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?  

Schedule

Tuesday
Apr 28 - Jul 14
4:00 - 5:30
PM ET 
Apr 28 - Jul 14
4:00 - 5:30 PM Eastern
3:00 - 4:30 PM Central
2:00 - 3:30 PM Mountain
1:00 - 2:30 PM Pacific
Click here to see more time zones
$340
$391 w/books
$340
With Books $391
CLOSED
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
$340
$391 w/books
$340
With Books $391
CLOSED
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
$340
$391 w/books
$340
With Books $391
CLOSED
Monday
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
$340
$391 w/books
$340
With Books $391
ENROLL
Monday
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
$340
$391 w/books
$340
With Books $391
ENROLL
Thursday
Jun 4 - Aug 20
7:30 - 9:00
PM ET
Jun 4 - Aug 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
$340
$391 w/books
$340
With Books $391
WAITLIST
Sunday
Jun 21 - Sep 20
7:30 - 9:00
PM ET
Jun 21 - Sep 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
$340
$391 w/books
$340
With Books $391
ENROLL
Wednesday
Sep 2 - Nov 18
7:30 - 9:00
PM ET
Sep 2 - Nov 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
ENROLL
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
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

AoPS Holidays

There are no classes July 3–5, September 5–7, and December 21–January 3.

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 liked this class because it taught me a lot of things that I didn't have the opportunity to learn in school. I learned a lot from it and I definitely think that this knowledge will help me in the future!

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