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.

This course is University of California a-g approved. Click here for more details.

12 weeks

Diagnostics

ARE YOU READY? DO YOU NEED THIS?

Documents

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

Schedule

Tuesday
Oct 11 - Jan 17
7:30 - 9:00
PM ET
Oct 11 - Jan 17
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
$285
$285
Summer 2017This course will be offered in Summer 2017. Click here to join our mailing list to be notified when the course schedule is available.

AoPS Holidays

There are no classes May 29 or 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

Before taking this class, I didn't know any major theorems for Number Theory, I couldn't do ANY olympiad-level Number Theory problems, and I was quite lost when talking about modular equations. Now, I am comfortable with a lot of Number Theory topics and have started appreciating how fun and great number theory really is (before, it was too difficult for me to enjoy)! Thanks for making this one of the best classes I have ever taken!

ACS WASC
ACCREDITED
SCHOOL

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