# MathJax ## Delimiters Delimiter | Delimiters | Example | Result | Support :--- | :---: | :--- | :---: | :---: No delimiters | `str` | `\sqrt{3x-1}+(1+x)^2` | \sqrt{3x-1}+(1+x)^2 | no Bracket without backslash | `[str]` | `[\sqrt{3x-1}+(1+x)^2]` | [\sqrt{3x-1}+(1+x)^2] | no Single backslash with bracket | `\[str\]` | `\[\sqrt{3x-1}+(1+x)^2\]` | \[\sqrt{3x-1}+(1+x)^2\] | **yes** Double backslash with bracket | `\\[str\\]` | `\\[\sqrt{3x-1}+(1+x)^2\\]` | \\[\sqrt{3x-1}+(1+x)^2\\] | no Parentheses without backslash | `(str)` | `(\sqrt{3x-1}+(1+x)^2)` | (\sqrt{3x-1}+(1+x)^2) | no Single backslash with parentheses | `\(str\)` | `\(\sqrt{3x-1}+(1+x)^2\)` | \(\sqrt{3x-1}+(1+x)^2\) | **yes** Double backslash with parentheses | `\\(str\\)` | `\\(\sqrt{3x-1}+(1+x)^2\\)` | \\(\sqrt{3x-1}+(1+x)^2\\) | no Single dollar sign | `$str$` | `$\sqrt{3x-1}+(1+x)^2$` | $\sqrt{3x-1}+(1+x)^2$ | **yes** Double dollar sign | `$$str$$` | `$$\sqrt{3x-1}+(1+x)^2$$` | $$\sqrt{3x-1}+(1+x)^2$$ | **yes** ## Empty - `\(\)` \(\) - `$$` $$ - `\[\]` \[\] - `$$$$` $$$$ ## Single Character - `\(a\)` \(a\) - `$a$` $a$ - `\[a\]` \[a\] - `$$a$$` $$a$$ ## Multiple on single line - `\(a\)` \(a\) `\(b\)` \(b\) - `$a$` $a$ `$b$` $b$ - `\[a\]` \[a\] `\[b\]` \[b\] - `$$a$$` $$a$$ `$$b$$` $$b$$ ## Underscore `_` ## `\(` single line `\)` `\(x_i = x_\gamma\)` \(x_i = x_\gamma\) ## `\(` multiline `\)` ``` \( x_i = x_\gamma \) ``` \( x_i = x_\gamma \) --- ## `\[` single line `\]` `\[x_i = x_\gamma\]` \[x_i = x_\gamma\] ## `\[` multiline `\]` ``` \[ x_i = x_\gamma \] ``` \[ x_i = x_\gamma \] --- ## `$` single line `$` `$x_i = x_\gamma$` $x_i = x_\gamma$ ## `$` multiline `$` Not Supported! ``` $ x_i = x_\gamma $ ``` $ x_i = x_\gamma $ --- ## `$$` single line `$$` `$$x_i = x_\gamma$$` $$x_i = x_\gamma$$ ## `$$` multiline `$$` ``` $$ x_i = x_\gamma $$ ``` $$ x_i = x_\gamma $$ --- ## `\begin{}` multiline `\end{}` ``` \begin{align} x_i = x_\gamma \end{align} ``` \begin{align} x_i = x_\gamma \end{align} --- ## Escapes ### Dollar Sign `\$6.20 and \$0.5` \$6.20 and \$0.5 `$4.40` $4.40 --- # Examples # Using TeX notation When $a \ne 0$, there are two solutions to \(ax^2 + bx + c = 0\) and they are $$x = {-b \pm \sqrt{b^2-4ac} \over 2a}.$$ --- # Several examples of TeX equations ## The Lorenz Equations \begin{align} \dot{x} & = \sigma(y-x) \\ \dot{y} & = \rho x - y - xz \\ \dot{z} & = -\beta z + xy \end{align} ## The Cauchy-Schwarz Inequality \[ \left( \sum_{k=1}^n a_k b_k \right)^{\!\!2} \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right) \] ## A Cross Product Formula \[ \mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ \frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\ \frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0 \\ \end{vmatrix} \] ## The probability of getting \(k\) heads when flipping \(n\) coins is: \[P(E) = {n \choose k} p^k (1-p)^{ n-k} \] ## An Identity of Ramanujan \[ \frac{1}{(\sqrt{\phi \sqrt{5}}-\phi) e^{\frac25 \pi}} = 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}} {1+\frac{e^{-8\pi}} {1+\ldots} } } } \] ## A Rogers-Ramanujan Identity \[ 1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots = \prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}, \quad\quad \text{for $|q|<1$}. \] ## Maxwell's Equations \begin{align} \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{align} ## In-line Mathematics Finally, while display equations look good for a page of samples, the ability to mix math and text in a paragraph is also important. This expression \(\sqrt{3x-1}+(1+x)^2\) is an example of an inline equation. As you see, MathJax equations can be used this way as well, without unduly disturbing the spacing between lines. --- # Misc - $E = mc^2$ - \( A_i = B_i + C_i \sum_{k=0}^{i} D_k E^k \) - \begin{eqnarray} A_i &=& B_i + C_i \sum_{k=0}^{i} D_k E^k \\ F_i &=& \int_{-\infty}^{x_i} f(x) dx \end{eqnarray} - $\frac{w_x}{\sum_z x_z}$ - $\frac{w}{\sum_{z} x_z}$ - $x_\gamma = x_i$ - $x_i = x_\gamma$ Cost function of logistic regression (revision): $$J(\theta) = - \frac{1}{m} \sum_{i=1}^m [ y^{(i)}\ \log (h_\theta (x^{(i)})) + (1 - y^{(i)})\ \log (1 - h_\theta(x^{(i)}))] + \frac{\lambda}{2m}\sum_{j=1}^n \theta_j^2$$ For Neural Networks, it is: $$ J(\Theta) = - \frac{1}{m} \sum_{i=1}^m \sum_{k=1}^K \left[y^{(i)}_k \log ((h_\Theta (x^{(i)}))_k) + (1 - y^{(i)}_k)\log (1 - (h_\Theta(x^{(i)}))_k)\right] + \frac{\lambda}{2m}\sum_{l=1}^{L-1} \sum_{p=1}^{s_l} \sum_{n=1}^{s_{l+1}} ( \Theta_{n,p}^{(l)})^2 $$