Study Guide — Classical theorems and functions
Number theory
Undergraduate study guide for Classical theorems and functions.
What this standard means
- Wilson's theorem and order of elements modulo n
- Chinese remainder theorem and applications
- Euler's totient function and multiplicative functions
- Quadratic residues and Legendre symbol
- Law of quadratic reciprocity (introduction or proof sketch)
_See printable PDF for diagram._
How to use the 20 practice sets
| Sets | When to use | | --- | --- | | 1–5 | Intro — explore together, short written items | | 6–10 | Core skills — diagrams and written practice | | 11–15 | Mixed review — explain thinking | | 16–20 | Stretch — word problems and mastery tasks |
Pacing: 10–15 minutes per session.
How to practice
1. Use trees or tables for counting 2. State the proof method up front 3. Check small cases before generalizing
_See printable PDF for diagram._
Common mistakes
- Double counting
- Missing base case in induction
Review and practice tests
1. Start Review 1/10 when sets 1–3 feel comfortable. 2. Move up one review level with little help. 3. Use Practice Test 4/10–6/10 for mid-standard checks. 4. Practice Test 10/10 is the mastery bar for Classical theorems and functions.
- [ ] Applies counting principles correctly
- [ ] Writes structured proofs
- [ ] Models problems with graphs or recurrences
Materials for this standard
- Practice Problems — 20 printable sets
- Review — 10 difficulty levels
- Practice Test — 10 difficulty levels
- Answer key — for parents and tutors