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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
|
Tuesday
Jun 2 - Aug 18 |
7:30 - 9:00
PM ET
Jun 2 - Aug 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 |
Eric Wofsey | $335 |
$335
CLOSED |
|
Tuesday
Jun 2 - Aug 18 |
7:30 - 9:00
PM ET
Jun 2 - Aug 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 |
Valentin Vornicu | $335 |
$335
CLOSED |
|
Sunday
Jun 21 - Sep 20 |
7:30 - 9:00
PM ET
Jun 21 - Sep 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 |
Dan Kneezel | $335 |
$335
ENROLL |
| Spring 2021 | This course will be offered in Spring 2021. Click here to join our mailing list to be notified when the course schedule is available. | |||
AoPS Holidays
There are no classes September 5–7, November 23–29, 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 |
