About the Course

Mathematical Logic

  • Grades 7-11
  • Advanced CTY-Level
  • Residential
  • Mathematics

Have you ever wondered what real mathematicians spend their time doing? This course will teach you the art of proving and disproving conjectures, and techniques for writing formal proofs and counterexamples. You’ll learn key concepts of logic, including validity, soundness, consistency, and satisfiability, and techniques for developing systems of logic in formal symbolic languages. You’ll test the validity of arguments, write precise formal proofs, and explore the rules of grammar and meanings behind the symbols. Then you and your classmates will engage in the process of metalogic, or reasoning logically about a system of logic. You’ll examine soundness and completeness, and along the way, you’ll become proficient at writing proofs accurately and rigorously, a skill essential to career mathematicians. Most importantly, you’ll develop strong problem-solving skills and learn to think analytically—traits vital for rigorous inquiry in any field.

Typical Class Size: 16-18
 

Course Overview

This course is

ungraded.

Summer Dates & Locations

Registration deadline:

After May 2, 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
Dickinson College
Carlisle, Pennsylvania
-
Residential cost: $7,259
Commuter cost: $6,459
Enroll
Image of the University of California Santa Cruz campus
UC-Santa Cruz
Santa Cruz, California
-
Residential cost: $7,501
Commuter cost: $6,701
Enroll

Session Two

Image of Dickinson College
Dickinson College
Carlisle, Pennsylvania
-
Residential cost: $7,259
Commuter cost: $6,459
Enroll

Testing and Prerequisites

  Math Verbal
Required Level Advanced 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

Course Prerequisites

Mathematical Logic requires:

1 prerequisite

Algebra 1

Cost and Financial Aid

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

We have concluded our financial aid application review process for 2025 On-Campus Programs. We encourage those who may need assistance in the future to apply for aid as early as possible. We are committed to serving all talented youth regardless of financial circumstances. Financial assistance is available based on need.

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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.

  • Logic: Techniques of Formal Reasoning, Donald Kalish, Richard Montague

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