About the Course

Paradoxes and Infinities

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
 

Course Overview

This course is

ungraded.

Summer Dates & Locations

Registration deadline:

After May 9, 2025, registration is available upon request pending eligibility and seat availability. To request placement, email [email protected] after submitting a program application.

Session One

Image of Dickinson College
Carlisle, Pennsylvania
-
Residential cost: $7,259
Commuter cost: $6,459
Image of Roger Williams University
Bristol, Rhode Island
-
Residential cost: $7,259
Commuter cost: $6,459
image of the Loyola Marymount University campus
Los Angeles, California
-
Residential cost: $7,501
Commuter cost: $6,701
Image of the University of California Santa Cruz campus
Santa Cruz, California
-
Residential cost: $7,501
Commuter cost: $6,701

Session Two

Image of Dickinson College
Carlisle, Pennsylvania
-
Residential cost: $7,259
Commuter cost: $6,459
Image of Roger Williams University
Bristol, Rhode Island
-
Residential cost: $7,259
Commuter cost: $6,459
image of the Loyola Marymount University campus
Los Angeles, California
-
Residential cost: $7,501
Commuter cost: $6,701
Image of the University of California Santa Cruz campus
Santa Cruz, California
-
Residential cost: $7,501
Commuter cost: $6,701

Testing and Prerequisites

  Math Verbal
Required Level CTY-Level Not required
Check your eligibility using existing test scores If you do not have existing test scores:

Students must achieve qualifying scores on an advanced assessment to be eligible for CTY programs. If you don’t have qualifying scores, you have several different testing options. We’ll help you find the right option for your situation.

Sign up for Testing Learn More

Cost and Financial Aid

  • Tuition
    • Varies
  • Application fee
    • Nonrefundable Application Fee - $55 (Waived for financial aid applicants)
    • Nonrefundable International Fee - $250 (outside US only)

Financial Aid is available
We are committed to serving all talented youth regardless of financial circumstances. Financial assistance is available based on need.

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About Mathematics at CTY

Explore the study of shapes

Many of our courses allow students to describe the world around them in basic and profound ways. Younger students build foundational skills by exploring shape, scale, and proportion in Geometry and Spatial Sense. Middle School students delve into real-world applications of lines and analyze data with curves that follow uniform, symmetric, bell-shaped, or skewed patterns in Data and Chance. Advanced students unveil the deep interplay between numbers and shapes, investigating how triangular, square, and polygonal numbers create patterns that bridge geometry and algebra in Number Theory. By examining these elegant number patterns and symmetries, students discover how mathematics captures the intricate beauty and underlying structure of the natural world.

Dive deep into logic and reasoning

Our courses in formal logic give you the tools to question the world around you. Inductive and Deductive Reasoning introduces younger students to different types of reasoning, as well as the strengths and weaknesses inherent in various forms of critical analysis. Older students explore how logical reasoning can explain (or fail to explain) counter-intuitive results in Paradoxes and Infinities, or take a more rigorous approach to formal logic in Mathematical Logic.

Meet our instructors and staff