Lab 2 — First LaTeX math

Write, render, and visually verify a short mathematical document in Quarto

This lab walks through producing a short mathematical writeup in Quarto, using LaTeX math syntax inside a .qmd document. It is the practical companion to Week 2 — Writing mathematics from source, which is the short conceptual reading for Week 2.

You should already have the stack from Lab 1 installed and working: VS Code with the Quarto and R extensions, R, Quarto, and TinyTeX. If your Week 1 hw01/ document rendered to PDF, you are ready.

What you’ll have at the end

  • A new hw02/ subfolder in your math-software-portfolio/.
  • A .qmd source file in that folder with prose, section headings, inline math, displayed math, and at least one multi-line aligned equation.
  • A rendered PDF of that file, with every piece of mathematics visually checked against what you intended.
  • A short AI Use Note in the standard three-line Tool / Purpose / Verification format (only required if you used AI assistance).

The exact assignment prompt and submission details for Week 2 live in the Assignments/LMS space.

1. Create a Week 2 portfolio subfolder

Inside your math-software-portfolio/ folder (the one you set up in Week 1), create a new subfolder called hw02/. The full path will look like:

  • macOS / Linux: ~/Documents/math-software-portfolio/hw02/
  • Windows: C:\Users\YourName\Documents\math-software-portfolio\hw02\

This is where your Week 2 source file and rendered PDF will live. Keep both files in this folder for the rest of the semester.

2. Open the hw02/ folder in VS Code

From VS Code: File → Open Folder… and pick the hw02/ folder.

Opening the folder (not a single file) is what lets the Quarto extension treat your work as a workspace — the Quarto: Preview command, file explorer, and integrated terminal all behave better with a folder open.

3. Create a .qmd source file

In VS Code’s Explorer sidebar, create a new file inside hw02/. For this walkthrough, call it week02-math.qmd. (The exact file name for the submitted assignment is specified in the Assignments/LMS space.)

Paste this starter content as the top of your new file:

---
title: "Week 2 — A short mathematical writeup"
author: "YOUR NAME"
format:
  pdf: default
---

# Introduction

A short paragraph of prose introducing what you're going to typeset.

# The mathematics

More prose, then equations, then more prose.

# Conclusion

A short closing paragraph.

The YAML at the top is the title block. format: pdf tells Quarto to produce a PDF. (You can add html: default on a new line if you also want an HTML version.)

The three # lines are section headings. They will appear in the rendered PDF as numbered sections (or labeled sections, depending on the format).

4. Write prose around the math

The mathematical writing matters. Prose is what tells the reader what an equation means. The grade is not “did you type LaTeX correctly”; the grade is “can a reader follow a piece of mathematics from your document.”

A typical paragraph might look like:

The quadratic formula gives the roots of a quadratic equation \(ax^2 + bx + c = 0\). We derive it by completing the square, isolating \(x\) on the left side, and solving the resulting square root.

Notice the prose introduces the equation, names what the symbols mean, and gestures at why the result holds. Bare equations floating without context are hard to read.

5. Write inline math

Inline math sits between single dollar signs and reads as part of a sentence. Add a sentence or two with inline math to your writeup. Examples:

The slope of the line $y = mx + b$ is the coefficient $m$.

The Pythagorean theorem states that $a^2 + b^2 = c^2$ for the legs
$a$ and $b$ and hypotenuse $c$ of a right triangle.

Let $f(x) = x^2 + 3x + 2$. The roots of $f$ are the values of $x$
for which $f(x) = 0$.

Use inline math for short expressions that fit in a line of prose: single variables, short formulas, named constants.

6. Write displayed math

Displayed math sits between double dollar signs and gets its own centered line. Add at least one displayed equation:

The quadratic formula is

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

Display equations when:

  • the equation is the thing the reader should look at,
  • the equation contains a fraction, a square root with non-trivial contents, a summation, an integral, or a limit,
  • the equation runs longer than a few characters.

A useful pattern: introduce the equation in prose, display it, then say one sentence about what it means.

7. Write one aligned multi-line equation

When you have a chain of equalities or a multi-step manipulation, the aligned environment inside $$ ... $$ is what you want:

Expanding $(a + b)^2$ gives

$$
\begin{aligned}
(a + b)^2 &= (a + b)(a + b) \\
         &= a^2 + ab + ab + b^2 \\
         &= a^2 + 2ab + b^2.
\end{aligned}
$$

Two pieces of syntax to notice:

  • The & immediately before each = is the alignment marker. Every line lines up at that &.
  • The \\ at the end of each line (except the last) is the line break.

Add one aligned block somewhere in your document. It can be a derivation, a worked example, or any place where you want a column of equations rather than a single equation.

8. Render to PDF

Render the file exactly the way you rendered hw01.qmd in Week 1. Either method works:

  • Preferred — Quarto: Preview. Open week02-math.qmd in the editor, then press Ctrl/Cmd + Shift + P and run Quarto: Preview, or press Ctrl/Cmd + Shift + K. (If the Quarto extension shows a Preview button in the upper-right editor toolbar, that works too.)

  • Always works — terminal. Open VS Code’s integrated terminal (View → Terminal), make sure it is in the hw02/ folder, then run:

    quarto render week02-math.qmd

A PDF file (week02-math.pdf) should appear next to your .qmd.

If VS Code shows no Quarto commands, check the lower-right corner of the window: if it says Plain Text, click it and choose Quarto (or Markdown), and confirm the Quarto extension is installed. If the terminal says “No valid input files passed to render,” the terminal is in the wrong folder or the filename is misspelled — confirm week02-math.qmd is in the current folder.

9. Inspect the rendered PDF

Open the PDF and look carefully. This is the load-bearing step of the Week 2 workflow. The render succeeding is not the same as the math being correct.

Go equation by equation. For each one, ask:

  • Are the variables italic and the operators upright? If \sin looks italic, you probably wrote sin instead.
  • Is the right thing in the numerator? A \frac{x+1}{x-1} should show x + 1 over x - 1, with a horizontal bar between them. If you see x+1/x-1 as raw text, you forgot the braces or the backslash.
  • Is the subscript on the right symbol? x^2 + y_i should put the 2 on the x and the i on the y.
  • Are the parentheses sized correctly? Tall fractions inside short (...) look cramped — use \left( ... \right).
  • In a sum or integral, do the bounds appear above and below the symbol? They do in displayed math. In inline math they collapse to the side, which is usually not what you want.
  • In an aligned block, do all the lines line up at =? They should, if you put & immediately before each =.
  • And most importantly: is this the equation I meant to write? Read it the way a reader would. If something is off — a sign, a variable name, a missing term — go back to the source and fix it.

Common problems

This is the realistic-troubleshooting section. Skim it before you start; come back to it when something breaks.

Missing dollar signs

  • Symptom. Your equation prints as garbled text in the PDF: x^2 + y^2 = r^2 instead of a formatted equation.
  • Fix. Wrap inline math in $...$ and displayed math in $$...$$. The opening and closing dollars must match.

Unmatched braces

  • Symptom. TinyTeX errors out with a message about an unexpected character or end of file, often citing a line number.
  • Fix. Every { in a LaTeX command needs a matching }. The usual culprits are \frac{...}{...}, \sqrt{...}, and multi-character super/subscripts like x^{ij}. The line number in the error message points at (or just after) the broken expression.

Forgetting backslashes

  • Symptom. frac appears as the literal letters “frac” in your PDF, or sum renders as italic letters next to your subscript.
  • Fix. LaTeX commands start with a backslash: \frac, \sum, \int, \sin, \cos, \leq, \alpha. If a command isn’t taking, the most common cause is a missing \.

Copying Unicode symbols instead of LaTeX commands

  • Symptom. Math sometimes renders, sometimes does not, and looks different on different machines. Or you typed ≤ and got something that looks like a box.
  • Fix. Type LaTeX commands, not Unicode glyphs. \leq not ≤, \infty not ∞, \pm not ±, \cdot not ·. Unicode in math mode is fragile.

Using display math where inline math is better (or vice versa)

  • Symptom. Either (a) a tiny symbol like \(x^2\) stops the flow of the sentence and sits on its own line, looking ridiculous, or (b) a complicated formula appears mid-sentence with collapsed bounds on a summation and barely readable nested fractions.
  • Fix. Inline ($...$) for short expressions inside prose; displayed ($$...$$) for anything you want the reader to contemplate.

align block missing &

  • Symptom. Your multi-line equation renders, but the lines do not line up at =. Each line starts at the left margin.

  • Fix. Add & immediately before each = (or whatever you want to align):

    \begin{aligned}
(a + b)^2 &= (a + b)(a + b) \\
         &= a^2 + 2ab + b^2.
\end{aligned}

Render succeeds but the math is wrong

  • Symptom. Everything compiles. The PDF looks clean. The equation in the PDF is not the equation you meant to write.
  • Fix. This is the most important Week 2 mistake to catch. There is no error message; the only way to find it is to read the rendered PDF and compare it to your intended math. Common cases: the wrong sign (+ vs -), the wrong variable, the wrong subscript, an off-by-one in a sum’s bounds. Fix the source and re-render.

AI gives plausible but incorrect LaTeX

  • Symptom. You asked an AI assistant for the LaTeX for some equation, pasted the result into your document, and the render produced something that compiles cleanly but is not the equation you described.
  • Fix. Every piece of AI-suggested LaTeX has to be rendered and visually verified against the mathematics you intended. “It compiled” is not verification. If the PDF does not match, the AI’s syntax is wrong — fix it in the source and re-render. Record what you checked in your AI Use Note’s Verification line.

Render fails with a long, cryptic LaTeX error

  • Symptom. A wall of red text in the terminal, mentioning files in TinyTeX you have never heard of.
  • Fix. Scroll up. Find the first line that mentions a line number in your .qmd (usually l.123 or lines 14 ff). Open your .qmd, go to that line, and look for an unmatched brace, a missing backslash, a stray & outside an align, or a missing \end{...} for an environment you opened.

What this prepares you to do

When you finish this lab you should be able to:

  • write mathematics directly in a .qmd source file using LaTeX math syntax,
  • choose between inline and displayed math based on context,
  • typeset fractions, roots, sums, integrals, subscripts, superscripts, Greek letters, and aligned multi-line equations,
  • render the document to PDF in VS Code or from the terminal,
  • visually inspect the rendered PDF and recognize the common Week 2 failure modes,
  • recover from typical LaTeX syntax errors by reading the line number in the error message,
  • use AI assistance for syntax lookup or error diagnosis while verifying the rendered output yourself.

The Week 2 assignment in the course LMS uses exactly this workflow. The course LMS holds the exact prompt, the file-naming convention, and the submission area.