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

Wednesday
Jun 1 - Aug 17
7:30 - 9:00
PM ET
Jun 1 - Aug 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
$370 (~$31/week)
$370 (~$31/week)
CLOSED
Sunday
Jun 19 - Sep 18
7:30 - 9:00
PM ET
Jun 19 - Sep 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
$370 (~$31/week)
$370 (~$31/week)
ENROLL
Tuesday
Sep 27 - Dec 20
7:30 - 9:00
PM ET
Sep 27 - Dec 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
$370 (~$31/week)
$370 (~$31/week)
ENROLL

AoPS Holidays

There are no classes May 28‐30, July 2‐4, September 3‐5, October 31, November 21‐27, 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

After taking this class, I am solving AIME-IMO Number Theory Problems. This class really builds the foundations necessary for Olympiad Number Theory problems. It is also very problem-solving oriented which is great. I've learned so much from this class; Keep up the great work AoPS!

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