Examples

A small library of workflow patterns — short snippets that show the shape of the things you do in this course, so you can recognize the syntax and the habits behind it. Use them to get unstuck, not to fill in.

ImportantThese are patterns, not assignment models

• Every snippet here is a small workflow pattern — not a finished assignment, portfolio, or reflection you can hand in.
• The exact requirements for any assignment live in the course LMS — this page never restates them.
• Adapt these patterns thoughtfully to your own work. Copying a snippet mechanically will not match what an assignment actually asks for, and the point of the course is work you can explain and re-run.

The code blocks below are shown as source so you can read the syntax. In your own document the {r} chunks run when you render; here they are displayed literally.

1. A tiny Quarto math note

The smallest useful Quarto document: a title, a sentence of prose, some inline math, and one display equation.

---
title: "A short note"
format: pdf
---

The area of a circle of radius $r$ is $A = \pi r^2$. The same idea, written
as a displayed equation, reads:

$$
\int_0^1 x^2 \, dx = \frac{1}{3}.
$$

A displayed equation should be introduced by the sentence before it and
explained by the sentence after it.

Render it, then read the PDF — does the math look the way you meant?

2. Aligned equations with prose

When one line of algebra leads to the next, an aligned block keeps the = signs lined up. Notice the sentence before the display sets it up, and the sentence after says what it means.

Expanding the square term by term gives:

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

The two lines are equal because addition is commutative; the second line
just reorders the terms.

An equation with no words around it makes the reader guess. Equations need explanation.

3. Figure, table, and citation pattern

The supporting apparatus of a technical document: a captioned figure, a small captioned table, and a citation. The citation key (@source2020) refers to an entry in a .bib file you keep beside the document.

As shown in @fig-shape, the outline is simple.

![A simple shape.](shape.png){#fig-shape width=60%}

A small summary table:

| Quantity | Value |
|----------|------:|
| Width    |   4.0 |
| Height   |   2.5 |

: A few measurements. {#tbl-measures}

This approach follows a standard construction [@source2020].

Use generic stand-in keys like @source2020 while you learn the pattern; the real reference goes in your .bib. Do not reconstruct a real paper here — that belongs in your own project, cited properly.

4. A tiny R-in-Quarto report

One chunk, one summary, one sentence of interpretation. This uses the built-in cars dataset (stopping distances of 1920s cars) so it runs anywhere with no setup.

```{r}
summary(cars$speed)
```

The median speed is 15 mph, and most speeds fall between about 12 and 19
mph in this small built-in dataset.

The shape is always the same: code → output → a sentence that says what the output means. The prose is the part that shows you understood it.

5. A tiny ggplot2 evidence example

ggplot2 builds a plot from data, an aesthetic mapping (aes(...)), a geometry (geom_*), and labels. This uses the built-in pressure dataset (vapor pressure of mercury vs. temperature).

```{r}
library(ggplot2)

ggplot(pressure, aes(x = temperature, y = pressure)) +
  geom_point() +
  labs(
    title = "Vapor pressure rises with temperature",
    x = "Temperature (°C)",
    y = "Pressure (mm Hg)"
  )
```

A short reading: the plot shows pressure increasing sharply as temperature rises. What it does not prove is why — a plot shows a pattern; the explanation is still your job.

6. A tiny simulation with set.seed()

Random functions give different output each run — unless you fix the starting point with set.seed(). That is what makes a simulation reproducible.

```{r}
set.seed(123)
sample(1:6, size = 5, replace = TRUE)
```

Anyone who runs this with the same seed gets the same five “rolls.” The seed matters because it lets a reader reproduce your exact result — without it, your numbers can never be checked.

7. A tiny AI verification note

When AI helps with your work, the course asks for a short AI Use Note with three labeled lines — Tool, Purpose, Verification. The load-bearing line is Verification: it should say what you checked, against what, and what you changed.

**AI Use Note**

- **Tool:** an AI assistant (name it, with an approximate date or version).
- **Purpose:** asked it to explain why a Quarto document would not render.
- **Verification:** it suggested an option name; I checked that name against
  the Quarto documentation and re-rendered the document. The suggested
  spelling was wrong, so I corrected it and confirmed the PDF built.

The point of the note is not that you used AI — it is that you verified the output against something trustworthy (a re-render, the docs, your own reasoning) and took responsibility for the result. AI output is a draft to check, never an answer to trust.

---

These examples are patterns to learn from, not templates to submit. The exact requirements for your assignments are in the course LMS.