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
Jun 5 - Aug 28
7:30 - 9:00
PM ET
Jun 5 - Aug 28
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
$370 (~$31/week)
$425 w/books
$370 (~$31/week)
With Books $425
CLOSED
Tuesday
Jun 14 - Aug 30
7:30 - 9:00
PM ET
Jun 14 - 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
$370 (~$31/week)
$425 w/books
$370 (~$31/week)
With Books $425
FULL
Thursday
Jun 16 - Sep 1
7:30 - 9:00
PM ET
Jun 16 - Sep 1
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
$370 (~$31/week)
$425 w/books
$370 (~$31/week)
With Books $425
ENROLL
Sunday
Aug 7 - Oct 30
7:30 - 9:00
PM ET
Aug 7 - Oct 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
$370 (~$31/week)
$425 w/books
$370 (~$31/week)
With Books $425
ENROLL
Thursday
Sep 1 - Nov 17
7:30 - 9:00
PM ET
Sep 1 - Nov 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
$370 (~$31/week)
$425 w/books
$370 (~$31/week)
With Books $425
ENROLL
Wednesday
Oct 5 - Jan 11
7:30 - 9:00
PM ET
Oct 5 - Jan 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
$370 (~$31/week)
$425 w/books
$370 (~$31/week)
With Books $425
ENROLL
Friday
Oct 28 - Feb 3
7:30 - 9:00
PM ET
Oct 28 - Feb 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
$370 (~$31/week)
$425 w/books
$370 (~$31/week)
With Books $425
ENROLL
Sunday
Dec 11 - Mar 12
7:30 - 9:00
PM ET
Dec 11 - Mar 12
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
$370 (~$31/week)
$425 w/books
$370 (~$31/week)
With Books $425
ENROLL

AoPS Holidays

There are no classes May 28‐30, July 2‐4, September 3‐5, October 31, November 21‐27, 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.

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!

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