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

Tuesday 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	Valentin Vornicu	$335	$335 ENROLL
Tuesday 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	Eric Wofsey	$335	$335 ENROLL
Sunday Jun 21 - Sep 20	7:30 - 9:00 PM ET Jun 21 - Sep 20 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	Dan Kneezel	$335	$335 ENROLL

AoPS Holidays

There are no classes July 3–5, September 5–7, and 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