Lyceum
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Textbooks, turned into lectures

Sit down. Open the board.

A path from Euclid and Euler through Courant and Strang. Each node is a recitation with a chalkboard, a pause, and a short drill — ask when a step does not land.

Start here

The number line

Integers as positions, absolute value as distance

Euler, Elements of Algebra · §§1–12

Begin the lectureBrowse the shelf

Unit 1 · basic

Foundations

Numbers, fractions, and the grammar of algebra — the board work everything else sits on.

  1. 1The number line12 min · Integers, order, and absolute value as distance.
  2. Fractions as operators
  3. Exponents and roots

Unit 2 · basic

Algebra

Equations, functions, and the quadratic — how to turn a sentence into a machine.

  1. Linear equations
  2. Functions
  3. Quadratics

Unit 3 · intermediate

Geometry

Euclid's language of space: postulates, triangles, and the circle.

  1. Euclid's postulates
  2. Triangles
  3. Circles

Unit 4 · intermediate

Calculus

Limits, the derivative as linear approximation, and the integral as accumulated change.

  1. Limits
  2. The derivative
  3. The integral

Unit 5 · advanced

Linear Algebra

Vectors, matrices, and the geometry of linear maps — Strang's view of the subject.

  1. Vectors
  2. Matrices
  3. Eigenvalues

Unit 6 · advanced

Structure

Proof, induction, and the first taste of analysis and groups.

  1. Logic and proof
  2. Induction
  3. Groups