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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
|
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 |
David Reynoso Valle | $400 (~$34/lesson) |
$400
(~$34/lesson)
CLOSED |
|
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 |
|
Sunday
Jun 1 - Aug 24 |
7:30 - 9:00 PM ET
Jun 1 - Aug 24
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 | $400 (~$34/lesson) |
$400
(~$34/lesson)
ENROLL |
|
Wednesday
Jun 18 - Sep 3 |
7:30 - 9:00 PM ET
Jun 18 - Sep 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 |
Dan Kinch | $400 (~$34/lesson) |
$400
(~$34/lesson)
ENROLL |
| Fall 2025 | This course will be offered in Fall 2025. Click here to join our mailing list to be notified when the course schedule is available. | |||
AoPS Holidays
There are no classes May 24 ‐ 26, July 4 ‐ 6, August 29 ‐ September 1, October 31, November 24 ‐ November 30, and December 20, 2025 ‐ January 2, 2026.
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 |
