Abstract-Algebra

• Introduction
• Isomorphism
• Binary Operations
• Groups
• More on Groups
• Subgroups
• Cyclic Subgroups
• Interlude: Magic & Math
• Symmetry Groups on N-gons
• Cayley's Theorem
• Groups of Permutation
• Coset
• Finitely Generated Abelian Groups
• Lagrange's Theorem
• Homomorphism & Normal Subgroups
• More on Normal Subgroups
• Rings and Fields
• Integral Domain and Characteristic
• Fields of Quotients
• Rings of Polynomials
• Zeros of Polynomials
• Polynomial Factorization
• Field Extension
• Algebraic Extension
• Matrix Representation of Field Extensions
• Algebraic Closures
• Finite Field
• Group Action
• More on Group Action
• Three Isomorphism Theorems
• Burnside's Lemma
• Group Structure of NH
• Normal Subgroups with Small Indexes & Normalizer
• Sylow Theorem
• Quaternion and Ring Homomorphism
• Ideals
• More on Ideals
• UFD, PID, ED
• Multiplicative Norm
• More on Automorphisms
• Galois Extensions
• Normal Extension and Separable Extension
• Galois Theory
• Trace and Norm
• Computation on Galois Groups