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pt. 1. Numbers and equations. What algebra is
Equations and their solutions
Where algebra comes from
Why algebra is important
Numerical solution of equations
pt. 2. The formulaic approach to equations. Combinatoric solutions I: quadratic equations
Combinatoric solutions II: cubic equations
pt. 3. Resolvents. From combinatorics to resolvents
The search for resolvents
pt. 4. Abstract algebra. Existence and constructibility of roots
The breakthrough: Galois Theory
Modern Algebra / Roger Cooke.

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