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MATH 01340 · 3 cr · Advanced (300+)
Modern Algebra I
Groups/rings/fields — advanced credit and deep structure sense for teaching algebra.
Suggested prep window: 4–6 weeks (new language for most CS grads)
Prerequisites to lock first
- Proof writing (your Discrete Structures is a start)
- Comfort with modular arithmetic & functions
A-grade strategy
- Learn definitions first — Abstract Algebra is a vocabulary sport.
- Do tiny proofs daily: closure, identity, inverses, homomorphisms.
- Examples library: ℤ, ℤ_n, S_n, U(n), symmetries of triangle/square.
What you must know
Click any item for a definition, short reading, flashcards, and a practice prompt.
Rings & fields (intro)
Tutorials & videos
Watch intuition first, then full lectures, then drill. Links open free resources (YouTube, Khan, MIT OCW, notes).
playlist
Socratica — Abstract Algebra playlist
Clear, short conceptual videos for groups/rings/fields.
Open resource →
video
Visual Group Theory style intros (search 'Visual Group Theory')
Geometric intuition for group actions and symmetries.
Open resource →
playlist
Harvard Abstract Algebra — Benedict Gross lectures
University-level lecture series if you want full rigor.
Open resource →
playlist
MathDoctorBob — Abstract Algebra
Worked examples and theorem walkthroughs.
Open resource →
Self-check (no notes)
If you can do these cold, you are ready to start the Rowan section strong.
- Prove ℤ_n under addition mod n is a group.
- Give examples of a subgroup and a non-subgroup.
- Define homomorphism and check one example (e.g. mod map).