Writing Proofs in Analysis
Springer International Publishing (Verlag)
978-3-319-30965-1 (ISBN)
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.
Jonathan Michael Kane is an emeritus professor of Mathematical and Computer Sciences at the University of Wisconsin – Whitewater and an honorary fellow of the Department of Mathematics at the University of Wisconsin – Madison. He has published papers in several complex variables, probability, algorithms, and the relationship between gender and culture in mathematics performance. He has taught dozens of courses in mathematics, statistics, actuarial mathematics, and computer science. Dr. Kane plays a major role in contest mathematics by chairing the American Invitational Mathematics Exam Committee, cofounding and coordinating the annual online Purple Comet! Math Meet, and teaching at the AwesomeMath summer program.
What Are Proofs, And Why Do We Write Them?.- The Basics of Proofs.- Limits.- Continuity.- Derivatives.- Riemann Integrals.- Infinite Series.- Sequences of Functions.- Topology of the Real Line.- Metric Spaces .
"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)
| Erscheinungsdatum | 08.10.2016 |
|---|---|
| Zusatzinfo | XX, 347 p. 79 illus., 75 illus. in color. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika |
| Mathematik / Informatik ► Mathematik ► Analysis | |
| Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre | |
| Schlagworte | Complex Analysis • fourier analysis • Functional Analysis • Mathematical Logic and Foundations • mathematical proofs • mathematics and statistics • proof writing • Real analysis |
| ISBN-10 | 3-319-30965-X / 331930965X |
| ISBN-13 | 978-3-319-30965-1 / 9783319309651 |
| Zustand | Neuware |
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