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	Luis Ares	$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	Justin Stevens	$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	Jerry Leung	$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