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

This was the best math course I have ever taken. I have always been very strong in math and have taken many challenging courses. Intermediate Algebra challenged me at a greater level. Writing problems are the main way that Intermediate Algebra challenged me at a new level. If I had not taken this course, I never would have known the complex proof methods I have learned. The writing problems have also made me more prepared to succeed at contests like the Mandelbrot Competition and the USAMO, as I have learned proof-writing strategies. I always like to know a lot about topics, especially topics that I have a passion for, like math. Intermediate Algebra fulfilled that desire. This was also a great help for preparing for contests like the AMC 12. All in all, this was an excellent course.