Maths and chemistry guide

1How to write a formula

Wrap maths in dollar signs and it is typeset for you, on a card face and in a notebook page alike.

There are three ways in, and you rarely need more. Put single dollars around something to keep it in the sentence, double dollars to give it a line of its own, and chemistry needs no dollars at all.

Inline: “The energy is $E = mc^2$ exactly.” — the formula sits in the sentence.
On its own line: “$$\int_0^1 x\,dx = \frac{1}{2}$$” — centred, with room around it.
Chemistry: “Titrate \ce{H2SO4} slowly.” — \ce{...} needs no dollar signs.

Tip

Wrap only the maths, not the whole sentence. “$The energy is E=mc^2$” comes out as one long italic run; “The energy is $E = mc^2$” reads properly.

2Finding a symbol without leaving your card

You do not have to memorise any of this. Every card face has a Help button beside its formatting buttons.

Press it, type what you are after in plain words, and pick the row you want, it goes straight into the card at your cursor. Searching “sigma”, “add up” or even “how do I insert a sigma symbol” all reach the same place.

In a notebook page the three formula buttons sit in the same toolbar as bold and italic. The syntax is identical, so everything below applies to both.

For example

Looking for ∑ but not sure what it is called? Type “add up”. Looking for ⇌ ? Type “equilibrium”.

3The maths you will use most

Fractions, powers and roots cover most of what a card needs. Everything below is typed inside dollar signs.

Tip

Capitalise a Greek letter's command to get the capital: \delta is δ and \Delta is Δ.

The basics

Fractions, powers and roots — the four or five you will use on almost every card.

Looks like	Type this	What it is
$\frac{a}{b}$	`\frac{a}{b}`	Fraction
$x^{2}$	`x^{2}`	Power (superscript)
$x_{1}$	`x_{1}`	Subscript
$\sqrt{x}$	`\sqrt{x}`	Square root
$\sqrt[3]{x}$	`\sqrt[3]{x}`	Cube or nth root
$3.0 \times 10^{8}$	`3.0 \times 10^{8}`	Scientific notation

Operators and comparisons

Multiplying, comparing and approximating.

Looks like	Type this	What it is
$\times$	`\times`	Multiply (cross)
$\cdot$	`\cdot`	Multiply (dot)
$\div$	`\div`	Divide
$\pm$	`\pm`	Plus or minus
$\neq$	`\neq`	Not equal to
$\approx$	`\approx`	Approximately equal to
$\leq$	`\leq`	Less than or equal to
$\geq$	`\geq`	Greater than or equal to
$\propto$	`\propto`	Proportional to
$\equiv$	`\equiv`	Identically equal to
$90^{\circ}$	`90^{\circ}`	Degrees
$\therefore$	`\therefore`	Therefore

Greek letters

Capitalise the command to get the capital letter: \alpha is α, \Delta is Δ.

Looks like	Type this	What it is
$\alpha$	`\alpha`	Alpha
$\beta$	`\beta`	Beta
$\gamma$	`\gamma`	Gamma
$\delta$	`\delta`	Delta (small)
$\Delta$	`\Delta`	Delta (capital)
$\theta$	`\theta`	Theta
$\lambda$	`\lambda`	Lambda
$\mu$	`\mu`	Mu
$\pi$	`\pi`	Pi
$\rho$	`\rho`	Rho
$\sigma$	`\sigma`	Sigma (small)
$\Sigma$	`\Sigma`	Sigma (capital)
$\phi$	`\phi`	Phi
$\omega$	`\omega`	Omega (small)
$\Omega$	`\Omega`	Omega (capital)

4Calculus, vectors and multi-line formulas

For anything with a limit, an integral or a grid in it. These are worth putting on their own line with double dollars, because they are taller than a line of text.

Sums, integrals and rates of change

The big operators, and the notation for differentiating and integrating.

Looks like	Type this	What it is
$\sum_{i=1}^{n} x_i$	`\sum_{i=1}^{n} x_i`	Summation
$\sum$	`\sum`	Summation sign on its own
$\prod_{i=1}^{n} x_i$	`\prod_{i=1}^{n} x_i`	Product
$\int_{a}^{b} f(x)\,dx$	`\int_{a}^{b} f(x)\,dx`	Integral
$\frac{dy}{dx}$	`\frac{dy}{dx}`	Derivative
$\frac{\partial f}{\partial x}$	`\frac{\partial f}{\partial x}`	Partial derivative
$\lim_{x \to 0}$	`\lim_{x \to 0}`	Limit
$\nabla$	`\nabla`	Nabla (gradient operator)
$\infty$	`\infty`	Infinity

Sets and vectors

Membership, number sets, and the notation for a vector quantity.

Looks like	Type this	What it is
$x \in A$	`x \in A`	Element of
$A \cup B, \; A \cap B$	`A \cup B, \; A \cap B`	Union and intersection
$A \subset B$	`A \subset B`	Subset
$\emptyset$	`\emptyset`	Empty set
$\mathbb{R}$	`\mathbb{R}`	Number sets
$\vec{v}$	`\vec{v}`	Vector
$\hat{n}$	`\hat{n}`	Unit vector (hat)
$\overline{x}$	`\overline{x}`	Bar or mean
$\lvert x \rvert$	`\lvert x \rvert`	Absolute value

Matrices and multi-line formulas

Where a formula needs a grid or a branch. These are worth putting on their own line.

Looks like	Type this	What it is
$\begin{pmatrix} a & b \\ c & d \end{pmatrix}$	`\begin{pmatrix} a & b \\ c & d \end{pmatrix}`	Matrix
$\begin{vmatrix} a & b \\ c & d \end{vmatrix}$	`\begin{vmatrix} a & b \\ c & d \end{vmatrix}`	Determinant
$f(x) = \begin{cases} 1 & x > 0 \\ 0 & x \leq 0 \end{cases}$	`f(x) = \begin{cases} 1 & x > 0 \\ 0 & x \leq 0 \end{cases}`	Piecewise (cases)
$\binom{n}{k}$	`\binom{n}{k}`	Binomial coefficient

Arrows and logic

For reasoning steps, mappings and processes.

Looks like	Type this	What it is
$\to$	`\to`	Arrow (gives, tends to)
$\Rightarrow$	`\Rightarrow`	Implies
$\Leftrightarrow$	`\Leftrightarrow`	If and only if
$\uparrow \downarrow$	`\uparrow \downarrow`	Increases / decreases

5Chemistry

Chemistry has its own shorthand, and it is far kinder than writing it as maths. Inside \ce{...} numbers drop to subscripts on their own, arrows are typed as you would say them, and charges and states come out right.

You do not need dollar signs around \ce{...}, though it works inside them too.

For example

“\ce{CaCO3 ->[\Delta] CaO + CO2 ^}” gives you the reaction, the heat above the arrow, and the gas symbol.

Chemistry

Chemistry uses \ce{...} and needs no dollar signs around it. Numbers drop to subscripts on their own.

Looks like	Type this	What it is
$\ce{H2SO4}$	`\ce{H2SO4}`	Chemical formula
$\ce{2H2 + O2 -> 2H2O}$	`\ce{2H2 + O2 -> 2H2O}`	Reaction
$\ce{N2 + 3H2 <=> 2NH3}$	`\ce{N2 + 3H2 <=> 2NH3}`	Reversible reaction
$\ce{CaCO3 ->[\Delta] CaO + CO2}$	`\ce{CaCO3 ->[\Delta] CaO + CO2}`	Conditions over the arrow
$\ce{NaCl(aq) + AgNO3(aq)}$	`\ce{NaCl(aq) + AgNO3(aq)}`	State symbols
$\ce{SO4^2-}$	`\ce{SO4^2-}`	Ion charge
$\ce{^{14}_{6}C}$	`\ce{^{14}_{6}C}`	Isotope
$\ce{CO2 ^}, \; \ce{AgCl v}$	`\ce{CO2 ^}, \; \ce{AgCl v}`	Gas released or precipitate

Words and units inside a formula

Anything that is a word rather than a variable needs saying so, or it comes out italic.

Looks like	Type this	What it is
$v = 5\;\text{m/s}$	`v = 5\;\text{m/s}`	Words inside maths
$5\,\text{kg}$	`5\,\text{kg}`	Small space
$25^{\circ}\text{C}$	`25^{\circ}\text{C}`	Degrees Celsius
$45\%$	`45\%`	Percent

6When a dollar sign is just money

Prices are safe. A card that says “it cost $5 and $10 in total” stays exactly that, because a formula is only recognised when it looks like one.

The rules are simple: what is inside the dollars cannot start or end with a space, an inline formula cannot run past the end of its line, and a closing dollar cannot be followed by a digit. If you ever need a literal dollar next to a formula, write it as \$.

Tip

If something you wrote is coming out italic and squashed, you have almost certainly opened a formula by accident. Look for an unpaired dollar sign earlier in the same line.

7What your phone shows

Formulas are stored as the characters you typed, not as a separate hidden attachment. That is deliberate, and it is what keeps your work safe to edit anywhere.

Typesetting is on the web for now. Open the same card or page on Android or iOS and you will see the source, “$E = mc^2$”, which you can still read, edit and sync without breaking anything. When you next open it on the web it is typeset again.

Tip

Because the formula is ordinary text, everything else still works on it: search finds it, and the phone apps sync it like anything else you have written.