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Intermediate Number TheoryNumber theory using algebraic techniques, multiplicative functions, Diophantine equations, modular arithmetic, Fermat's/Euler's Theorem, primitive roots, and quadratic residues. Much of the first half of the class emphasizes using the basic tools of the Introduction class in clever ways to solve difficult problems. In the second half, more theory will be developed, leading students to the beginning Olympiad level. |
12 weeks |
| 12 weeks ARE YOU READY? DO YOU NEED THIS? SYLLABUS |
Schedule
|
Wednesday
Feb 15 - May 3 |
7:30 - 9:00 PM ET
Feb 15 - May 3
7:30 - 9:00 PM Eastern 6:30 - 8:00 PM Central 5:30 - 7:00 PM Mountain 4:30 - 6:00 PM Pacific Click here to see more time zones |
Heather Finotti | $380 (~$32/week) |
$380
(~$32/week)
CLOSED |
|
Sunday
Apr 9 - Jul 2 |
7:30 - 9:00 PM ET
Apr 9 - Jul 2
7:30 - 9:00 PM Eastern 6:30 - 8:00 PM Central 5:30 - 7:00 PM Mountain 4:30 - 6:00 PM Pacific Click here to see more time zones |
Luis Ares | $380 (~$32/week) |
$380
(~$32/week)
ENROLL |
|
Thursday
Jun 1 - Aug 17 |
7:30 - 9:00 PM ET
Jun 1 - Aug 17
7:30 - 9:00 PM Eastern 6:30 - 8:00 PM Central 5:30 - 7:00 PM Mountain 4:30 - 6:00 PM Pacific Click here to see more time zones |
Charles Buehrle | $380 (~$32/week) |
$380
(~$32/week)
ENROLL |
|
Friday
Jun 16 - Sep 1 |
7:30 - 9:00 PM ET
Jun 16 - Sep 1
7:30 - 9:00 PM Eastern 6:30 - 8:00 PM Central 5:30 - 7:00 PM Mountain 4:30 - 6:00 PM Pacific Click here to see more time zones |
Dan Kneezel | $380 (~$32/week) |
$380
(~$32/week)
ENROLL |
| Fall 2023 | This course will be offered in Fall 2023. Click here to join our mailing list to be notified when the course schedule is available. | |||
AoPS Holidays
There are no classes May 27‐29, July 4, September 2‐4, October 31, November 20‐27, and December 21‐January 3, 2024.
Who Should Take?
Students should have a complete understanding of modular arithmetic, and a mastery of algebra through our Intermediate Algebra class (or a typical honors Algebra 2 class and some Precalculus) before taking this class.Lessons
| Lesson 1 | Introduction |
| Lesson 2 | Bases |
| Lesson 3 | Divisibility |
| Lesson 4 | Divisors and Multiplicative Functions |
| Lesson 5 | Prime Factorizations |
| Lesson 6 | Algebra in Modular Arithmetic |
| Lesson 7 | Linear Diophantine Equations |
| Lesson 8 | Perfect Squares |
| Lesson 9 | Fermat's Little Theorem and Euler's Theorem |
| Lesson 10 | Orders and Primitive Roots |
| Lesson 11 | Quadratic Residues and Squares |
| Lesson 12 | Sums of Two Squares |
