Tutorial 7: Write math without learning a new language

Goal: put math into a document in a few different ways: pick a ready-made formula, type one yourself, and explore one by ear. Then check that it looks right, send it to Word as a real equation (not a picture), and open it again later, still editable. It takes about thirty minutes and there is nothing to install. This is for anyone writing algebra, such as homework, lecture notes or a lab report, who has never used a "math typing" tool and does not want a lesson in codes first.

You will not need to memorize anything before you start. The fastest path needs no typing at all; the next needs only ^ for a power; only the fancier formulas need a couple of extra words.

1. The easiest way in: pick a ready-made formula

QUILL ships ten common algebra and geometry formulas you can insert with no typing at all:

1. Open a document and type a line of context, like "The quadratic formula solves any equation of the form ax squared plus bx plus c equals zero:".
2. Insert > Snippet Gallery...
3. Find Quadratic Formula in the list and insert it.

That is it. A correctly formatted equation is now in your document, and you did not have to type it. The gallery also has the Pythagorean Theorem, Slope-Intercept Form, Point-Slope Form, the Slope, Distance, and Midpoint formulas, Difference of Squares, and the Area and Circumference of a Circle. If the formula you need is one of these ten, you are already done with this tutorial. The rest is for formulas the gallery does not have, or for understanding what is now in your document.

2. Your first equation from scratch

For anything the gallery does not have, typing one yourself is just as easy:

1. Type a line of context, like "The Pythagorean theorem relates the sides of a right triangle:".
2. Press Ctrl+Shift+E (or Insert > Insert Equation...).
3. A box appears asking for the equation, and it even suggests an example right in the prompt (E=mc^2) so you can see the expected shape. Type:

   a^2 + b^2 = c^2

   That is all. ^ just means "to the power of." No codes, nothing to look up.
4. QUILL asks whether this should sit on its own line (Block) or flow inside a sentence (Inline). Since this formula deserves its own line, pick Block.
5. Look at what is now in your document: plain text, wrapped in $$ $$. That is just how QUILL marks "this bit is math" so it can show it properly later. You can select it and press Ctrl+Shift+E again any time you want to change it, the same way you'd reopen any dialog.

Try a second one the same way, inline this time: type "the graph of a straight line follows", press Ctrl+Shift+E, type y = mx + b, and choose Inline so it stays in the sentence. Two equations in, and you still haven't typed anything you wouldn't type on a calculator.

3. When a formula needs a fraction or a square root

Some formulas, like the quadratic formula if you type it yourself, have a fraction and a square root. For just these two, QUILL needs a small hint: put the top of a fraction in \frac{...}{...} and a square root in \sqrt{...}. That is all you need to learn; everything else stays the same as before.

Press Ctrl+Shift+E and type:

x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

\pm just means "plus or minus". Choose Block. If you only remember one thing from this section, remember this: \frac{top}{bottom} and \sqrt{...}. Nothing else about plain equations changes.

4. A shortcut, once you're comfortable (totally optional)

Once the basics feel normal, here's a convenience worth knowing about: if you type a few of those backslash words while writing an ordinary sentence, not inside the equation box, QUILL turns them into the real symbol right away. Type \pi (with a trailing space) and it becomes π. Type \ne and it becomes ≠. You do not have to use this. Everything in sections 1 to 3 works without it. It is just a quick way to put one symbol into a sentence without opening the equation box. It lives under Preferences > Editing > Insert Automation if you ever want to turn it off. A fuller list is in the reference section at the end.

5. See it look right

Choose View > Browser Preview.... Your equations show up as real math: the fraction stacked, the square root drawn, and ^2 raised. You do not have to picture what $$...$$ means; QUILL shows it properly for you every time.

6. Explore a formula's structure by ear

Reading a long formula start to finish, in one breath, is hard whether you are listening or looking. Select an equation (or type one fresh) and run Insert > Explore Equation Structure..., or press Ctrl+Shift+Grave, F, to step through it one piece at a time.

How it works from the keyboard:

1. Select x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} (or any equation) and run the command, or press Ctrl+Shift+Grave, F. If nothing is selected, a text box asks you to type or paste one. Enter accepts it, and Escape cancels.
2. QUILL speaks where you are ("Whole equation" the first time, or the current piece's name after that), then opens a list of the parts of the current piece. For the whole equation above, that is x, equals, and the fraction. It is an ordinary Windows list: Up/Down arrows move through the items, typing a letter jumps to the next item starting with it, and the list always ends with Read this part aloud, then Back up one level (only once you've descended at least one level), then Done exploring.
3. Enter, or the OK button, activates whichever item is highlighted:
   • Choosing a numbered piece (like the fraction) goes into it. QUILL says its name ("Fraction") and the list now shows its pieces (Numerator, Denominator).
   • Read this part aloud reads just the piece you are on, for example "the square root of b squared minus 4 a c", and then brings the list back so you can keep exploring.
   • Back up one level moves to the parent piece and reopens the list there.
   • Done exploring closes the explorer and returns you to the editor.
4. Escape, or the Cancel button, at any point, closes the explorer straight away, just like Done exploring. It does not go back one level; use Back up one level for that.

Stepping through the parts works as soon as you install QUILL, with nothing to download. Read this part aloud can sound more natural if you install the free MathCAT engine (Help > Download Optional Components... > MathCAT math speech engine, about 3 MB). It is the same math speech NVDA uses. Without it, QUILL uses its own simpler reading, which still works. Neither one gives you Nemeth or UEB math braille. If you use JAWS, its own Math Viewer works on the equation once it is in Word (see the next step) and gives you that fuller experience. QUILL's explorer is a quick way to find your way around a formula while you are still writing it.

7. Hand it to Word

File > Export > Word Document..., then open the result in Word (or LibreOffice). Move to the equation. It is a real Word equation you can edit, the same kind Word makes itself, not a picture. That matters for anyone using a screen reader: a real equation is read as math, and a picture of one is not read at all. If you use JAWS, this is also the point where its own Math Viewer becomes available on the equation.

8. Get it back

Reopen that Word file later (File > Open...) and the equation comes back exactly as you typed it, as plain text you can select and change with Ctrl+Shift+E. You can pass a file back and forth with a teacher or study partner who uses Word and never lose the formula.

If something doesn't look right

• The preview still shows literal $$...$$ or \(...\) text. Check that both delimiters actually surround the formula. A stray character inside the equation (a { with no matching } is the most common one) can stop it from being recognized as math. Reopen it with Ctrl+Shift+E to see and fix the plain LaTeX.
• A fraction or square root shows the raw \frac{}{} / \sqrt{} text instead of showing properly. This almost always means a missing closing brace }. Check that every { has a matching }.
• The equation looks fine in QUILL but not after exporting to Word. Open the exported file in QUILL (File > Open). If the formula comes back correctly, it is fine, and the problem is with the program you opened it in elsewhere. Try a different one.

Quick reference

The ten gallery formulas (Insert > Snippet Gallery...): Quadratic Formula, Pythagorean Theorem, Slope-Intercept Form, Point-Slope Form, Slope Formula, Distance Formula, Midpoint Formula, Difference of Squares, Area of a Circle, Circumference of a Circle.

The typed shortcuts, in full. Type the code plus a trailing space or punctuation, anywhere in ordinary prose (not inside the equation box), and it becomes the symbol straight away. These come from the Word Math AutoCorrect list published by DAISY (daisy.org/MSMathCodes), so if you have typed math in Word, you already know them. You can turn any of them off, or all of them, in Preferences > Editing > Insert Automation.

Operators

Type this	Get this	Type this	Get this
\cdot	⋅	\times	×
\div	÷	\pm	±
\mp	∓	\sqrt	√
\cbrt	∛	\qdrt	∜
\infty	∞	\circ	∘

Relations

Type this	Get this	Type this	Get this
\ne / \neq	≠	\le / \leq	≤
\ge / \geq	≥	\approx	≈
\propto	∝	\cong	≅
\sim	∼	\ll / \gg	≪ / ≫

Sets and logic

Type this	Get this	Type this	Get this
\in	∈	\notin	∉
\subset	⊂	\subseteq	⊆
\cup / \cap	∪ / ∩	\rightarrow / \to	→
\leftrightarrow	↔︎	\wedge / \vee	∧ / ∨
\neg	¬	\forall / \exists	∀ / ∃
\emptyset	∅

Number sets

Type this	Get this	Type this	Get this
\doubleN	ℕ	\doubleZ	ℤ
\doubleQ	ℚ	\doubleR	ℝ
\doubleC	ℂ

Greek letters

Type this	Get this	Type this	Get this
\alpha / \beta	α / β	\gamma / \delta	γ / δ
\Delta	Δ	\theta / \lambda	θ / λ
\mu / \pi	μ / π	\rho / \Sigma	ρ / Σ
\tau / \phi	τ / ϕ	\chi / \omega	χ / ω

Capital letters matter: \delta gives lowercase δ and \Delta gives uppercase Δ, the same way they're different symbols in math itself.

Calculus

Type this	Get this	Type this	Get this
\int	∫	\iint / \iiint	∬ / ∭
\partial	∂	\sum	∑
\prod	∏	\nabla	∇
\prime	′	\pprime	″

Geometry and vectors

Type this	Get this	Type this	Get this
\vec	→	\angle	∠
\perp	⊥	\parallel	∥
\degree	°	\degc / \degf	°C / °F

Miscellaneous

Type this	Get this	Type this	Get this
\therefore	∴	\because	∵
\cdots	⋯	\vdots / \ddots	⋮ / ⋱
\dots / \ldots	…

A routine to try

Check the Snippet Gallery first. It has more than you might expect. For anything else, start with equations that only need ^, /, +, and -; reach for \frac{}{} and \sqrt{} only when a formula needs them. Use Explore Equation Structure when a formula is hard to hold in your head all at once. Check Browser Preview before you submit anything. Export to Word only when it actually needs to leave QUILL.

Want an equation explained instead of just typed? Select it and ask the AI menu's Math Tutor. It explains what each part means and tells you the formula's name if it is a well-known one. It does not solve anything or change your document.

Next: GitHub inside QUILL.