- Grades 7-11
- Advanced CTY-Level
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
- Develop and write mathematical proofs in a clear and concise manner by examining tautologies, contradictions, and contingencies, among others
- Develop oral and written arguments by constructing truth tables, examining De Morgan’s Laws and conditional/biconditional exchanges, and the logical replacement laws
- Formulate and analyze propositional arguments to prove and disprove mathematical results
- Demonstrate ability to think critically by proof by induction, contradiction, contraposition, and contradiction
- Demonstrate the difference between a conjecture, an example, and a rigorous mathematical proof
- Demonstrate the ability to integrate knowledge and ideas in a coherent and meaningful manner for constructing well-written mathematical proofs
Summer Dates & Locations
Testing and Prerequisites
|Required Level||Advanced CTY-Level||Not required|
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 PrerequisitesMathematical Logic requires:
Cost and Financial Aid
- Nonrefundable Application Fee - $50 (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.
Please acquire all course materials by the course start date, unless noted as perishable. Items marked as “perishable” should not be acquired until the student needs them in the course. If you have questions about these materials or difficulty locating them, please contact [email protected].
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. 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.