About the Course
This course explores conundrums and analyzes a range of mathematical and philosophical paradoxes. You'll consider Zeno's paradoxes of space and time, such as The Racecourse, in which Achilles continually travels half of the remaining distance and seemingly can never reach the finish line. To address these types of paradoxes, you'll be introduced to the concepts of infinite series and limits, and then explore paradoxes of set theory, self-reference, and truth, and paradoxes of probability and inductive reasoning. Finally, you'll examine the concept of infinity and its paradoxes, and learn how to demonstrate that some infinities are bigger than others. Through these investigations, you'll acquire skills and concepts that are foundational for higher-level mathematics, and leave the course with more nuanced problem-solving skills, an enriched mathematical vocabulary, and insight into some of the most perplexing questions ever posed.
Typical Class Size: 16-18
Learning Objectives
- Formulate critical and quantitatively reasonable thoughts orally and in writing with clear and concise arguments
- Create and justify proofs of theorems like that of Cantor, Banack-Tarski, and Gödel
- Construct and rigorously examine paradoxes and open-ended problems
- Elaborate and create self-referential paradoxes
- Explain and justify the difficulties of classical philosophical problems
- Determine whether a set is finite, countably infinite or uncountably infinite
- Identify, examine, and test computer problems that are solvable or unsolvable
- Explore the hierarchy of larger and larger infinities
About Advanced Enrichment courses
These courses offer above-grade-level material that is presented in a novel context, explored with other advanced learners, and guided by a CTY educator to help prepare students for higher-order thinking and college-style academic challenges. Students work individually and may finish the course early if they complete all requirements before the course end date.
Requirements
CTY courses have grade-level requirements and most require minimum test scores. Some courses may also have prerequisites.
Identification DetailsDates and Tuition
In Person
Roger Williams University
Bristol, RI
Residential Site
You will be asked to join or sign in first.
Register by: June 14, 2026
Time Commitment:
Course Materials
Students should bring basic school supplies like pens, notebooks, and folders to their summer program. You will be notified of any additional items needed before the course begins. All other materials will be provided by CTY.
Sample Reading
These titles have been featured in past sessions of the course, and may be included this summer. CTY provides students with all texts; no purchase is required.
Paradoxes from A to Z, by Michael Clark
Dickinson College
Carlisle, PA
Residential Site
You will be asked to join or sign in first.
Register by: June 21, 2026
Filling up fast! 3 spots left
Time Commitment:
Course Materials
Students should bring basic school supplies like pens, notebooks, and folders to their summer program. You will be notified of any additional items needed before the course begins. All other materials will be provided by CTY.
Sample Reading
These titles have been featured in past sessions of the course, and may be included this summer. CTY provides students with all texts; no purchase is required.
Paradoxes from A to Z, by Michael Clark
Loyola Marymount University
Los Angeles, CA
Residential Site
You will be asked to join or sign in first.
Register by: June 8, 2026
Time Commitment:
Course Materials
Students should bring basic school supplies like pens, notebooks, and folders to their summer program. You will be notified of any additional items needed before the course begins. All other materials will be provided by CTY.
Sample Reading
These titles have been featured in past sessions of the course, and may be included this summer. CTY provides students with all texts; no purchase is required.
Paradoxes from A to Z, by Michael Clark
Registration Fee and Financial Aid
Tuition and fees will be waived or reduced for students who qualify for financial aid.
Learn more about Financial Aid