1. Intuition, analogies and abstraction
  2. Ring theory I: Motivating ring theory, domains with integer-polynomial analogies
  3. Ring theory II: Visualizing various domains
  4. Group theory I: Presentations and representations
  5. Group theory II: Visualizing non-abelianness, normality and group products
  6. Galois theory I: Walkthrough of Galois theory
  7. Galois theory II: Essence of the Galois correspondence
  8. Galois theory III: Polynomials seen more generally
  9. Homomorphism theorems and a primer on category theory

Algebraic geometry

  1. Introduction to Algebraic Geometry 
  2. Bezout's identity [3]
  3. Zariski topology [1][2]
  4. Nullstellensatz problem
  5. Spectrum; rings seen more generally 

Algebraic number theory

  1. Number theory: Part I
  2. Class field theory, reciprocity laws, factorization of ideals
  3. Group characters and reciprocity laws
  4. Mordell equations
  5. p-adic numbers

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