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The tools of mathematical reasoning. (English) Zbl 06639730
Pure and Applied Undergraduate Texts 26. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-2899-0/hbk; 978-1-4704-3496-0/ebook). xiii, 217 p. (2016).
Preliminary review / Publisher’s description: This accessible textbook gives beginning undergraduate mathematics students a first exposure to introductory logic, proofs, sets, functions, number theory, relations, finite and infinite sets, and the foundations of analysis. The book provides students with a quick path to writing proofs and a practical collection of tools that they can use in later mathematics courses such as abstract algebra and analysis. The importance of the logical structure of a mathematical statement as a framework for finding a proof of that statement, and the proper use of variables, is an early and consistent theme used throughout the book.

MSC:
97-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mathematics education
97E10 Comprehensive works on education of foundations of mathematics
97E30 Logic (educational aspects)
97E40 Language of mathematics (educational aspects)
97E50 Reasoning and proving in the mathematics classroom
97E60 Sets, relations, set theory (educational aspects)
00A05 Mathematics in general
00A35 Methodology of mathematics
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