Art of Problem Solving
AoPS Online AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

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
Computer Programming
Little or No Experience Some Experience Extensive Experience
Science Courses
Little or No Experience Some Experience Extensive Experience
Prospective Students & Parents
Math Jams
Need Help?

Need help finding the right class? Have a question about how classes work?

Click here to Ask AoPS!

Paradoxes and Infinity Seminar

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!

2 days
2 days  

Schedule

Summer 2024This course will be offered in Summer 2024. Click here to join our mailing list to be notified when the course schedule is available.

Lessons

Lesson 1 Paradoxes
Lesson 2 Infinity

I have taken many other online and in-person extracurricular math courses but this was the first one that I found engaging, difficult, and instructive. I particularly enjoy that the problems we do require actual thinking and creativity, not just repetition/memorization. The format for the lectures is something I've never seen and I think it works really well. I have learned a lot. Thank you so much!