| Art of Problem Solving celebrates the many accomplishments of its students and community members. |
(Click here for the complete list of courses)
From students
"It was an amazing experience. I learned more in this one class than I do in an yearlong class at school. I'm definitely going to take more classes at AoPS!"
"I loved this course. A couple of times it used a theorem I didn't know... generally I was enlightened about how to solve abstract problems concerning integers. I'm definitely looking forward to my next class with AoPS."
"This class was incredible, the best bit of number theory I've ever taken. Throughout the class we encountered tough problems and theorems in which we worked out the proof on our own, as a group. This 'discovery learning' is incredibly effective."
This 8 week problem solving seminar (no evaluated problem sets) covers number theory using algebraic and counting approaches, Diophantine equations (Pell equations), Fermat's Little Theorem, the Phi Function, and Euler's Theorem.
Week 1: Algebraic Methods of Number Theory
Week 2: Base Numbers with Modeling
Week 3: Divisibility with Algebra; Counting/Parity Tactics
Week 4: Divisors with Algebra
Week 5: Diophantine Equations
Week 6: Modular Arithmetic with Algebra
Week 7: Perfect Squares
Week 8: Fermat's Little Theorem; Phi Function; Euler's Theorem
Students should have a complete understanding of modular arithmetic, and a mastery of basic algebra up through algebra II (or the Art of Problem Solving Algebra 3 class) before taking this class.
We recommend trying the following tests to determine whether the class is appropriate for you:
Are You Ready?
Do You Need This?
This course does not require a textbook.
|
|
