 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

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SYLLABUS
12 weeks

### Schedule

 Spring 2020 This 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! Sign In