1. see how any formula was written in any question or answer, including this one, right-click on the expression it and choose "Show Math As > TeX Commands". (When you do this, the '$' will not display. Make sure you add these. See the next point.)

2. For inline formulas, enclose the formula in $...$. For displayed formulas, use $$...$$.

   These render differently. For example, type

   $\sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6}$

   to show ∑ n i=0 i 2 =(n 2 +n)(2n+1)6  ∑i=0ni2=(n2+n)(2n+1)6 (which
   is inline mode) or type

   $$\sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6}$$

   to show

   ∑ i=0 n i 2 =(n 2 +n)(2n+1)6  ∑i=0ni2=(n2+n)(2n+1)6

   (which is display mode).

3. For Greek letters, use \alpha, \beta, …, \omega: α,β,…ω α,β,…ω.
   For uppercase, use \Gamma, \Delta, …, \Omega: Γ,Δ,…,Ω Γ,Δ,…,Ω.

4. For superscripts and subscripts, use ^ and _. For example, x_i^2: x 2 i  xi2, \log_2 x: log 2 x log2⁡x.

5. Groups. Superscripts, subscripts, and other operations apply only to the next “group”. A “group” is either a single symbol, or any formula surrounded by curly braces{…}. If you do 10^10, you will get
   a surprise: 10 1 0 1010.
   But 10^{10} gives what you probably wanted: 10 10  1010.
   Use curly braces to delimit a formula to which a superscript or subscript applies: x^5^6 is an error; {x^y}^z is x y  z  xyz,
   and x^{y^z} is x y z   xyz.
   Observe the difference between x_i^2 x 2 i  xi2 and x_{i^2} x i 2   xi2.

6. Parentheses Ordinary symbols ()[] make parentheses and brackets (2+3)[4+4] (2+3)[4+4].
   Use \{ and \} for curly braces {} {}.

   These do not scale with the formula in between, so if you write (\frac{\sqrt x}{y^3}) the parentheses will be too small: (x  √ y 3  ) (xy3).
   Using \left(…\right) will make the sizes adjust automatically to the formula they enclose: \left(\frac{\sqrt x}{y^3}\right) is (x  √ y 3  ) (xy3).

   \left and\right apply to all the following sorts of parentheses: ( and ) (x) (x), [ and ] [x] [x], \{ and \} {x} {x}, | |x| |x|, \langle and \rangle ⟨x⟩ ⟨x⟩, \lceil and\rceil ⌈x⌉ ⌈x⌉,
   and \lfloor and \rfloor ⌊x⌋ ⌊x⌋.
   There are also invisible parentheses, denoted by .: \left.\frac12\right\rbrace is 12 } 12}.

7. Sums and integrals \sum and \int; the subscript is the lower limit and the superscript is the upper limit, so for example \sum_1^n ∑ n 1  ∑1n.
   Don't forget {…} if the limits are more than a single symbol. For example, \sum_{i=0}^\infty i^2 is ∑ ∞ i=0 i 2  ∑i=0∞i2.
   Similarly, \prod ∏ ∏, \int ∫ ∫, \bigcup ⋃ ⋃, \bigcap ⋂ ⋂, \iint ∬ ∬.

8. Fractions There are two ways to make these. \frac ab applies to the next two groups, and produces ab  ab;
   for more complicated numerators and denominators use{…}: \frac{a+1}{b+1} is a+1b+1  a+1b+1.
   If the numerator and denominator are complicated, you may prefer \over, which splits up the group that it is in: {a+1\over b+1}is a+1b+1  a+1b+1.

9. Fonts

   • Use \mathbb or \Bbb for "blackboard bold": CHNQRZ CHNQRZ.
   • Use \mathbf for boldface: ABCDEFGHIJKLMNOPQRSTUVWXYZ ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz abcdefghijklmnopqrstuvwxyz.
   • Use \mathtt for "typewriter" font: ABCDEFGHIJKLMNOPQRSTUVWXYZ ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz abcdefghijklmnopqrstuvwxyz.
   • Use \mathrm for roman font: ABCDEFGHIJKLMNOPQRSTUVWXYZ ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz abcdefghijklmnopqrstuvwxyz.
   • Use \mathsf for sans-serif font: ABCDEFGHIJKLMNOPQRSTUVWXYZ ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz abcdefghijklmnopqrstuvwxyz.
   • Use \mathcal for "calligraphic" letters: ABCDEFGHIJKLMNOPQRSTUVWXYZ ABCDEFGHIJKLMNOPQRSTUVWXYZ
   • Use \mathscr for script letters: ABCDEFGHIJKLMNOPQRSTUVWXYZ ABCDEFGHIJKLMNOPQRSTUVWXYZ
   • Use \mathfrak for "Fraktur" (old German style) letters: ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz.

10. Radical signs Use sqrt, which adjusts to the size of its argument: \sqrt{x^3} x 3  − −  √  x3; \sqrt[3]{\frac xy} xy   √ 3  xy3.
    For complicated expressions, consider using{...}^{1/2} instead.

11. Some special functions such as "lim", "sin", "max", "ln", and so on are normally set in roman font instead of italic font. Use \lim, \sin, etc. to make these: \sin x sinx sin⁡x,
    not sin x sinx sinx.
    Use subscripts to attach a notation to \lim: \lim_{x\to 0}

    lim x→0  limx→0

12. There are a very large number of special symbols and notations, too many to list here; see this shorter listing, or this exhaustive listing. Some of the most common include:

    • \lt \gt \le \ge \neq <>≤≥≠ <>≤≥≠.
      You can use \not to put a slash through almost anything: \not\lt ≮ ≮ but
      it often looks bad.
    • \times \div \pm \mp ×÷±∓ ×÷±∓. \cdot is
      a centered dot: x⋅y x⋅y
    • \cup \cap \setminus \subset \subseteq \subsetneq \supset \in \notin \emptyset \varnothing ∪∩∖⊂⊆⊊⊃∈∉∅∅ ∪∩∖⊂⊆⊊⊃∈∉∅∅
    • {n+1 \choose 2k} or \binom{n+1}{2k} (n+12k) (n+12k)
    • \to \rightarrow \leftarrow \Rightarrow \Leftarrow \mapsto →→←⇒⇐↦ →→←⇒⇐↦
    • \land \lor \lnot \forall \exists \top \bot \vdash \vDash ∧∨¬∀∃⊤⊥⊢⊨ ∧∨¬∀∃⊤⊥⊢⊨
    • \star \ast \oplus \circ \bullet ⋆∗⊕∘∙ ⋆∗⊕∘∙
    • \approx \sim \simeq \cong \equiv \prec ≈∼≃≅≡≺ ≈∼≃≅≡≺.
    • \infty \aleph_0 ∞ℵ 0  ∞ℵ0 \nabla \partial ∇∂ ∇∂ \Im \Re IR ℑℜ
    • For modular equivalence, use \pmod like this: a\equiv b\pmod n a≡b(modn) a≡b(modn).
    • \ldots is the dots in a 1 ,a 2 ,…,a n  a1,a2,…,an \cdots is
      the dots in a 1 +a 2 +⋯+a n  a1+a2+⋯+an
    • Some Greek letters have variant forms: \epsilon \varepsilon ϵε ϵε, \phi \varphi ϕφ ϕφ,
      and others. Script lowercase l is \ell ℓ ℓ.

    Detexify lets you draw a symbol on a web page and then lists the TE X TEX symbols
    that seem to resemble it. These are not guaranteed to work in MathJax but are a good place to start. To check that a command is supported, note that MathJax.org maintains a list of currently supported LA TE X LATEX commands,
    and one can also check Dr. Carol JVF Burns's page of TE X TEX Commands Available in MathJax.

13. Spaces MathJax usually decides for itself how to space formulas, using a complex set of rules. Putting extra literal spaces into formulas will not change the amount of space MathJax puts in: a␣b and a␣␣␣␣b are both ab ab.
    To add more space, use \, for a thin space ab ab; \; for
    a wider space ab ab. \quad and \qquad are
    large spaces: ab ab, ab ab.

    To set plain text, use \text{…}: {x∈s∣x is
    extra large} {x∈s∣x is
    extra large}. You can nest $…$ inside of \text{…}.

14. Accents and diacritical marks Use \hat for a single symbol x ^  x^, \widehat for
    a larger formula xy ˆ  xy^.
    If you make it too wide, it will look silly. Similarly, there are\bar x ¯  x¯ and \overline xyz ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯   xyz¯,
    and \vec x ⃗  x→ and \overrightarrow xy − →   xy→ and \overleftrightarrow xy ← →   xy.
    For dots, as in ddx xx ˙ =x ˙  2 +xx ¨  ddxxx˙=x˙2+xx¨,
    use \dot and \ddot.

15. Special characters used for MathJax interpreting can be escaped using the \ character: \$ $ $, \{ { {, \_ _ _,
    etc. If you want \ itself, you should use \backslash ∖ ∖,
    because \\ is for a new line.

(Tutorial ends here.)