# Mathematical Reasoning: Writing and Proof, Version 2.1

## Authors

Mathematical Reasoning: Writing and Proof Version 3 is also available: https://scholarworks.gvsu.edu/books/24/

## Files

Note to Students (61 KB)

Preface (106 KB)

Introduction to Writing Proofs in Mathematics (327 KB)

Logical Reasoning (459 KB)

Constructing and Writing Proofs in Mathematics (826 KB)

Mathematical Induction (457 KB)

Set Theory (632 KB)

Functions (827 KB)

Equivalence Relations (522 KB)

Topics in Number Theory (396 KB)

Finite and Infinite Sets (422 KB)

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

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

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

Appendix D: List of Symbols (65 KB)

Index (88 KB)

## Description

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.

9781492103851

6-2014

## Keywords

proofs course, transition course, mathematical writing, proof writing

Screencasts designed for use with the book can be found at http://www.youtube.com/playlist?list=PL2419488168AE7001.

Note to Instructors: Please contact Ted Sundstrom at mathreasoning@gmail.com 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. http://www.aimath.org/textbooks/