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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.This course is University of California a-g approved. Click here for more details. |
12 weeks |
| 12 weeks ARE YOU READY? DO YOU NEED THIS? |
Schedule
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Friday
Jun 9 - Aug 25 |
7:30 - 9:00
PM ET
Jun 9 - Aug 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 |
Daniel Kneezel | $295 |
$295
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Wednesday
Jun 28 - Sep 13 |
7:30 - 9:00
PM ET
Jun 28 - Sep 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 |
Kate Thompson | $295 |
$295
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Tuesday
Jul 18 - Oct 3 |
7:30 - 9:00
PM ET
Jul 18 - Oct 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 |
Luis Ares | $295 |
$295
ENROLL |
| Spring 2018 | This course will be offered in Spring 2018. Click here to join our mailing list to be notified when the course schedule is available. | |||
AoPS Holidays
There are no classes September 4, November 18 - 26, 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 |