Congratulations Team USA, all of whom are AoPS WOOT alumni, for their 1st Place win at the 65th International Mathematical Olympiad! Discover WOOT.

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Intermediate Number Theory

Number 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

Diagnostics

ARE YOU READY? DO YOU NEED THIS?

Documents

SYLLABUS
12 weeks ARE YOU READY? DO YOU NEED THIS? SYLLABUS  

Schedule

Sunday
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
$390 (~$33/lesson)
$390 (~$33/lesson)
CLOSED
Wednesday
Jun 19 - Sep 4
7:30 - 9:00
PM ET
Jun 19 - Sep 4
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
$390 (~$33/lesson)
$390 (~$33/lesson)
CLOSED
Friday
Sep 20 - Dec 13
7:30 - 9:00
PM ET
Sep 20 - Dec 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
$390 (~$33/lesson)
$390 (~$33/lesson)
ENROLL

AoPS Holidays

There are no classes August 30 ‐ September 2, October 31, November 25 ‐ December 1, and December 21, 2024 ‐ January 3, 2025.

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

1 Introduction
2 Bases
3 Divisibility
4 Divisors and Multiplicative Functions
5 Prime Factorizations
6 Algebra in Modular Arithmetic
7 Linear Diophantine Equations
8 Perfect Squares
9 Fermat's Little Theorem and Euler's Theorem
10 Orders and Primitive Roots
11 Quadratic Residues and Squares
12 Sums of Two Squares

This class was amazing! It was definitely one of the most interesting math classes I've ever taken. It was actually challenging (and I like a challenge). The problems in general did get harder as the course continued which I liked a lot since it really does help you become a better problem solver. I learned so much and much more than just theory. This class was always fun and challenging and it definitely builds confidence for attacking harder problems. I'm so glad I took this class. AoPS, I love you guys. You're awesome!