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

Friday Jun 4 - Aug 20	7:30 - 9:00 PM ET Jun 4 - Aug 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	Eric Wofsey	$350	$350 CLOSED
Sunday Jun 20 - Sep 19	7:30 - 9:00 PM ET Jun 20 - Sep 19 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	Luís Finotti	$350	$350 ENROLL
Monday 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	TBA	$350	$350 ENROLL

AoPS Holidays

There are no classes July 3–5, September 4–6, October 31, November 22–28, and December 20–January 2.

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