Authors:
- Teaches how to write proofs by describing what students should be thinking about when faced with writing a proof
- Provides proof templates for proofs that follow the same general structure
- Blends topics of logic into discussions of proofs in the context where they are needed
- Thoroughly covers the concepts and theorems of introductory in Real Analysis including limits, continuity, differentiation, integration, infinite series, sequences of functions, topology of the real line, and metric spaces
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Table of contents (10 chapters)
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Front Matter
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Back Matter
About this book
This book aims to give the student precise training in the writing of proofs by explaining exactly what elements make up a correct proof, how one goes about constructing an acceptable proof, and, by learning to recognize a correct proof, how to avoid writing incorrect proofs. To this end, all proofs presented in this text are preceded by detailed explanations describing the thought process one goes through when constructing the proof. Over 150 example proofs, templates, and axioms are presented alongside full-color diagrams to elucidate the topics at hand.
Reviews
“This book is well written and so it is also very convenient as a textbook for a standard one-semester course in real analysis.” (Petr Gurka, zbMATH 1454.26001, 2021)
“This is a well-written book with definitions embedded in the text—these are easily identified by bold type throughout the work. The theorems and proofs are set apart from the text and appear in boxes that follow discussions that motivate them. … Summing Up: Recommended. Lower- and upper-division undergraduates; researchers and faculty.” (J. R. Burke, Choice, Vol. 54 (7), March, 2017)
“Its objective is to make the reader understand the thought processes behind the proofs. In this it succeeds admirable, and then book should be in every mathematical library, public and private. … The book is excellently produced with many coloured diagrams.” (P. S. Bullen, Mathematical Reviews, January, 2017)
“I think this is indeed a fabulous book for the kind of course I just suggested. I think that it will indeed serve as Kane projects it should, and the surviving student will truly know a good deal about writing a mathematical proof, in fact, about thinking about the problems and assertions beforehand and then going about the task of constructing the proof.” (Michael Berg, MAA Reviews, August, 2016)
Authors and Affiliations
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Department of Mathematics, University of Wisconsin - Madison, Madison, USA
Jonathan M. Kane
About the author
Bibliographic Information
Book Title: Writing Proofs in Analysis
Authors: Jonathan M. Kane
DOI: https://doi.org/10.1007/978-3-319-30967-5
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2016
Hardcover ISBN: 978-3-319-30965-1Published: 06 June 2016
Softcover ISBN: 978-3-319-80931-1Published: 30 May 2018
eBook ISBN: 978-3-319-30967-5Published: 28 May 2016
Edition Number: 1
Number of Pages: XX, 347
Number of Illustrations: 4 b/w illustrations, 75 illustrations in colour
Topics: Functional Analysis, Fourier Analysis, Mathematical Logic and Foundations