Abstract Algebra
Modern Algebra II (MATH735, SFSU)
Abstract Algebra (MATH417, UIUC)
- Lecture 01: Groups and Symmetries
- Lecture 02: Rotations in Space
- Lecture 03/04: Permutation Groups and Cycle Decomposition
- Lecture 04: Integers, Primes
- Lecture 05: Greatest Common Divisor
- Book Notes: [1.6] Alternative Greatest Common Divisor Proof
- Book Notes: [1.6] Prime Factorization is Unique
- Lecture 06: Least Common Multiple
- Lecture 06/07: Modular Arithmetic
- Lecture 08: Groups and Isomorphism
- Lecture 09/10: Subgroups
- Lecture 11: Dihedral Groups
- Lecture 12: Homomorphism
- Lecture 13: Cosets
- Lecture 14: Lagrange's Theorem, Order Theorem & Equivalence Relations
- Lecture 15: Quotient Groups
- Lecture 16: Theorems: Homomorphism and Isomorphism
- Lecture 17: Correspondence Theorem
- Lecture 18: Groups and the Chinese Remainder Theorem
- Lecture 19: Direct Product Group
- Lecture 20: Semi-direct Products
- Lecture 21/22: Finite Abelian Groups
- Lecture 23/24: Invariant Factor Decompositions
- Lecture 25: Symmetry Groups of the Regular Polyhedra
- Lecture 26/27: Group Actions and Orbits
- Lecture 28: Group Actions
- Lecture 29: Burnside Formula
- Lecture 30: Finite Subgroups of \(SO(3)\)
- Lecture 31: Fixed Point Theorem and Cauchy Theorem
- Lecture 32: Rings
- Lecture 33: Polynomial Rings
- Lecture 34: Homomorphisms of Rings and the Substitution Principle
- Lecture 35: Principle Ideal
- Lecture 36: Homomorphism Theorem and Isomorphism Theorem
- Lecture 37/38: \(R\)-Domains
- Lecture 39: Unique Factorization Domain
- Lecture 40: Fermat's Theorem on Sum of Squares
- Study Notes: Extra Proofs ...