fair amount of math, so in the hopes of keeping you reading, I promise a Star Wars reference towa... | {"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": 128, "mimetex.cgi": 0, "/images/m... |
http://math.stackexchange.com/questions/234704/approximating-a-sum-of-two-binomial-distributions | # Approximating a sum of two binomial distributions
A club basketball team will play a 60-game season. Thirty-two of these games are against class A teams, and 28 are against class B teams. The outcomes of all the games are independent. The team will win each game against a class A opponent with probability .5 and it ... | {"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": 15, "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/7475/magnetic-susceptibility-in-1-ev/7486 | # Magnetic susceptibility in 1/eV
In this paper the authors refer to
transverse susceptibility $\chi_{ \perp}$ [meV $^{−1}$]
I was taught that the magnetic susceptibility is dimensionless.
How do I get $\chi$ in the above units??
-
In one place it is given in emu/mol, whatever that may be. – Georg Mar 23 '11 at 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": 13, "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/tags/string-theory/new | # Tag Info
## New answers tagged string-theory
0
### Question on Type HO/HE string theory
I just found that my question (2) is trivially easy and that indeed it is: $$\begin{array}{l} m = \sqrt {\frac{{2\pi T}}{{{c_0}}}\left( {B + {{\tilde N}_{II}} - {a_B} - {{\tilde a}_{II}}} \right)} \\ {\rm{ }} = \sqrt {\frac{{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": 22, "mathjax_display_tex": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/math-puzzles/209475-logic-help-print.html | # Logic help.
Printable View
• December 9th 2012, 07:18 PM
hisajesh
Logic help.
2 men and 7 boys can do a piece of work in 14 days,
3 men and 8 boys can do it in 11 days.
8 men and 6 boys can do this 3 times of work in how many days?
Logic: I found either the first or the second sentence is redundant, but when I ign... | {"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": 32, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/97250/consecutive-coin-toss-with-static-tosses | # Consecutive Coin Toss with static tosses
I'm writing an algorithm for a coin toss problem. But I have a problem understanding the calculation given.
Here is the question:
You have an unbiased coin which you want to keep tossing until you get N consecutive heads. You've tossed the coin M times and surprisingly, 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": 45, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathforum.org/mathimages/index.php?title=Volume_of_Revolution&diff=7465&oldid=7401 | Volume of Revolution
From Math Images
(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": 23, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/194605/calculate-cosv-frac-pi6-when-cos-v-frac23 | Calculate $\cos(v+\frac{\pi}{6})$ when $\cos v = -\frac{2}{3}$
I am to calculate $\cos(v+\frac{\pi}{6})$ when $\cos v = -\frac{2}{3}$ and $0 \lt v \lt \pi$.
I know I can change $\cos(v+\frac{\pi}{6})$ into
$$\cos v \times \cos \frac{\pi}{6} - \sin v \times \sin \frac{\pi}{6}$$
but I fail to see how this helps me, o... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 23, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://calculus7.org/2012/05/08/two-subspaces/ | being boring
## Two subspaces
Posted on 2012-05-08 by
The title is borrowed from a 1969 paper by Paul Halmos. Two subspaces $M$ and $N$ of a Hilbert space $H$ are said to be in generic position if all four intersections $M\cap N$, $M^\perp\cap N$, $M\cap N^\perp$, $M^\perp\cap N^\perp$ are trivial. It may be easier ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 29, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/257093/iterative-model-fitting | # Iterative model fitting
I have a sequence of points $\{(x_k,y_k,z_k)\}$ and I need to fit some $2D$ model $P(x,y)$ that approximates $z$ in some sense.
The $z_k$$'s$ are noisy samples of some $2D$ function $z_k = f(x,y) + n(x,y)$.
The noise $n$ is mainly shot noise ($std(n(x,y)) \approx \sqrt{f(x,y)}$).
The noise 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": 18, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://gmatclub.com/mwiki/index.php?title=Geometry&oldid=6020 | # Geometry
### From GMATClub
Revision as of 15:35, 25 July 2008 by Dzyubam (Talk | contribs)
(diff) ← Older revision | Current revision (diff) | Newer revision → (diff)
GMAT Study Guide - a prep wikibook
index - edit - roadmap
## Lines
"Line" is a basic concept in geometry. It refers to a straight line extending ... | {"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": 0, "/images/mat... |
http://mathhelpforum.com/discrete-math/178786-finding-min-max-number-edges-connected-graph.html | # Thread:
1. ## Finding min and max number of edges of a connected graph
A simple graph of 25 vertices and 6 connected components.
What is the minimum and maximum number of edges can the graph have?
Is there a formula to calculate the min and max? 25 vertices is too huge to draw and there are several possibilities 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/algebra/138558-arithmetic-progression.html | # Thread:
1. ## Arithmetic progression
the $N^{th}$ term of an A.P is denoted by $U_{n}$ and the sum of the $1^{st}n$ terms by $S_{N}$ in a certain A.P ;; $U_{5}+U_{16}=44$ and $S_{18}=3S_{10}.$calculate the value of the first term and the common difference.
i have been trying to get two equations from the given 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 17, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/40586/list | ## Return to Answer
2 added 78 characters in body
Here is a complete answer; I think it is more or less what Steve wrote in his comment, except I don't understand the appearance of $\mathbb{R}$ there. If $I$ is the infinite index set, let $L=\mathbb{Z}^{(I)}\subset P$ be the obvious free submodule. Then $\mathrm{Ext}... | {"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": 42, "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/43973/proving-that-a-function-is-bounded/43975 | # Proving that a function is bounded
This is one part of an exercise in my homework, which for some reason I can't think of any way to prove.
$\displaystyle f(x,y)=\frac{xy^2}{x^2+y^4}$, if $(x,y)\neq (0,0)$ and $0$ otherwise.
I'm trying to prove that this function is bounded. I have figured that I only need to prov... | {"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://mathoverflow.net/questions/107491?sort=oldest | Mackey(also Green and Tambara) functors and Greenlees-May
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This is somewhat related to a question that I asked on Math.SE but, sadly, received no response. I apologize ahead of time if this is not appropriate for MO. ... | {"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": 40, "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/176019/about-poisson-equation | # About Poisson Equation.
I want to solve $- \Delta u = f$ in $\Omega$ with $u = \phi$ on $\partial \Omega$. But if I have the solutions of (1) and (2) below : $$- \Delta u_1 = f \; \text{in } \Omega , \; u_1 = 0 \; \text{on } \partial \Omega \tag{1}$$ $$- \Delta u_2 = 0 \; \text{in } \Omega , \; u_2 = \phi \; \text{o... | {"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": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/264771/cross-product-and-pseudovector-confusion?answertab=oldest | # Cross product and pseudovector confusion.
So called pseudovectors pop up in physics when discussing quantities defined by cross products, such as angular momentum $\mathbf L=\mathbf r\times\mathbf p$. Under the active transformation $\mathbf x \mapsto \mathbf{-x}$, we claim that such a vector gets mapped to itself 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": 41, "mathjax_display_tex": 8, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://terrytao.wordpress.com/tag/syndetic-sets/ | 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 ‘syndetic sets’ tag.
## 254A, Lecture 3: Minimal dynamical systems, recurrence, and the Stone-Čech compactification
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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 22, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/advanced-algebra/91495-finding-basis.html | # Thread:
1. ## Finding a basis
Can anyone verify that I am doing this correctly?
I have to find a basis for
$W=\{(a_{1}, a_{2}, a_{3}, a_{4}, a_{5} \in F^{5} | a_{1}-a_{3}-a_{4}=0\}$
So, does this mean that $a_{2}$ and $a_{5}$ can be any numbers?
I began by setting them both equal to one, giving me (0, 1, 0, 0 ,... | {"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": 52, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://en.wikipedia.org/wiki/Metric_spaces | # Metric space
(Redirected from Metric spaces)
In mathematics, a metric space is a set where a notion of distance (called a metric) between elements of the set is defined.
The metric space which most closely corresponds to our intuitive understanding of space is the 3-dimensional Euclidean space. In fact, the notion... | {"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": 179, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://math.stackexchange.com/questions/103208/relations-between-various-definitions-of-a-radon-measure | # Relations between various definitions of a Radon measure
The following various definitions of a Radon measure seem to be given for the Borel sigma algebra of different types of topological spaces: general, Hausdorff, locally compact, or locally compact Hausdorff.
I was wondering if the definitions are related in so... | {"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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/25229/list | Return to Question
2 added 11 characters in body; deleted 16 characters in body
For example, I take differentiability, analyticity, and algebraicity(of a function). All(more or less) imply continuity. So when we define a differentiable function on $\mathbb R^n$ or an analytic function on $\mathbb C^n$, or a regular 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": 4, "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/51718-prove-group.html | # Thread:
1. ## Prove that in a group
(xy)^(-1) = b^(-1)a^(-1),
keeping in mind the group may not be commutative. Thanks.
2. Originally Posted by universalsandbox
(xy)^(-1) = b^(-1)a^(-1),
keeping in mind the group may not be commutative. Thanks.
To show $(ab)^{-1} = b^{-1}a^{-1}$ you need to show $(ab)(b^{-1}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": 9, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathforum.org/mathimages/index.php?title=Compass_%26_Straightedge_Construction_and_the_Impossible_Constructions&diff=15823&oldid=13187 | # Compass & Straightedge Construction and the Impossible Constructions
### From Math Images
(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": 370, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathoverflow.net/questions/52874/statistics-of-extended-gcd/53637 | ## Statistics of Extended GCD
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Consider a coprime pair of integers $a, b.$ As we all know ("Bezout's theorem") there is a pair of integers $c, d$ such that $ac + bd=1.$ Consider the smallest (in the sense of Eucli... | {"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": 135, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathoverflow.net/questions/87424?sort=oldest | ## Critical points in Hilbert space [closed]
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Let $f$ be a $C^1$ functional on a Hilbert space $X$, and $Y$ a closed subspace of $X$. Suppose the restriction of $f$ on $Y$ has a critical point $x_0 \in Y$.
Q: Is ... | {"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://unapologetic.wordpress.com/2012/08/28/the-jordan-chevalley-decomposition/?like=1&_wpnonce=122935e828 | # The Unapologetic Mathematician
## The Jordan-Chevalley Decomposition
We recall that any linear endomorphism of a finite-dimensional vector space over an algebraically closed field can be put into Jordan normal form: we can find a basis such that its matrix is the sum of blocks that look like
$\displaystyle\begin{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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 29, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/tagged/electromagnetic-radiation?sort=votes&pagesize=15 | # Tagged Questions
Propagating solutions to Maxwell’s equations in classical electromagnetism and real photons in quantum electrodynamics. A superset of thermal-radiation.
7answers
25k views
### If you view the Earth from far enough away can you observe its past?
From my understanding of light, you are always looki... | {"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": 1, "mathjax_asciimath": 2, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/278631/eigenvalues-and-equalizers/278668 | # Eigenvalues and equalizers
I am asked to relate eigen{value,vectors} with equalizers in the category of matrices. However, in the category of matrices $g\circ f$ means the (matrix) product $fg$. And $\lambda$ is an eigenvalue of $A$ if there exists $v$ such that $Av=\lambda v$.
To relate this with equalizers, I was... | {"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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/54929/multiplication-tables-for-hg-p/54973 | ## Multiplication tables for H*(G/P)?
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Hi everyone. My recent work has me developing software to compute in $H^\ast(G/P)$, where $G$ is a complex connected semisimple algebraic group and $P$ is a standard paraboli... | {"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://physics.stackexchange.com/questions/3495/does-decoherence-need-non-determinism | # Does decoherence need non-determinism?
Consider standard quantum mechanics, but forget about the collapse of the wavefunction. Instead, use decoherence through interaction with the environment to bring the evolving quantum state into an eigenstate (rspt arbitrarily close by). Question: Can this theory be fundamental... | {"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://math.stackexchange.com/questions/tagged/mathematical-modeling?page=1&sort=votes&pagesize=30 | # Tagged Questions
A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modelling.
16answers
6k views
### Optimizing response times of an ambulance corp: short-term versus average
Background: I work for an 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": 37, "mathjax_display_tex": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?p=3565509 | Physics Forums
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## How does GR handle metric transition for a spherical mass shell?
Quote by PeterDonis Actually, since I posted the assessment in #8, I owe you a mea culpa, Q-reeus; after thinking this over and thinking about DaleSpam's comment, I think... | {"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://mathoverflow.net/questions/92631/unique-beltrami-differential-of-the-form-k-frac-barqq | ## Unique Beltrami Differential of the form $k\frac{\bar{q}}{q}$?
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I'm having a brain freeze.
Let $B$ be the space of complex valued measurable functions on the unit disk in the complex plane with essential supre... | {"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://mathoverflow.net/questions/95160/solid-rings-and-tor | ## Solid Rings and Tor
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A solid ring is a ring $R$ such that the multiplication $R\otimes_{\mathbb{Z}} R \to R$ is an isomorphism.
These were classified by Bousfield and Kan; they are
1. subrings of $R\subseteq\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": 32, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showpost.php?p=3783210&postcount=3 | View Single Post
Recognitions:
Science Advisor
I'm not an expert in you topic, but I'd find it interesting to chat about it until one comes along.
Quote by Hare Hi. I have a few questions about sensor specifications and its implementation in a Kalman Filter and simulation of gyroscope/accelerometer ou... | {"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://physics.stackexchange.com/questions/11978/impact-of-covering-glass-on-lens-performance?answertab=oldest | # Impact of covering glass on lens performance
I've seen microscope lenses optimized for 0.17mm covering glass. I don't see what needs to be optimized here? As glass does not touch the lens (as in case of oil/water immersion) - it should just affect focal distance without introducing any aberrations.
Is that correct,... | {"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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.all-science-fair-projects.com/science_fair_projects_encyclopedia/Mechanical_work | All Science Fair Projects
Science Fair Project Encyclopedia for Schools!
Search Browse Forum Coach Links Editor Help Tell-a-Friend Encyclopedia Dictionary
Science Fair Project... | {"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": 7, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/237679/help-with-proof-of-chain-rule | Help with proof of chain rule
I'm following along on this proof of the chain rule. All is clear to me except the step where they say:
Differentiablility implies continuity; therefore $\Delta_u \to 0$ as $\Delta_x \to 0$ in $f\big(g(x)\big)$.
Could someone explain to a calculus newb why that's the case, in simple ter... | {"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": 15, "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/tagged/lagrangian-formalism | Tagged Questions
For questions involving the Lagrangian formulation of a dynamical system. Namely, the application of an action principle to a suitably chosen Lagrangian or Lagrangian Density in order to obtain the equations of motion of the system.
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Lagrangian with a general constraint [closed]
Ca... | {"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": 60, "mathjax_display_tex": 13, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathhelpforum.com/differential-equations/201878-eigenvalues-eigenvectors.html | # Thread:
1. ## Eigenvalues and eigenvectors?
i been given this 3x3 matrix and can't find the eigenvaules and eigenvectors.
-3 -2 -2
-1 -4 -1
2 4 1
can someone show me how to do it?
2. ## Re: Eigenvalues and eigenvectors?
Have you found the characteristic equation? It has three small integer solutions. On... | {"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://mathoverflow.net/questions/59222/importance-of-poincare-recurrence-theorem-any-example/59225 | ## Importance of Poincaré recurrence theorem? Any example?
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Recently I am learning ergodic theory and reading several books about it.
Usually Poincaré recurrence theorem is stated and proved before ergodicity 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": 41, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://unapologetic.wordpress.com/2009/09/24/differentials/?like=1&source=post_flair&_wpnonce=1c947633de | # The Unapologetic Mathematician
## Differentials
Okay, partial derivatives don’t work as an extension of derivation to higher-dimensional spaces. Even generalizing them to directional derivatives doesn’t give us what we want. What we need is not just the separate existence of a bunch of directional derivatives, but ... | {"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": 68, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/35700/fields-of-steady-currents-using-electrostatics?answertab=oldest | # Fields of Steady Currents Using Electrostatics
Suppose you have a uniform ring charge rotating at constant angular velocity so that you also have a uniform ring of steady current, and thus you can use the Biot-Savart Law to compute the magnetic field. But I also remember from college that to good approximation you 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": 0, "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/286333/proof-on-catalan-numbers?answertab=votes | # Proof on Catalan numbers
In the book I'm using on Catalan numbers, the author gives a scenario in order to develop the formula for Catalan numbers.
The scenario is that a boy has an empty jar. Every day he either puts in a dollar coin or takes on out for $2n$ days. At the end of the $2n$ days, the jar is empty. 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": 9, "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/65900?sort=oldest | ## A stupid question about Automorphic forms
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Okay, so an automorphic form $f$ on a reductive group $G/ \mathbb{Q}$ and arithmetic subgroup $\Gamma$ is a smooth function satisfying the following conditions:
(a) 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": 29, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://all-science-fair-projects.com/science_fair_projects_encyclopedia/Lie_algebra | # All Science Fair Projects
## Science Fair Project Encyclopedia for Schools!
Search Browse Forum Coach Links Editor Help Tell-a-Friend Encyclopedia Dictionary
# Science Fair ... | {"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": 7, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/calculus/40206-weird-integral.html | # Thread:
1. ## Weird Integral
A question that I have been given asks me to use a certain substitution to find the answer exactly. The only thing is not only do I think I can manage without it the substitution is the most random thing one I've seen.
Upper Boundary = 2, Lower Boundary = 0
Integrate: (4-x)^(1/2).dx
... | {"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://mathhelpforum.com/calculus/59471-analysis-function.html | # Thread:
1. ## Analysis Function
Is there a function such that, f is continuous on (1,5), reaches a maximum on (1,5), but does not reach a minimum on (1,5). Does such a function exist or is it impossible?
2. Originally Posted by thahachaina
Is there a function such that, f is continuous on (1,5), reaches a maximum ... | {"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://unapologetic.wordpress.com/2009/10/16/higher-order-differentials/?like=1&_wpnonce=34114a6dfa | # The Unapologetic Mathematician
## Higher-Order Differentials
Just like we assembled partial derivatives into the differential of a function, so we can assemble higher partial derivatives into higher-order differentials. The differential measures how the function itself changes as we move around, and the higher diff... | {"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": 30, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/20107?sort=newest | ## Surprising Analogue of Q
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
I was describing Manish Kumar's work a few weeks ago to a fellow graduate student, and she stumped me with a big-picture question I couldn't answer.
Manish Kumar proved that the commu... | {"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://mathhelpforum.com/calculus/94467-finding-relative-maximum-minimum.html | Thread:
1. Finding Relative Maximum and Minimum
Q1. Test the Function $g(x)=6x^3-(108)x^2+(630)x-2$ for relative maximum and minimum. Find the critical values. Use the 2nd derivative test if possible.
My solution:
$g'(x)=18x^2-216x+630$ if follows that the critical values of g are x1= -7 and x2=-5.
*
To find the 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 11, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://cnr.lwlss.net/CircleObjectivesR/ | # Testing optimisation algorithms: Part II - Implementing objective function in R
22:16 Wednesday 7th September 2011
In Part I of this series, I presented the reasons I'm interested in optimisation, and gave a mathematical statement of the example constrained optimisation problem I will solve. In this post, I am goin... | {"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://mathhelpforum.com/pre-calculus/50605-graphing-composite-functions.html | # Thread:
1. ## Graphing Composite Functions
Hello, I am given two graphics, F(x), G(x) and I am supposed to graph g(f(x))
I am a bit rusty with composite functions, so I was hoping someone could give me some general information on how to do this? From what I recall, you need to take the range of f(x) and input it 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": 24, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/tagged/special-relativity?page=2&sort=active&pagesize=15 | Tagged Questions
The special theory of relativity describes the motion and dynamics of objects moving at significant fractions of the speed of light.
learn more… | top users | synonyms
2answers
156 views
Relativity of Simultaneity
Relativity of Simultaneity seems to be about OBSERVING two events simultaneously (pl... | {"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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/20480/should-i-heat-my-room-when-im-not-here-energy-efficiently-speaking?answertab=active | # Should I heat my room when I'm not here, energy-efficiently speaking?
I was wondering as it's getting cold : is it better for my electricity bill to shut down completely my (electric) heater during day, and to turn it on again when I come home (then it will have to heat the room from something like 5°C to around 20°... | {"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": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://unapologetic.wordpress.com/2008/05/22/ | # The Unapologetic Mathematician
## Matrices II
With the summation convention firmly in hand, we continue our discussion of matrices.
We’ve said before that the category of vector space is enriched over itself. That is, if we have vector spaces $U$ and $V$ over the field $\mathbb{F}$, the set of linear transformatio... | {"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... |
http://mathhelpforum.com/algebra/103090-find-values.html | # Thread:
1. ## find values
hi, i've got the question:
the polynomials f(x) and g(x) are defined by $f(x) = x^3 + px^2 - x + 5$, $g(x) = x^3 - x^2 + px + 1$ where p is a constant. when f(x) and g(x) are divided by x - 2 the remainder is R in each case. find the values of p and R
i got it down to
R = f(2) = 8 + 4p -... | {"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": 12, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/trigonometry/76143-finding-angle-x-radians.html | # Thread:
1. ## finding and angle x in radians?
Find an angle x in radians such that 8pi<x<9pi and cosx=1/2
What is this question asking for? I came up with pi/3, but I don't think that's in between 8 and 9 pi. Can anyone explain? Thanks
2. Originally Posted by captaintoast87
Find an angle x in radians such that 8p... | {"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://gilkalai.wordpress.com/2009/01/16/telling-a-simple-polytope-from-its-graph/?like=1&source=post_flair&_wpnonce=c1ce40f6e1 | Gil Kalai’s blog
## Telling a Simple Polytope From its Graph
Posted on January 16, 2009 by
Peter Mani (a photograph by Emo Welzl)
## Simple polytopes, puzzles
Micha A. Perles conjectured in the ’70s that the graph of a simple $d$-polytope determines the entire combinatorial structure of the polytope. This conject... | {"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": 233, "mimetex.cgi": 0, "/images/m... |
http://soffer801.wordpress.com/2012/05/16/a-proof-from-erdos/ | #### Andy Soffer
UCLA Mathematics Ph.D Student
# A proof from Erdős
May 16, 2012
I have a friend from HCSSiM who reminded me of this proof, and a few others, that he put together for MIT Splash. Thanks Ben!
Let $\{p_1,\dots,p_n\}$ be the set of primes less than some number $N$. Pick a number $x$ which is less than... | {"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": 29, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/175804/another-question-in-graph-theory | Another question in Graph Theory
Question: Let $H$ be a graph of order 10 such that $3\le d(v)\le5$ for each vertex $v$ in $H$ [where $d(v)$ is the degree of $v$]. Not every vertex is of even degree. No two odd-degree vertices are of the same degree. What is the size [number of edges] of $H$?
Answer: Size of $H$ is 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": 9, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/56056/work-done-to-tighten-a-screw | # Work done to tighten a screw [closed]
We use a wrench to turn nuts on bolts because they require less force. Consider a hexagonal nut 1 cm in diameter. We can tighten this nut with one of two wrenches, wrench A with lever arm 10 cm and wrench B with lever arm 20 cm. Both wrenches have a very small mass, so you may n... | {"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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://www.physicsforums.com/showthread.php?s=60133cbd6442f915027a0433f5918350&p=4192777 | Physics Forums
Recognitions:
Gold Member
## What will the gravitational field inside the Earth be?
There is a question: If we dig a channel from the North pole of the Earth to the South pole of the Earth, then we release a ball into this channel from the North pole, what will be the motion of this be like?
I think ... | {"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": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/revisions/34640/list | ## Return to Question
2 added 52 characters in body
Can someone please explain the difference between local rigidity and infinitesimal rigidity? Does either version of rigidity imply the other?
In particular, I'm thinking about Weil's rigidity theorem for hyperbolic metrics on manifolds of dimension $\geq 3$. I've 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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/algebra/203613-need-easy-way-solve-print.html | # need a easy way to solve it
Printable View
• September 17th 2012, 09:23 AM
Petrus
need a easy way to solve it
For which integers are x^5+4x^4+3x+1 divisible by 5?
i have solved this prob and there is none but i did it on a "hard way"
i did make it to x(x^3(x+4)+3)+1 and try put like x to 1,2,3 etc.. is there any ea... | {"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://math.stackexchange.com/questions/1901/why-is-fundamental-group-insufficient-to-classify-manifolds/1907 | # Why is fundamental group insufficient to classify manifolds?
I have heard that some issues in group theory prevent classifying all manifolds upto homotopy using the fundamental group invariant. Does anyone know what are those issues?
Thanks, K.
-
3
– Soarer Aug 9 '10 at 13:51
6
I think that the OP is alluding 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": 24, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://stochastix.wordpress.com/category/mathematics/control-theory-mathematics/ | # Rod Carvalho
## Archive for the ‘Control Theory’ Category
### Sailing in state space
April 11, 2011
Consider the following controlled (autonomous) dynamical system [1]
$\dot{x} (t) = f (x (t), u (t))$
where $x : [0, \infty) \to \mathbb{R}^n$ is the state trajectory, $u : [0,\infty) \to \mathcal{U}$ is the contr... | {"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": 29, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/15899/why-the-principle-of-least-action/15958 | # Why the Principle of Least Action?
I'll be generous and say it might be reasonable to assume that nature would tend to minimize, or maybe even maximize, the integral over time of $T-V$. Okay, fine. You write down the action functional, require that it be a minimum (or maximum), and arrive at the Euler-Lagrange equat... | {"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/49946/principal-curvatures-and-curvature-directions-closed | ## Principal curvatures and curvature directions [closed]
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Last week I considered again principal curvature (pc) and principal curvature directions (pcd) of a, for the sake of simplicity, 2-manifold embedded in 3-... | {"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/142015/is-my-riemann-sum-correct-example-2?answertab=votes | # Is my Riemann Sum correct (Example # 2)? [duplicate]
Possible Duplicate:
Is my Riemann Sum correct?
This is my second attempt, the answer seems rather odd so I thought I would have it checked as well. For the integral: $$\int_{-5}^{2} \left( x^{2} -4 \right) dx$$
My calculations:
$$\begin{align*}\Delta x &= \frac... | {"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": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://www.physicsforums.com/showthread.php?p=1197128 | Physics Forums
## Compton Generator
*I don't know if this belongs to homework section or not.
I just found the description in my book interesting and want to know more. If this is inappropriate, please move it to homework section.
Compton Generator is basically a device invented by Compton which is used to measure 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": 0, "mathjax_display_tex": 9, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/260937/does-this-set-contain-the-given-integer | # Does this set contain the given integer?
Let $a = 31$. Consider the set of integers $T = \{a, 8a, 8^{2}a, 8^{3}a, \cdots \}$. Does $T$ contain the integer:
999999999900000000000090909090000000000000000008?
So far I've deduced that if we work mod 9 that the set $T$ can be reduced to a reduced residue system modulo ... | {"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://quant.stackexchange.com/questions/519/missing-step-in-stock-price-movement-equations/520 | # Missing step in stock price movement equations
Assuming a naive stochastic process for modelling movements in stock prices we have:
$dS = \mu S dt + \sigma S \sqrt{dt}$
where S = Stock Price, t = time, mu is a drift constant and sigma is a stochastic process.
I'm currently reading Hull and they consider a simple ... | {"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": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/169623/how-complex-exponential-converges-and-sum-of-exponents-rule-holds/169663 | # How complex exponential converges and “sum of exponents” rule holds
1. How is it the complex exponential converges for any value of $z$ in the complex plane? $$e^{z} = 1 + \frac{z}{1!} + \frac{z^2}{2!} \cdots\cdots$$
2. How is it the "sum of exponents" rule holds for complex exponential, that is $e^{w}e^{z} = e^{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": 17, "mathjax_display_tex": 7, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/advanced-algebra/125559-external-direct-product.html | # Thread:
1. ## External Direct Product
Let $C_n$ denote a cyclic group of order n. Show that if p is a prime number then every abelian group of order $p^2$ is isomorphic to one of the two groups $C_{p^2}, C_p \times C_p$.
OK!
Let G be an abelian group, with $|G|=p^2$. Suppose G is not isomorphic to a cyclic group ... | {"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": 43, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?t=616867 | Physics Forums
Equations with integrals,
Hi,
How would one go about solving equations like $∫^{b}_{a}f(s,t)g(s)ds$=g(t),for f(s,t). Could we turn it into a differential equation somehow?
Thanks
PhysOrg.com science news on PhysOrg.com >> Front-row seats to climate change>> Attacking MRSA with metals from antibact... | {"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://mathhelpforum.com/geometry/89963-find-angles-triangle.html | # Thread:
1. ## Find the angles of the triangle?
Each of the two triplets of numbers $(a, b, c)\ \& \left(\frac{a}{2b},\ \frac{2b}{3c},\ \frac{3c}{a}\right)$ is a Geometric Progression. Can the numbers $a,b,c$ be the lengths of the sides of a triangle? If they can what triangle is it? Find the angles of the triangle.... | {"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://mathhelpforum.com/calculus/67061-help-delta-epsilon-proofs-print.html | # Help with delta epsilon proofs...
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• January 6th 2009, 11:32 AM
bemidjibasser
Help with delta epsilon proofs...
I need to prove that lim (mx+b) as x approaches c = mc +b. Any tips or help would be greatly appreciated.
Also, What exactly is the relationship of the definite integral to the derivative?
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": 15, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/38763/is-lp-mathbbr-minus-the-zero-function-contractible/38764 | ## Is $L^p(\mathbb{R})$ minus the zero function contractible?
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Is $L^p(\mathbb{R}) \setminus 0$ contractible? My intuition says that the answer is yes, but I'm afraid that this is based on thinking of this as some... | {"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": 74, "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/6603/index?nomenu=1 | ## 'How Steep Is the Slope?' printed from http://nrich.maths.org/
### Show menu
#### The gradient of a line tells us how far up or down we go when
we take one step to the right:
On a grid like the one below we can draw lines with different gradients.
Check you agree that the black line is one of several that could 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... |
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