Writing Proofs in Analysis

  • Jonathan M.┬áKane

Table of contents

  1. Front Matter
    Pages i-xx
  2. Jonathan M. Kane
    Pages 1-8
  3. Jonathan M. Kane
    Pages 9-45
  4. Jonathan M. Kane
    Pages 47-98
  5. Jonathan M. Kane
    Pages 99-132
  6. Jonathan M. Kane
    Pages 133-158
  7. Jonathan M. Kane
    Pages 159-200
  8. Jonathan M. Kane
    Pages 201-237
  9. Jonathan M. Kane
    Pages 239-267
  10. Jonathan M. Kane
    Pages 269-293
  11. Jonathan M. Kane
    Pages 295-340
  12. Back Matter
    Pages 341-347

About this book

Introduction

This is a textbook on proof writing in the area of analysis, balancing a survey of the core concepts of mathematical proof with a tight, rigorous examination of the specific tools needed for an understanding of analysis. Instead of the standard "transition" approach to teaching proofs, wherein students are taught fundamentals of logic, given some common proof strategies such as mathematical induction, and presented with a series of well-written proofs to mimic, this textbook teaches what a student needs to be thinking about when trying to construct a proof. Covering the fundamentals of analysis sufficient for a typical beginning Real Analysis course, it never loses sight of the fact that its primary focus is about proof writing skills.

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.

Keywords

Proof writing Mathematical proofs Complex Analysis Fourier Analysis Functional Analysis Real Analysis

Authors and affiliations

  • Jonathan M.┬áKane
    • 1
  1. 1.Department of MathematicsUniversity of Wisconsin - MadisonMadisonUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-30967-5
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-30965-1
  • Online ISBN 978-3-319-30967-5
  • About this book