Algebra

• Groups: definition, axioms, examples — T3
• Subgroups; Subgroup Criterion — T4
• Cyclic groups — T1
• Cosets and Lagrange's theorem — T3
• Normal subgroups; quotient groups — T3
• Group homomorphisms: kernel, image — T3
• Isomorphism theorems (First, Second, Third) — T3
• Permutation Groups (S_n): Cycle Decomposition, Sign, A_n — T4
• Cayley's Theorem — T4
• Rings: Definition, Axioms, Examples — T4
• Subrings and ideals — T3
• Ring homomorphisms; quotient rings — T3
• Integral domains; characteristic — T3
• Principal Ideal Domains (PID) — T4
• Euclidean domains — T2
• Fields and finite fields — T2
• Field Extensions; Tower Law; Algebraic Closure — T4