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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
|
Friday
Sep 20 - Dec 13 |
7:30 - 9:00 PM ET
Sep 20 - Dec 13
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 |
Jerry Leung | $400 (~$34/lesson) |
$400
(~$34/lesson)
CLOSED |
|
Thursday
Feb 20 - May 8 |
7:30 - 9:00 PM ET
Feb 20 - May 8
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 |
Dana Paquin | $400 (~$34/lesson) |
$400
(~$34/lesson)
ENROLL |
|
Friday
Apr 11 - Jun 27 |
7:30 - 9:00 PM ET
Apr 11 - Jun 27
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 | $400 (~$34/lesson) |
$400
(~$34/lesson)
ENROLL |
AoPS Holidays
There are no classes November 25 ‐ December 1, December 21 ‐ January 3, May 24 ‐ 26, July 4 ‐ 6, August 29 ‐ September 1, and October 31, 2025.
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
| 1 | Introduction |
| 2 | Bases |
| 3 | Divisibility |
| 4 | Divisors and Multiplicative Functions |
| 5 | Prime Factorizations |
| 6 | Algebra in Modular Arithmetic |
| 7 | Linear Diophantine Equations |
| 8 | Perfect Squares |
| 9 | Fermat's Little Theorem and Euler's Theorem |
| 10 | Orders and Primitive Roots |
| 11 | Quadratic Residues and Squares |
| 12 | Sums of Two Squares |
