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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
Sep 16 - Dec 9 |
7:30 - 9:00
PM ET
Sep 16 - Dec 9
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 |
Patrick Barringer | $335 |
$335
CLOSED |
Tuesday
Feb 23 - May 11 |
7:30 - 9:00
PM ET
Feb 23 - May 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 |
Luis Ares | $350 |
$350
ENROLL |
Monday
Mar 22 - Jun 14 |
7:30 - 9:00
PM ET
Mar 22 - Jun 14
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 |
TBA | $350 |
$350
ENROLL |
Sunday
Apr 25 - Jul 25 |
7:30 - 9:00
PM ET
Apr 25 - Jul 25
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 |
TBA | $350 |
$350
ENROLL |
AoPS Holidays
There are no classes November 23–29, December 21–January 3, May 29–31, July 3–5, and September 4–6.
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 |