About the Course
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
Learning Objectives
- 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
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.
Requirements
CTY courses have grade-level requirements and most require minimum test scores. Some courses may also have prerequisites.
Identification DetailsDates and Tuition
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Registration Fee and Financial Aid
Tuition and fees will be waived or reduced for students who qualify for financial aid.
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