MA 274: Mathematical Reasoning is a course that teaches students how to effectively write and talk mathematics. Additionally, it introduces students to concepts used in every area of mathematics, including axiom systems, relations, cardinalities. On a philosophical level, this course explores the nature of knowledge (how do we know something is true?) and the nature of infinity (how big is an infinite set?). The aim is to produces people who are competent learners and doers of mathematics.
Selected Course Notes:
Axioms:
Exam Prep:
- Practice Exam 1 Use this Practice Exam to get a feel for the style of the actual exam. Specific material covered by the exam may, of course, vary.
- Examples of proofs by induction
- A proof of the Chinese Remainder Theorem using the Well-Ordering Principle.
- Rotations of a circle by an irrational angle.
- Study Guide for Exam 2.
- Solutions to the study guide for Exam 2.
- Study Guide for Exam 3 (Some solutions included)