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From students
"I really enjoyed this class. I would take another course from AoPS. I found the course very challenging, but I think that was a good thing. I was VERY impressed with feedback on problems and challenges. Thank you for a GREAT class."
"I loved your class! Your course was VERY useful and I think I learned a lot. I walked in a regular person, but I walked out a genius (more or less)"
"I enjoyed the class very much! I think that future students will learn a lot from this course, and have tons of fun with it. Thank you for the detailed explanations in the solutions to the problem sets!"
This course covers fundamental principles of number theory, including primes and composites, divisors and multiples, divisibility, remainders, modular arithmetic, and number bases.
Week 1: The Integers, Divisibility, Primes, Composites, Prime Factorization
Week 2: GCD, LCM, The Euclidean Algorithm
Week 3: Counting Divisors, Divisor Problems, Factorials
Week 4: Algebra with Integers, Base Numbers
Week 5: Base Number Arithmetic
Week 6: Units Digits, Linear Diophantine Equations
Week 7: Decimals and Fractions
Week 8: Addition and Subtraction in Modular Arithmetic
Week 9: Multiplication in Modular Arithmetic, Divisibility Rules
Week 10: Multiplicative Inverses, Linear Congruences
Week 11: Systems of Linear Congruences
Week 12: Challenging Problems in Number Theory
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 are already proficient with modular arithmetic and basic Diophantine equations do not need this course. For those preparing for contests, this course should help with MATHCOUNTS and the AMC 8/10/12 tests.
We recommend trying the following diagnostic tests to determine whether the class is appropriate for you:
Are You Ready?
Do You Need This?
This course requires the textbook Introduction to Number Theory. There is a discount if you buy the text when registering for the course.
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