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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
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 |
Eli Brottman | $370 (~$31/week) |
$370
(~$31/week)
CLOSED |
|
Sunday
Jun 19 - Sep 18 |
7:30 - 9:00 PM ET
Jun 19 - Sep 18
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 |
Jeffrey Hankins | $370 (~$31/week) |
$370
(~$31/week)
ENROLL |
|
Tuesday
Sep 27 - Dec 20 |
7:30 - 9:00 PM ET
Sep 27 - Dec 20
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 |
Joseph Stahl | $370 (~$31/week) |
$370
(~$31/week)
ENROLL |
AoPS Holidays
There are no classes May 28‐30, July 2‐4, September 3‐5, October 31, November 21‐27, and December 21‐January 3.
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 |
