LATEX
http://www.texify.com/#
http://jenyay.net/index.php?n=Soft.Texgui
http://www.xm1math.net/texmaker/ Latex Editor
http://www.winedt.com/
https://engineering.purdue.edu/~mark/latex/
http://www.thestudentroom.co.uk/wiki/LaTex
http://en.wikibooks.org/wiki/LaTeX/Mathematics
http://en.wikipedia.org/wiki/Help:Formula
TEX cheet sheet: TEX.pdf
\sum_{i=0}^{k}i =k(k+1)/2 \sim \Theta(k^2) \\
\sqrt[5]{\frac{n} {n-1} S} \\ \binom{k}{2}2^{k-2}
(\frac{x^2}{y^3})
\left(\frac{x^2}{y^3}\right)
\[ \left[
\begin{array}{ c c }
1 & 2 \\
3 & 4
\end{array} \right]
\]
Amsmath introduces several commands that will help typing matrices.
In plain TeX, the only way is to use the array
environment, but you have to define how many columns you want and how
you want them aligned, just like a table. If you use the environments
amsmath introduces, you don't have to worry about it anymore
\usepackage{amsmath}
\begin{pmatrix}
\alpha& \beta^{*}\\
\gamma^{*}& \delta
\end{pmatrix}
The environments pmatrix, bmatrix, Bmatrix, vmatrix and Vmatrix
have (respectively) ( ), [ ], { }, | |, and || || delimiters built in. There is also a matrix environment sans delimiters, and an array environment that can be used to obtain left alignment or other variations in the column specs
Question: Why did \matrix, \pmatrix, and \cases stop working when
I added the amsmath package?
Answer: The old form of those commands should be considered obsolete.
When LaTeX was first written back in 1983--1985, those three commands
were carried over directly from plain.tex, for lack of anything better.
When the amsmath package was ported to LaTeX (its origin was in
AMS-TeX), it came with commands of the same name but different syntax.
Both of them are ill-matched with the rest of LaTeX. The only tenable
solution was to depart from both the AMS-TeX syntax and the plain TeX
syntax. Therefore users of the amsmath package should follow standard
LaTeX "environment" syntax and write
\begin{matrix}
... \\
... \\
...
\end{matrix}
(similarly for pmatrix and cases).
1.
\sum_{i=0}^{k}i=k(k+1)/2 \Theta(k^2)
2.
\log_2(3i^4)=\log_23+4\log_2i
3.
\sum_{i=1}^{2n} \logi=
4.
\int_{1}^{n^2 }\frac{1}{x^2 }dx=1-\frac{1}{n^2}
5.
{n \choose k}
6. Use calculus to show that
\sum_{i=1}^{n} \log_2i \in \Theta(n\log n)
7.
\begin{bmatrix} 1 & 2 & 3 \\ 3 & 2 &1 \\1 & 2 &3 \end{bmatrix}
\begin {bmatrix} 1 & 2 & 1 \\ 0 & 0 &0 \\3 & 3 &3 \end{bmatrix}
8.
\lg^*n - 2n - 2^(lg^*) - \sqrt{n}
- \log(n!) - n^2 - 2n+\lg n - 2^\frac{n}{2}
- \log \log n - 2^{\lg n} - n^\frac{1}{\lg n} - 5