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MATH 01352 · 3 cr · Advanced (300+)
Theory of Numbers
Advanced elective that strengthens proofs + Praxis number/algebra thinking.
Suggested prep window: 2–4 weeks
Prerequisites to lock first
- Discrete math / proof comfort; modular arithmetic basics
A-grade strategy
- Master divisibility lemmas and modular arithmetic early.
- Practice induction and well-ordering proofs weekly.
- Keep a theorem list: Euclid, FTA, Euler/Fermat little theorem.
What you must know
Click any item for a definition, short reading, flashcards, and a practice prompt.
Tutorials & videos
Watch intuition first, then full lectures, then drill. Links open free resources (YouTube, Khan, MIT OCW, notes).
practice
Khan Academy — Number Theory (pre-college into early college)
Fast modular arithmetic fluency.
Open resource →
playlist
Michael Penn — Number Theory videos
Problem-driven college number theory explanations.
Open resource →
playlist
Numberphile — intuition & famous theorems
Motivation and stories; pair with real problem sets.
Open resource →
notes
MIT OCW — Theory of Numbers (search current offering)
Problem sets at true college difficulty.
Open resource →
Self-check (no notes)
If you can do these cold, you are ready to start the Rowan section strong.
- Run Euclidean algorithm and back-substitute Bézout coefficients.
- Solve a linear congruence ax ≡ b (mod n).
- State and use Fermat's Little Theorem on a small example.