An Introduction to Proof via Inquiry-Based Learning

Dana Ernst

Digital versions HTML and PDF
PreTeXt source Yes
Exercises Yes, but see explanation below
Solutions No
Instructor’s Manual Yes
License Creative Commons-Attribution-Share Alike

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.


  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