Whenever you typeset mathematical notation, it needs to have “Math” style. For example: If \(a\) is an integer, then \(2a+1\) is odd.
Superscripts and subscripts are created using the characters ^
and _
, respectively: \(x^2+y^2=1\) and \(a_n=0\). It is fine to have both on a single letter: \(x_0^2\).
If the superscript [or subscript] is more than a single character, enclose the superscript in curly braces: \(e^{-x}\).
Greek letters are typed using commands such as \gamma
(\(\gamma)\) and \Gamma
(\(\Gamma\)).
Named mathematics operators are usually typeset in roman. Most of the standards are already available. Some examples: \(\det A\), \(\cos\pi\), and \(\log(1-x)\).
When an equation becomes too large to run in-line, you display it in a “Math” paragraph by itself.
The \begin{aligned}...\end{aligned}
environment is superb for lining up equations.
To insert ordinary text inside of mathematics mode, use \text
:
This is the \(3^{\text{rd}}\) time I’ve asked for my money back.
The \begin{cases}...\end{cases}
environment is perfect for defining functions piecewise:
Equality-like: \(x=2\), \(x \not= 3\), \(x \cong y\), \(x \propto y\), \(y\sim z\), \(N \approx M\), \(y \asymp z\), \(P \equiv Q\).
Order: \(x < y\), \(y \le z\), \(z \ge 0\), \(x \preceq y\), \(y\succ z\), \(A \subseteq B\), \(B \supset Z\).
Arrows: \(x \to y\), \(y\gets x\), \(A \Rightarrow B\), \(A \iff B\), \(x \mapsto f(x)\), \(A \Longleftarrow B\).
Set stuff: \(x \in A\), \(b \notin C\), \(A \ni x\). Use \notin
rather than \not\in
. \(A \cup B\), \(X \cap Y\), \(A \setminus B = \emptyset\).
Arithmetic: \(3+4\), \(5-6\), \(7\cdot 8 = 7\times8\), \(3\div6=\frac{1}{2}\), \(f\circ g\), \(A \oplus B\), \(v \otimes w\).
Mod: As a binary operation, use \bmod
: \(x \bmod N\). As a relation use \mod
, \pmod
, or \pod
:
Calculus: \(\partial F/\partial x\), \(\nabla g\).
Do not type three periods; instead use \cdots
between operations and \ldots
in lists: \(x_1 + x_2 + \cdots + x_n\) and \((x_1,x_2,\ldots,x_n)\).
Fractions: \(\frac{1}{2}\), \(\frac{x-1}{x-2}\).
Binomial coefficients: \(\binom{n}{2}\).
Sums and products. Do not use \Sigma
and \Pi
.
Integrals:
The extra bit of space before the \(dx\) term is created with the \,
command.
Limits:
Also \(\limsup_{n\to\infty} a_n\).
Radicals: \(\sqrt{3}\), \(\sqrt[3]{12}\), \(\sqrt{1+\sqrt{2}}\).
Matrices:
A big matrix:
Parentheses and square brackets are easy: \((x-y)(x+y)\), \([3-x]\).
For curly braces use \{
and \}
: \(\{x : 3x-1 \in A\}\).
Absolute value: \(|x-y|\), \(|\vec{x} - \vec{y}|\).
Floor and ceiling: \(\lfloor \pi \rfloor = \lceil e \rceil\).
To make delimiters grow so they are properly sized to contain their arguments, use \left
and \right
:
Occasionally, it is useful to coerce a larger sized delimiters than \left
/\right
produce. Look at the two sides of this equation:
I think the right is better. Use \bigl
, \Bigl
, \biggl
, and the matching \bigr
, etc.
Underbraces:
Primes: \(a'\), \(b''\).
Hats: \(\bar a\), \(\hat a\), \(\vec a\), \(\widehat{a_j}\).
Vectors are often set in bold: \(\mathbf{x}\).
Calligraphic letters (for sets of sets): \(\mathcal{A}\).
Blackboard bold for number systems: \(\mathbb{C}\).
The text above is based on a paper by Edward R. Scheinerman^{1}.
A few more examples from mathTeX tutorial^{2}.
Solution for quadratic:
Definition of derivative:
Continued fraction:
Demonstrating \left\{…\right.
and accents.
Overbrace and underbrace:
Illustrating array:
See Wikibook on LaTeX for more examples.