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Introduction to Number Theory

Fundamental principles of number theory, including primes and composites, divisors and multiples, divisibility, remainders, modular arithmetic, and number bases.

12 weeks

Diagnostics

ARE YOU READY? DO YOU NEED THIS?

Documents

SYLLABUS
12 weeks ARE YOU READY? DO YOU NEED THIS? SYLLABUS  

Schedule

Thursday
Oct 10 - Jan 23
7:30 - 9:00
PM ET
Oct 10 - Jan 23
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
$400 (~$34/lesson)
$455 w/books
$400 (~$34/lesson)
With Books $455
CLOSED
Monday
Dec 2 - Mar 3
7:30 - 9:00
PM ET
Dec 2 - Mar 3
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
$400 (~$34/lesson)
$455 w/books
$400 (~$34/lesson)
With Books $455
ENROLL
Tuesday
Jan 28 - Apr 15
7:30 - 9:00
PM ET
Jan 28 - Apr 15
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
$400 (~$34/lesson)
$455 w/books
$400 (~$34/lesson)
With Books $455
ENROLL
Sunday
Feb 16 - May 4
7:30 - 9:00
PM ET
Feb 16 - May 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
$400 (~$34/lesson)
$455 w/books
$400 (~$34/lesson)
With Books $455
ENROLL
Monday
Mar 17 - Jun 9
7:30 - 9:00
PM ET
Mar 17 - Jun 9
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
$400 (~$34/lesson)
$455 w/books
$400 (~$34/lesson)
With Books $455
ENROLL
Thursday
Apr 17 - Jul 3
7:30 - 9:00
PM ET
Apr 17 - Jul 3
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
$400 (~$34/lesson)
$455 w/books
$400 (~$34/lesson)
With Books $455
ENROLL

AoPS Holidays

There are no classes December 21 ‐ January 3, May 24 ‐ 26, July 4 ‐ 6, August 29 ‐ September 1, October 31, and November 24 ‐ November 30, 2025.

Who Should Take?

This course is appropriate for students in grades 6-9 who have mastered basic algebra up through solving linear equations and manipulating multi-variable expressions. Students who have completed our Introduction to Algebra A course should have sufficient background. Students who are already proficient with modular arithmetic and basic Diophantine equations do not need this course. This course is roughly the same difficulty as our Introduction to Counting and Probability class. For those preparing for contests, this course should help with MATHCOUNTS and the AMC 8/10/12 tests.

Lessons

1 Integers, Fractions, Decimals, and Number Bases
2 Base Number Arithmetic
3 Multiples, Divisors, and Prime Numbers
4 Common Factors, Common Multiples, Euclidean Algorithm
5 Divisor Problems, More with the Euclidean Algorithm
6 Factorials, Special Integers, Algebra with Integers
7 Units Digit, Introduction to Modular Arithmetic
8 Calculations with Modular Arithmetic
9 Divisibility Rules and Multiplicative Inverses
10 Multiplicative Inverses, Solving Linear Congruences
11 Systems of Linear Congruences and the Chinese Remainder Theorem
12 Number Sense and Applications of Number Theory

Required Textbook

Introduction to Number Theory
By Mathew Crawford
A thorough introduction for students in grades 7-10 to topics in number theory such as primes & composites, multiples & divisors, prime factorization and its uses, base numbers, modular arithmetic, divisibility rules, linear congruences, how to develop number sense, and more.
Related course: Introduction to Number Theory

As the first online course I've ever taken, I can say without doubt that it has been a tremendously great experience. I know that a lot people that took Intro to Number Theory were still in grade school, but taking it as a senior in high school, I still feel challenged and frankly I don't feel the same kind of embarrassment I feel in a normal classroom when I don't understand the material or want to ask a question. The instructor was extremely knowledgeable and enthusiastic about the subject which made it all the more motivating to learn. Props to AoPS for such excellent classes!