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Introduction to Number TheoryFundamental principles of number theory, including primes and composites, divisors and multiples, divisibility, remainders, modular arithmetic, and number bases. |
12 weeks |
| 12 weeks ARE YOU READY? DO YOU NEED THIS? SYLLABUS |
Schedule
|
Monday
Jan 26 - Apr 13 |
7:30 - 9:00 PM ET
Jan 26 - Apr 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 |
Ashley Ahlin |
$415
(~$35/lesson)
$470 w/books
|
$415
(~$35/lesson)
CLOSED
With Books $470
|
|
Sunday
Feb 15 - May 3 |
7:30 - 9:00 PM ET
Feb 15 - May 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 |
Eli Brottman |
$415
(~$35/lesson)
$470 w/books
|
$415
(~$35/lesson)
CLOSED
With Books $470
|
|
STARTING SOON |
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Thursday
Mar 19 - Jun 4 |
7:30 - 9:00 PM ET
Mar 19 - Jun 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 |
Luís Finotti |
$415
(~$35/lesson)
$470 w/books
|
$415
(~$35/lesson)
ENROLL
With Books $470
|
|
Sunday
Apr 19 - Jul 19 |
7:30 - 9:00 PM ET
Apr 19 - Jul 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 |
Ray Garner |
$415
(~$35/lesson)
$470 w/books
|
$415
(~$35/lesson)
ENROLL
With Books $470
|
|
Tuesday
May 19 - Aug 4 |
7:30 - 9:00 PM ET
May 19 - 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 |
Dan Kneezel |
$415
(~$35/lesson)
$470 w/books
|
$415
(~$35/lesson)
ENROLL
With Books $470
|
|
Sunday
Jun 7 - Aug 30 |
7:30 - 9:00 PM ET
Jun 7 - Aug 30
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 |
Homero Gallegos |
$415
(~$35/lesson)
$470 w/books
|
$415
(~$35/lesson)
ENROLL
With Books $470
|
|
Wednesday
Jun 17 - Sep 2 |
7:30 - 9:00 PM ET
Jun 17 - Sep 2
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 |
Sarah Seales |
$415
(~$35/lesson)
$470 w/books
|
$415
(~$35/lesson)
ENROLL
With Books $470
|
|
Monday
Jul 13 - Oct 5 |
7:30 - 9:00 PM ET
Jul 13 - Oct 5
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 |
$415
(~$35/lesson)
$470 w/books
|
$415
(~$35/lesson)
ENROLL
With Books $470
|
| Fall 2026 | This course will be offered in Fall 2026. Click here to join our mailing list to be notified when the course schedule is available. | |||
AoPS Holidays
There are no classes May 23 ‐ 25, July 3 ‐ 5, September 5 ‐ 7, October 31, November 23 ‐ 29, and December 21 ‐ January 3, 2027.
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
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 |
