Dana Ernst

• One-semester introduction to proofs course
• Low-cost print edition published by AMS/MAA Press
• Inquiry-based learning approach
• Nine chapters, 149 pages
• Problems are interwoven throughout the exposition
• For more information and to download PDF or to access HTML

This textbook presents an inquiry-based learning (IBL) approach to a one-semester introduction to proofs course. A typical section consists of exposition intertwined with a considerable number of examples and problems. Following the IBL paradigm, these problems are meant to engage students in sense-making activities and can serve as the basis for homework sets and in-class student presentations. Though there is likely more material than could fit into a one-semester course, the author provides guidance for sequencing topics within such a course. In addition, an instructor’s manual available from the book’s landing page provides additional support for instructors using the book, including links to syllabi and a journal describing day-to-day class activities.

Contents:

1. Introduction
2. Mathematics and Logic
3. Set Theory
4. Induction
5. The Real Numbers
6. Three Famous Theorems
7. Relations and Partitions
8. Functions
9. Cardinality