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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
|
Sunday
Feb 22 - May 10 |
7:30 - 9:00 PM ET
Feb 22 - May 10
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 |
Martha Maria Bernal Guillen | $415 (~$35/lesson) |
$415
(~$35/lesson)
ENROLL |
|
Monday
Apr 13 - Jul 6 |
7:30 - 9:00 PM ET
Apr 13 - Jul 6
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 |
Jeffery Yu | $415 (~$35/lesson) |
$415
(~$35/lesson)
ENROLL |
|
Sunday
Jun 7 - Aug 30 |
7:30 - 9:00 PM ET
Jun 7 - Aug 30
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 |
Eli Brottman | $415 (~$35/lesson) |
$415
(~$35/lesson)
ENROLL |
|
Friday
Jun 19 - Sep 11 |
7:30 - 9:00 PM ET
Jun 19 - Sep 11
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 |
Martha Maria Bernal Guillen | $415 (~$35/lesson) |
$415
(~$35/lesson)
ENROLL |
| Fall 2026 | This course will be offered in Fall 2026. Click here to join our mailing list to be notified when the course schedule is available. | |||
AoPS Holidays
There are no classes May 23 ‐ 25, July 3 ‐ 5, September 5 ‐ 7, October 31, November 23 ‐ 29, and December 21 ‐ January 3, 2027.
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 |
