Summer is a great time to explore cool problems and keep your skills sharp!  Schedule a class today!

Need Help?

Need help finding the right class? Have a question about how classes work?

Click here to Ask AoPS!

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

Sunday
May 12 - Aug 4
7:30 - 9:00
PM ET
May 12 - Aug 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
$390 (~$33/week)
$445 w/books
$390 (~$33/week)
With Books $445
CLOSED
Tuesday
Jun 11 - Aug 27
7:30 - 9:00
PM ET
Jun 11 - Aug 27
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
$390 (~$33/week)
$445 w/books
$390 (~$33/week)
With Books $445
ENROLL
Tuesday
Jun 11 - Aug 27
7:30 - 9:00
PM ET
Jun 11 - Aug 27
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
$390 (~$33/week)
$445 w/books
$390 (~$33/week)
With Books $445
ENROLL
Friday
Jun 21 - Sep 13
7:30 - 9:00
PM ET
Jun 21 - Sep 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
$390 (~$33/week)
$445 w/books
$390 (~$33/week)
With Books $445
ENROLL
Sunday
Jun 30 - Sep 22
3:30 - 5:00
PM ET  
Jun 30 - Sep 22
3:30 - 5:00 PM Eastern
2:30 - 4:00 PM Central
1:30 - 3:00 PM Mountain
12:30 - 2:00 PM Pacific
Click here to see more time zones
$390 (~$33/week)
$445 w/books
$390 (~$33/week)
With Books $445
ENROLL
Sunday
Aug 11 - Nov 3
7:30 - 9:00
PM ET
Aug 11 - Nov 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
$390 (~$33/week)
$445 w/books
$390 (~$33/week)
With Books $445
ENROLL
Friday
Sep 6 - Nov 22
7:30 - 9:00
PM ET
Sep 6 - Nov 22
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
$390 (~$33/week)
$445 w/books
$390 (~$33/week)
With Books $445
ENROLL
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
$390 (~$33/week)
$445 w/books
$390 (~$33/week)
With Books $445
ENROLL
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
$390 (~$33/week)
$445 w/books
$390 (~$33/week)
With Books $445
ENROLL

AoPS Holidays

There are no classes July 4, August 30 ‐ September 2, October 31, November 25 ‐ December 1, and December 21, 2024 ‐ January 3, 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

Great Class! We had a marvelous instructor and we learned so many things. As the course continues, life does too, and I start to see the course's elements incorporated in real-life situations. Again, really good class with lots of fun topics.