Mathematical Reasoning: Writing and Proof, Version 2.1

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Ted Sundstrom, Grand Valley State University

Pub Date: 2014

ISBN 13: 978-1-4921038-5-1

Publisher: Grand Valley State University

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Table of Contents

  • Note to Students
  • Preface
  • Introduction to Writing Proofs in Mathematics
  • Logical Reasoning
  • Constructing and Writing Proofs in Mathematics
  • Mathematical Induction
  • Set Theory
  • Functions
  • Equivalence Relations
  • Topics in Number Theory
  • Finite and Infinite Sets
  • Appendix A: Guidelines for Writing Mathematical Proofs
  • Appendix B: Answers for the Progress Checks
  • Appendix C: Answers and Hints for Selected Exercises
  • Appendix D: List of Symbols
  • Index

About the Book

Mathematical Reasoning: Writing and Proof is designed to be a text for the ?rst 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.

About the Contributors


Ted Sundstrom, Professor of Mathematics, Grand Valley State University. PhD, (Mathematics), University of Massachusetts. Dissertation: Groups of Automorphisms of Simple Rings.