Introduction to Number Theory Online Math Course
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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
Sep 10 - Dec 3
7:30 - 9:00
PM ET
Sep 10 - Dec 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
$340
$391 w/books
$340
With Books $391
CLOSED
Friday
Sep 25 - Dec 18
7:30 - 9:00
PM ET
Sep 25 - Dec 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
$340
$391 w/books
$340
With Books $391
FULL
Sunday
Dec 6 - Mar 7
7:30 - 9:00
PM ET
Dec 6 - Mar 7
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
$340
$391 w/books
$340
With Books $391
ENROLL
Thursday
Dec 10 - Mar 11
7:30 - 9:00
PM ET
Dec 10 - Mar 11
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
$340
$391 w/books
$340
With Books $391
ENROLL
Monday
Feb 8 - Apr 26
7:30 - 9:00
PM ET
Feb 8 - Apr 26
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
$355
$406 w/books
$355
With Books $406
ENROLL
Wednesday
Mar 3 - May 19
7:30 - 9:00
PM ET
Mar 3 - May 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
$355
$406 w/books
$355
With Books $406
ENROLL
Thursday
Mar 25 - Jun 10
7:30 - 9:00
PM ET
Mar 25 - Jun 10
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
$355
$406 w/books
$355
With Books $406
ENROLL
Sunday
Mar 28 - Jun 20
7:30 - 9:00
PM ET
Mar 28 - Jun 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
$355
$406 w/books
$355
With Books $406
ENROLL

AoPS Holidays

There are no classes November 23–29, December 21–January 3, May 29–31, July 3–5, and September 4–6.

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

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

I really enjoyed this class. I think it was very fun and I learned a lot of new stuff in this class, especially in the last few weeks. Our teacher was very funny and made the class very interesting. Overall, I think this class was a very fun and great class. Thank you!

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