Mathematical Reasoning: Writing and Proof Version 3 is also available:



Download Full Text (6.0 MB)

Download Note to Students (61 KB)

Download Preface (106 KB)

Download Introduction to Writing Proofs in Mathematics (327 KB)

Download Logical Reasoning (459 KB)

Download Constructing and Writing Proofs in Mathematics (826 KB)

Download Mathematical Induction (457 KB)

Download Set Theory (632 KB)

Download Functions (827 KB)

Download Equivalence Relations (522 KB)

Download Topics in Number Theory (396 KB)

Download Finite and Infinite Sets (422 KB)

Download Appendix A: Guidelines for Writing Mathematical Proofs (87 KB)

Download Appendix B: Answers for the Progress Checks (401 KB)

Download Appendix C: Answers and Hints for Selected Exercises (455 KB)

Download Appendix D: List of Symbols (65 KB)

Download Index (88 KB)


Mathematical Reasoning: Writing and Proof is designed to be a text for the first course in the college mathematics curriculum that introduces students to the processes of constructing and writing proofs and focuses on the formal development of mathematics. The primary goals of the text are to help students:

· Develop logical thinking skills and to develop the ability to think more abstractly in a proof oriented setting.

· Develop the ability to construct and write mathematical proofs using standard methods of mathematical proof including direct proofs, proof by contradiction, mathematical induction, case analysis, and counterexamples.

· Develop the ability to read and understand written mathematical proofs.

· Develop talents for creative thinking and problem solving.

· Improve their quality of communication in mathematics. This includes improving writing techniques, reading comprehension, and oral communication in mathematics.

· Better understand the nature of mathematics and its language.

This text also provides students with material that will be needed for their further study of mathematics.



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Creative Commons Attribution-Noncommercial-Share Alike 3.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.


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Screencasts designed for use with the book can be found at

Note to Instructors: Please contact Ted Sundstrom at for information about instructor resources such as solutions to the preview activities and solutions to the exercises. In your email, please include the name of your institution (school, college, or university), the course for which you are considering using the text, and a link to a website that can be used to verify your position at your institution.

This book has been reviewed by the American Institute of Mathematics Open Textbook Initiative.

This work is licensed under the Creative Commons Attribution-NonCommercial- ShareAlike 3.0 Unported License.

This book can be purchased through Amazon.

Additional information about this book can be found here.

Mathematical Reasoning: Writing and Proof, Version 2.1