## Friday, December 9, 2011

This is a test of using MathJax in Blogger   Note that enclosing math in single $'s does not work in the default setting for MathJax. However, you may use "$$\backslash($$" and "$$\backslash)$$" for inline math and double dollar signs or "$$\backslash[$$" and "$$\backslash]$$" for displayed math. Examples:$(y+\sqrt z)^{-1}$and $$\sin^2 x^2$$. And, a displayed equation is: $$\frac 2 3$$ Another displayed equation is here: $\forall x \exists y (x\le y \land y\le x \leftrightarrow x=y) .$ To setup the MathJax capability, I added the following line to the HTML code, after the <head> command (as a single line, no line break): <script src='http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML' type='text/javascript'/> You can find more information from the MathJax website about this at http://www.mathjax.org/docs/1.1/start.html. For slightly different ways to set up MathJax with Blogger, see http://holdenweb.blogspot.com/2011/11/blogging-mathematics.html, or http://irrep.blogspot.com/2011/07/mathjax-in-blogger-ii.html. #### 45 comments: 1. However, so far, I do not have MathJax working in the comments. For example: $$e^{i\pi} = -1$$. Suggestions on how to fix this are welcome. 2. Correction: The mathematics will appear correctly once the comment is posted, but it does not appear correctly in the preview window when you are preparing your comment. 3. Test: $$\sin x$$ 4. \begin{matrix} a & b\cr c & d \end{matrix} 5. \begin{matrix} a & b\cr c & d \end{matrix} 6. $P(E) = {n \choose k} p^k (1-p)^{n-k}$ 7. \def\arccosAlt{\cos^{-1}} so that$\arccosAlt(x)8. $$\cosh^2 x - \sinh^2 x = 1$$ Testing only 9. $$\sin^2 x + \cos^2 x = 1$$ 10. \sin^2 x + \cos^2 x = 1 11. \cosh^2 x - \sinh^2 x = 1 12. $$\cosh^2 x - \sinh^2 x = 1$$ 13. $$\sin x$$ $$\sin x) 14. \(\dim T^2V^*=n^2$$ 15. This comment has been removed by the author. 16. This comment has been removed by the author. 17. This comment has been removed by the author. 18. This comment has been removed by the author. 19. This comment has been removed by the author. 20. This comment has been removed by the author. 21. This comment has been removed by the author. 22. This comment has been removed by the author. 23. 1.why $$\tilde f (z)={\bar \psi}^{-1}(f(\phi(z)))$$ but not $$\tilde f (z)={\psi}^{-1}(f(\phi(z)))$$? 2.do we have $$d\tilde \phi_x$$? if yes, what does it mean? 3.can u show us how $$Tf_p$$ is independent of the choice of $$\phi$$ and $$\psi$$ 24. This comment has been removed by the author. 25. Testing.. $\LaTeX$ 26. Test: $$x^2 + y^2 = z^2$$ 27. This comment has been removed by the author. 28. $$10^{100}$$ 29. I'd like to have a $$1/2$$ glass of common sense please. 30. I'd like to have a $1/2$ glass of common sense please. 31. $\left ( \alpha +\beta \right )^2 = \alpha ^2+\beta ^2+2\alpha \beta$ 32. $$\sum_{i=0}^{n} 2^i = 2^{n+1}$$ 1. $$\sum_{i=0}^n 2^i = 2^{n+1}-1$$ 33. This comment has been removed by the author. 34. $\frac{13333}{2}$ 35. \begin{aligned} \nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\ \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\ \nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\ \nabla \cdot \vec{\mathbf{B}} & = 0 \end{aligned} 36. This comment has been removed by the author. 37. $$(y+\sqrt z)^{-1}$$ 38. test\displaystyle \int_0^{\infty} \sqrt{4x} \, e^{-x} \, dx$=$2\displaystyle \int_0^{\infty} \sqrt{x} \, e^{-x} \, dx = 2 \Gamma\left(\frac{3}{2}\right) = 2 \frac{1}{2} \, \Gamma\left(\frac{1}{2}\right) = \sqrt{\pi}\$

1. $$2\displaystyle \int_0^{\infty} \sqrt{x} \, e^{-x} \, dx = 2 \Gamma\left(\frac{3}{2}\right) = 2 \frac{1}{2} \, \Gamma\left(\frac{1}{2}\right) = \sqrt{\pi}$$

39. $\bar{x}=\frac{1}{n}\sum\limits_{i=1}^{n}{x_i}$