# Algebra

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Category: Mathematics
Slides: 31
Updated: 2026-05-15T22:18:37.126Z
Tags: mathematics, algebra

## Summary

Algebra is the mathematics of structure: of operations, of equations, of the symmetries that connect one quantity to another. It begins with the idea that a number you don't yet know can still be reasoned about — that x is a respectable noun. Key sections include: Algeb ra.; Opening What algebra is.; Chapter I Before the symbol.; Chapter II The word itself.; Chapter III Cardano, 1545.; Chapter IV Symbolic notation.; Chapter V Algebraic geometry, version one.; Chapter VI Vectors and matrices.; Chapter VII Solving for many unknowns.; Chapter VIII The single number..

## Slide Outline

1. Algeb ra.
2. Opening What algebra is.
3. Chapter I Before the symbol.
4. Chapter II The word itself.
5. Chapter III Cardano, 1545.
6. Chapter IV Symbolic notation.
7. Chapter V Algebraic geometry, version one.
8. Chapter VI Vectors and matrices.
9. Chapter VII Solving for many unknowns.
10. Chapter VIII The single number.
11. Chapter IX Vectors that don't turn.
12. Chapter X The abstract framework.
13. Chapter XI The unsolvable quintic.
14. Chapter XII The mathematics of symmetry.
15. Chapter XIII The four laws.
16. Chapter XIV Two essential families.
17. Chapter XV Two operations.
18. Chapter XVI Where division works.
19. Chapter XVII The fundamental theorem.
20. Chapter XVIII Linear algebra everywhere.
21. Chapter XIX The ring R[x].
22. Chapter XX Boolean algebra.
23. Chapter XXI Continuous symmetry.
24. Chapter XXII Category theory.
25. Chapter XXIII Algebra in physics.
26. Chapter XXIV Equations as spaces.
27. Chapter XXV The Langlands program.
28. Chapter XXVI Twenty essentials.
29. Chapter XXVII Watch & read.
30. Chapter XXVIII Where to begin.
31. The end of the deck.

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