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

Summer Dates & Locations

Registration deadline:

After May 31, 2024, registration is available upon request pending eligibility and seat availability. To request placement, email [email protected] after submitting a program application.

Session One

Roger Williams University
Bristol, Rhode Island
-
Residential cost: $6,599
Commuter cost: $5,799
Session in Progress
Dickinson College
Carlisle, Pennsylvania
-
Residential cost: $6,599
Commuter cost: $5,799
Session in Progress
University of California Santa Cruz
Santa Cruz, California
-
Residential cost: $6,819
Commuter cost: $5,999

Session Two

Roger Williams University
Bristol, Rhode Island
-
Residential cost: $6,599
Commuter cost: $5,799
Dickinson College
Carlisle, Pennsylvania
-
Residential cost: $6,599
Commuter cost: $5,799
University of California Santa Cruz
Santa Cruz, California
-
Residential cost: $6,819
Commuter cost: $5,999

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 - $50 (Waived for financial aid applicants)
    • Nonrefundable International Fee - $250 (outside US only)

Financial Aid

We have concluded our financial aid application review process for 2024 On-Campus Programs. We encourage those who may need assistance in the future to apply for aid as early as possible.

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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. Our younger students learn about shape, scale, and proportion in Geometry and Spatial Sense. Middle School students explore beautiful real-world applications of lines; analyze data based on curves that fit a uniform, symmetric and bell-shaped, or skewed pattern in Data and Chance. And advanced students explore the underlying mathematics and fundamental characteristics of shapes, distance, and continuous deformations in our proof-based Topology course.

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