Mathematical Reasoning: Writing and Proof

Ted Sundstrom

Digital versions PDF
Latex source No
Exercises Yes
Solutions Answers and hints to selected problems
License Creative Commons Attribution-NonCommercial-ShareAlike
Unofficial HTML version Yes
Unofficial PreTeXt source Yes
  • Sophomore level text for an introduction to proofs course
  • Winner of the inaugural MAA Solow Award in 2017
  • Version 2.1, 2022
  • Originally published by Pearson (two editions: 2003 and 2007)
  • Printed version ($22) or Kindle version ($10) available from Amazon
  • Nine chapters, 588 pages
  • Solution manual for instructors available from author
  • Progress checks, Preview activities, Evaluation of proofs, Study guides
  • 107 videos, each four to ten minutes long
  • Course adoption list on book’s homepage
  • For more information and to download
  • Unofficial HTML version, sanctioned by the author, that diverges slightly from the official PDF version
  • Unofficial PreTeXt source

This book emphasizes effective communication of mathematics through writing and it promotes active learning by the students. Notable features include preview activities for each section intended for students to do before class and progress checks within the text for the student to do on the spot, with answers at the end of the book.

Some exercises are “Evaluation of Proofs,” described in the preface:

For these exercises, there is a proposed proof of a proposition. However, the proposition may be true or may be false. If a proposition is false, the proposed proof is, of course, incorrect, and the student is asked to find the error in the proof and then provide a counterexample showing that the proposition is false. However, if the proposition is true, the proof may be incorrect or not well written. In keeping with the emphasis on writing, students are then asked to correct the proof and/or provide a well-written proof according to the guidelines established in the book.


  1. Introduction
  2. Logical Reasoning
  3. Constructing and Writing Proofs
  4. Mathematical Induction
  5. Set Theory
  6. Functions
  7. Equivalence Relations
  8. Topics in Number Theory
  9. Finite and Infinite Sets