Example Lectures#

Complete example lectures demonstrating Scholium’s features.

Computer Science: Binary Search Trees#

---
title: "Binary Search Trees"
author: "CS 201 - Data Structures"
date: "Week 5"
title_notes: |
  [DUR 3s]
  Welcome to week five. Today: binary search trees.
---

# What is a BST?

A binary tree with ordering property:
- Left subtree < parent
- Right subtree > parent
- Both subtrees are BSTs

::: notes
:: Reference: CLRS Chapter 12

[PRE 1s]

A binary search tree maintains a specific ordering.
Every node's left children are smaller.
Every node's right children are larger.
This property holds recursively for all subtrees.
:::

# Operations

>- Search: O(log n) average
>- Insert: O(log n) average
>- Delete: O(log n) average

::: notes
BSTs support efficient operations.

Search is logarithmic because we eliminate half at each step.

Insertion is also logarithmic as we navigate to correct position.

Deletion is most complex but still logarithmic on average.
:::

Mathematics: Calculus#

Demonstrates LaTeX math and all four timing directives — [PRE], [POST], [MIN], and inline [PAUSE].

---
title: "The Fundamental Theorem"
author: "Calculus I"
title_notes: |
  Today's topic is the Fundamental Theorem of Calculus.
---

# The Theorem

If $f$ is continuous on $[a,b]$, then:

$$\int_a^b f'(x)\,dx = f(b) - f(a)$$

::: notes
[PRE 3s] [MIN 12s] [POST 2s]

The Fundamental Theorem connects differentiation and integration.
[PAUSE 1.5s]
Integration and differentiation are inverse operations — this changed mathematics forever.
[PAUSE 2s]
Take time to absorb both parts of the equation before moving on.
:::

See Also#