Art of Problem Solving
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Dive into learning adventures this summer with our math, science, and contest courses.  Enroll today!
How Classes Work
Course Catalog
Recommendations
Subject Courses
Before Prealgebra Ready for Prealgebra After Prealgebra Some Algebra 1 After Algebra 1 After Geometry After Algebra 2 After Precalculus Beyond Calculus
Contest Preparation
MATHCOUNTS/AMC 8 AMC 10 AMC 12 AIME USAMO
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Paradoxes and Infinity

In this class we'll explore several popular paradoxes and attempt to wrap our brains around the world of infinity. For example, we'll discover a hotel that's never full: somehow, this hotel can always add another guest, or two, or three. We'll also run into paradoxes about goats, haystacks, pop-quizzes and more. If you're interested in mind-bending ideas and theories and have a background in basic algebra, this class is for you!

4 days
4 days  

Schedule

Mon, Tue, Wed & Thurs
Jul 15 - Jul 18 		7:30 - 9:00
PM ET
Jul 15 - Jul 18
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
Jeffery Yu $145
$145
ENROLL

AoPS Holidays

There are no classes May 25 ‐ 27, July 4, August 30 ‐ September 2, October 31, November 25 ‐ December 1, and December 21, 2024 ‐ January 3, 2025.

Lessons

Lesson 1 Paradoxes in Philosophy
Lesson 2 Paradoxes in Mathematics
Lesson 3 Hilbert's Grand Hotel and Infinite Cardinals
Lesson 4 Zeno's Paradox of Dichotomy

I really enjoyed taking my first AoPS class. I always thought that online classes weren't very good. I was mistaken after I took this class. Not only did Introduction to Geometry help me become a better math student, it also helped me to think more abstractly and look for multiple roads to solve a problem. I enjoy the way the classroom is run and the pace was very nice. The class wasn’t boring at all. This class challenged me to become a better thinker and was way more challenging than regular school courses. I am also very glad that AoPS also included a little bit of a social aspect to math with the message boards. I made a lot of friends through this course. In school, I am always made fun of for being ahead of all of the other students. On AoPS I actually feel accepted for once because I can interact with kids that are more advanced than I am and also I learn from them. I will definitely take another AoPS class.