PROOFS & MATHEMATICAL STRUCTURES
college of the atlantic
spring 2023
This course is an introduction to mathematical structures, proof techniques, and the language and style of formal mathematics. Topics to be covered include: intuitive and direct proofs, sets and functions, induction, logic, the contrapositive, and proof by contradiction. Additionally, this course aims to introduce students to some of the key elements of higher mathematics, and so, as time permits, we will cover introductory topics from areas such as number theory, topology, real analysis, and group theory. Throughout the course we will emphasize clear mathematical exposition and methods of proof. In addition to gaining an understanding of the topics listed above, students who complete this course will be able to: read and understand mathematical exposition; think critically as mathematicians and present convincing arguments; and read and write formal proofs. This class will help prepare students for further advanced study in mathematics and related fields. It will also be of value to those who wish to explore the logical structure of mathematics, gain increased facility with abstract mathematical thought, or sharpen analytic and critical reasoning skills. This course will be taught in a seminar style; students will frequently be asked to prepare proofs and examples for discussion in class and to work collaboratively on problems. Evaluation will be based on problem sets and active and collaborative class participation. Level: Intermediate. Prerequisites: Calculus II and permission of instructor. Class limit: 5. Lab Fee: None. Meets the following degree requirements: QR.
