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Download Mathematical Induction (460 KB)

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

Download Appendix B: Answers for the Progress Checks (400 KB)

Download Appendix C: Answers and Hints for Selected Exercises (457 KB)

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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.

ISBN

9781492103851

Publication Date

6-2014

Keywords

proofs course, transition course, mathematical writing, proof writing

Comments

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

For solutions, please contact the author at mathreasoning@gmail.com.

This book has been reviewed by the American Institute of Mathematics Open Textbook Initiative. http://www.aimath.org/textbooks/

This work is licensed under the Creative Commons Attribution-NonCommercial- ShareAlike 3.0 Unported License. http://creativecommons.org/licenses/by-nc-sa/3.0/

This book can be purchased through CreateSpace or Amazon.

Mathematical Reasoning: Writing and Proof, Version 2.0

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