Introduction to Number Theory

Fundamental principles of number theory, including primes and composites, divisors and multiples, divisibility, remainders, modular arithmetic, and number bases.

This course is University of California a-g approved. Click here for more details.

12 weeks

Diagnostics

ARE YOU READY? DO YOU NEED THIS?

Documents

SYLLABUS
12 weeks ARE YOU READY? DO YOU NEED THIS?  

Schedule

Monday
Sep 26 - Dec 19
7:30 - 9:00
PM ET
Sep 26 - Dec 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
$285
$332 w/books
$285
With Books $332
Wednesday
Oct 19 - Jan 25
7:30 - 9:00
PM ET
Oct 19 - Jan 25
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
$285
$332 w/books
$285
With Books $332
Wednesday
Feb 1 - Apr 19
7:30 - 9:00
PM ET
Feb 1 - Apr 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
$295
$342 w/books
$295
With Books $342
ENROLL
Monday
Feb 20 - May 8
7:30 - 9:00
PM ET
Feb 20 - May 8
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
$295
$342 w/books
$295
With Books $342
ENROLL
Friday
Mar 17 - Jun 2
7:30 - 9:00
PM ET
Mar 17 - Jun 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
$295
$342 w/books
$295
With Books $342
ENROLL
Summer 2017This course will be offered in Summer 2017. Click here to join our mailing list to be notified when the course schedule is available.

AoPS Holidays

There are no classes May 29 or July 4.

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 loved the course Introduction to Number Theory. I learned so many new ways to think about integers and numbers in general. After this course, I think my number sense is definitely better than when I started. Also, I had lots of fun doing it!

ACS WASC
ACCREDITED
SCHOOL

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