Introduction to Proofs

Course Title: Introduction to Proofs
Course Description:
This course is designed for students who are ready to move beyond solving problems and into the deeper structure of mathematical thinking. Introduction to Proofs helps build the logical and conceptual foundation necessary for upper-level math courses.
Using Mathematical Proofs: A Transition to Advanced Mathematics by Chartrand, Polimeni, and Zhang, students will learn to construct and analyze rigorous mathematical arguments. Topics include logic, set theory, proof techniques (direct, contrapositive, contradiction, induction), and the formal language of mathematics.
This is an ideal course for:

• Math education majors who need to pass proof-based courses as part of their degree requirements
• Math majors looking to get ahead and strengthen their understanding before tackling courses like abstract algebra, real analysis, or discrete math

By the end of the course, students will be comfortable writing clear and precise proofs and will be prepared to succeed in proof-intensive mathematics courses.
Topics Covered:

• Logical reasoning and truth tables
• Sets, relations, and functions
• Quantifiers and predicates
• Proof techniques: direct, contrapositive, contradiction, induction
• Mathematical writing and structure

Prerequisites: Comfort with high school algebra; some experience with college-level math (e.g., precalculus or calculus) is recommended.