Intermediate Number Theory Online Math Course

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

Sunday
Feb 23 - May 10
7:30 - 9:00
PM ET
Feb 23 - May 10
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
$335
$335
ENROLL
Thursday
Mar 12 - May 28
7:30 - 9:00
PM ET
Mar 12 - May 28
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
$335
$335
ENROLL
Summer 2020This course will be offered in Summer 2020. Click here to join our mailing list to be notified when the course schedule is available.

AoPS Holidays

There are no classes December 21–January 3, May 23–25, July 3–5, and September 5–7.

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

I enjoyed Intermediate Number Theory very much and I learned very many new things in it. Most of the topics in the second half of the class were new to me (e.g. orders, primitive roots, Pell equation, etc.) It was also valuable to have my proofs graded by an outside source, rather than by myself as when I just used AoPS books by themselves. The classes were very interesting and informative.

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