rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Writing Proofs in Analysis
  name:
    name part: Kane, Jonathan M.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2016
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XX, 347 p. 79 illus., 4 illus. in color. online resource.
  abstract: 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.
  table of contents: 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 .
  note: by Jonathan M. Kane.
  subject:
    topic: Mathematics
  subject:
    topic: Fourier analysis
  subject:
    topic: Functional analysis
  subject:
    topic: Mathematical logic
  subject:
    topic: Mathematics
  subject:
    topic: Functional Analysis
  subject:
    topic: Fourier Analysis
  subject:
    topic: Mathematical Logic and Foundations
  classification: QA319-329.9
  classification: 515.7
  related item:
    title info:
      title: Springer eBooks
  identifier: 9783319309675
  identifier: http://dx.doi.org/10.1007/978-3-319-30967-5
  record info:
    record creation date: 160528
    record change date: 20160528142540.0
    record identifier: 978-3-319-30967-5