### Generalities

This page contains a collection of very simple hints on TeX/LaTeX, and intended primarily to help students in my writing-intensive classes.
For a more comprehensive description of the MathJax dialect which is made use of, this link may be helpful.

The delimiters to make use of are  $$...$$ (or, alternatively,  $...$) for displayed formulas. For example, $$\sum_{i=0}^n i^2 = \frac{n^2+n}{2}\tag{displayed}$$ displays as $$\sum_{i=0}^n i^2 = \frac{n^2+n}{2}\tag{displayed}.$$
Inline mathmetics should be always enclosed into  $...$. Note the difference between a (indefinite article) and $a$ (a quantity denoted by the letter).

### How do I type this thing?

If the table below does not suffice, it is highly recommended to use this service.

 Formula How to type it in Remarks $$\frac{a}{b}$$  $$\frac{a}{b}$$ fraction $$a b c$$  $$a b c$$ product of $a$, $b$, and $c$ the blank spaces inside delimiters do not matter $$\mathbb{N}, \ \mathbb{Z}, \ \mathbb{Q}, \ \mathbb{R}, \ \mathbb{C}$$  $$\mathbb{N}, \ \mathbb{Z}, \ \mathbb{Q}, \ \mathbb{R}, \ \mathbb{C}$$ standard notations for positive integers, integers, rational, real, and complex numbers accordingly; backslash followed by a blank space yields a blank in the formula $$\forall, \exists, \lor, \land, \neg, \Leftarrow, \Rightarrow$$  $$\forall, \exists, \lor, \land, \neg, \Leftarrow, \Rightarrow$$ quantifiers and lofical symbols $$a_i, \ \ b^j, \ \ \left( \frac{u}{v} \right)^k$$  $$a_i, \ \ b^j, \ \ \left( \frac{u}{v} \right)^k$$ indexes and powers; in order to produce $$\left( \frac{u}{v} \right)^k \ \text{instead of merely} \ ( \frac{u}{v} )^k,$$ the rescaling  \left( ... \right)  instead simple parenthesis are used $$\sum_{i=0}^n a_i = a_0 + \ldots + a_n; \ \ \ \prod_{j=0}^m b_j = b_1 \cdot \ldots \cdot b_m$$  $$\sum_{i=0}^n a_i = a_0 + \ldots + a_n; \ \ \ \prod_{j=0}^m b_j = b_1 \cdot \ldots \cdot b_m$$ sums and products; note the usage of curly braces for the correct display of indeces $$\pm\sqrt{a^2+b^2}, \ \ \ \sqrt[7]{a^2+b^2}$$  $$\pm\sqrt{a^2+b^2}, \ \ \ \sqrt[7]{a^2+b^2}$$ square root, seventh root, plus-minus $$\alpha,\beta, \gamma, \delta, \Delta, \ldots, \psi, \xi, \epsilon, \varepsilon, \omega, \Omega$$  $$\alpha,\beta, \gamma, \delta, \Delta, \ldots, \psi, \xi, \epsilon, \varepsilon, \omega, \Omega$$ some Greek letters $$\left( \begin{array}{cccc} a_{1,1} & a_{1,2} & \ldots & a_{1,n} \\ & & \ldots & \\ & & \ldots & \\ & & \ldots & \\ a_{m,1} & a_{m,2} & \ldots & a_{m,n} \end{array}\right)$$  $$\left( \begin{array}{cccc} a_{1,1} & a_{1,2} & \ldots & a_{1,n} \\ & & \ldots & \\ & & \ldots & \\ & & \ldots & \\ a_{m,1} & a_{m,2} & \ldots & a_{m,n} \end{array}\right)$$ a matrix