 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?

SYLLABUS
12 weeks

### AoPS Holidays

There are no classes September 5–7, November 23–29, 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! Sign In