Sundstrom T. Mathematical Reasoning: Writing and Proof

Version 2.1. — Grand Valley State University, 2017. — 607 p.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. Another important goal of this text is to provide students with material that will be needed for their further study of mathematics. This type of course has now become a standard part of the mathematics major at many colleges and universities. It is often referred to as a “transition course” from the calculus sequence to the upper-level courses in the major. The transition is from the problem-solving orientation of calculus to the more abstract and theoretical upper-level courses. This is needed today because many students complete their study of calculus without seeing a formal proof or having constructed a proof of their own. This is in contrast to many upper-level mathematics courses, where the emphasis is on the formal development of abstract mathematical ideas, and the expectations are that students will be able to read and understand proofs and be able to construct and write coherent, understandable mathematical proofs. Students should be able to use this text with a background of one semester of calculus.
There are no changes in content between Version 2.0 of this book and Version 2.1. A few minor errors in Version 2.0 have been corrected in Version 2.1. In addition, there are no changes in content between Version 1.1 of this book and Version 2.0. The only change is that Appendix C, Answers and Hints for Selected Exercises, now contains solutions and hints for more exercises. Those exercises with an answer or a hint in the appendix are preceded by a star (*).