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
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
CLOSED
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
CLOSED
Monday
May 10 - Aug 9
7:30 - 9:00
PM ET
May 10 - Aug 9
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
Tuesday
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
$355
$406 w/books
$355
With Books $406
ENROLL
Friday
Jun 4 - Aug 20
4:00 - 5:30
PM ET 
Jun 4 - Aug 20
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
$355
$406 w/books
$355
With Books $406
ENROLL
Wednesday
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
$355
$406 w/books
$355
With Books $406
ENROLL
Sunday
Jun 20 - Sep 19
7:30 - 9:00
PM ET
Jun 20 - Sep 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
Aug 26 - Nov 11
7:30 - 9:00
PM ET
Aug 26 - Nov 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
$355
$406 w/books
$355
With Books $406
ENROLL
Fall 2021This course will be offered in Fall 2021. Click here to join our mailing list to be notified when the course schedule is available.

AoPS Holidays

There are no classes May 29–31, July 3–5, September 4–6, October 31, November 22–28, and December 20–January 2.

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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