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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
Friday
Jun 16 - Sep 1 |
7:30 - 9:00 PM ET
Jun 16 - Sep 1
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 | $380 (~$32/week) |
$380
(~$32/week)
CLOSED |
Monday
Sep 25 - Dec 18 |
7:30 - 9:00 PM ET
Sep 25 - Dec 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 |
Chuck Garner | $380 (~$32/week) |
$380
(~$32/week)
ENROLL |
AoPS Holidays
There are no classes October 31, November 20 ‐ 26, December 21 ‐ January 3, May 25 ‐ May 27, and July 4.
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 |