Intermediate Number Theory Online Math Course
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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?  

Schedule

Spring 2020This course will be offered in Spring 2020. Click here to join our mailing list to be notified when the course schedule is available.

AoPS Holidays

There are no classes November 25–December 1, or 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

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!

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