Theoretical / proof-based
Abstract algebra · Undergraduate · Math
Topics
Groups
- Binary operations, equivalence relations, and modular arithmetic
- Groups: definitions, examples (Z, Z_n, dihedral, symmetric groups)
- Subgroups and cyclic groups; generators and order
- Cosets, Lagrange's theorem, and index
- Normal subgroups and quotient groups
- Group homomorphisms and the first isomorphism theorem
- Direct products and simple groups (introduction)
Rings and fields
- Rings: definitions and examples (Z, polynomial rings, matrix rings)
- Integral domains, fields, and ideals
- Quotient rings and ring homomorphisms
- Polynomial rings; irreducibility and factorization over Q and R
- Field extensions and constructibility (introduction)
Optional capstone
- Sylow theorems (optional capstone in a second semester)
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$1,162 · Abstract algebra · 18 tutoring hrs
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