abstract algebra

Permutations

Combinations

Pigeon-hole principle

Inclusion-exclusion principle

Derangements

Fundamental theorem of arithmetic

Divisibility in Z

Congruences

Chinese Remainder Theorem

Euler’s Ø- function

Primitive roots

Groups

Subgroups

Normal subgroups

Quotient groups

Homomorphisms

Cyclic groups

Permutation groups

Cayley’s theorem

Class equations

Sylow theorems

Rings

Ideals

Prime and maximal ideals

Quotient rings

Unique factorization domain

Principal ideal domain

Euclidean domain

Polynomial rings and irreducibility criteria

Fields

Finite fields

Field extensions

Galois Theory