Attribute | Rank |
---|---|

Difficulty | 5 |

Proof Quality | 1 |

Readability | 1 |

Self-Study | 1 |

Good for Teaching? | 2 |

Quality of Exercises | 3 |

- Basics: sets, equivalence classes, functions, relations
- Group Theory
- semigroups, monoids, groups
- homomorphisms and subgroups
- cyclic groups
- cosets
- normality and quotient groups
- symmetric and dihedral groups
- products, coproducts, and free objects
- direct products/sums
- free groups, free products, generators, and relations

- Group Structures
- Free Abelian groups
- Finitely generated abelian groups
- action of a group
- Sylow Theorems

- Rings
- Ideals
- Factorization
- Rings of Quotients
- Formal Power Series

- Modules
- free modules, vector spaces
- Hom and Duality
- Tensor Products

- Fields and Galois Theory
- Structure of Fields
- Linear Algebra
- Matrices/maps
- Rank/Equivalence
- Determinants

- Commutative Rings/Modules
- Primary Decompositions
- Dedekind Domains

- Ring Structure
- Categories
- Functors and Natural Transformations
- Adjoint Functors
- Morphisms