Course Nº IV · Mathematics

The Geometry of Persuasion

Twelve lessons in how vectors, transformations, and bases let us argue about space.

Intermediate4h 48m1,842 readers4.8 of five

Linear algebra is the literature of space — its grammar, its idioms, its quiet jokes. Every transformation tells a small story about what was lost and what was kept. Across twelve lessons we will trace a single line of argument: that the geometry of mathematics is also a kind of rhetoric, and that to compose a proof is to take a position.

Each module begins with a notebook entry — a single object, photograph, or paragraph — and ends with a problem you can carry into the next. Bring a pen. The work happens on paper, and only later on the screen.

Table of contents

Twelve lessons, in order.

  1. 01

    What a vector wants

    A demonstration in three parts.

  2. 02

    Adding a direction

    Plate II — the parallelogram, finally.

  3. 03

    Scaling and the rhetoric of size

    On stretching things on purpose.

  4. 04

    Linear independence, in plain English

    Three vectors, two arguments.

  5. 05

    Maps that preserve a line

    What the matrix decides to keep.

  6. 06

    Bases as small arguments

    Four bases, one room.

  7. 07

    The geometry of persuasion

    A demonstration in three parts.

  8. 08

    Composition, the long sentence

    Two maps, one paragraph.

  9. 09

    The fixed point and the room

    Plate VIII — what stays.

  10. 10

    Eigenvalues, in three readings

    Three readings, three rooms.

  11. 11

    Diagonalising a difficult mood

    An exercise in patience.

  12. 12

    A short conclusion, with notes

    On leaving the room.

Outcomes

  • 01Read a transformation as a deliberate argument about space
  • 02Compose proofs that sound like prose, not like assembly instructions
  • 03Recognise when a basis is doing real intellectual work

Your progress

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