MARC 主機 00000nam a2200457 i 4500
001 978-3-319-30967-5
003 DE-He213
005 20161102095523.0
006 m o d
007 cr nn 008maaau
008 160528s2016 gw s 0 eng d
020 9783319309675|q(electronic bk.)
020 9783319309651|q(paper)
024 7 10.1007/978-3-319-30967-5|2doi
040 GP|cGP|erda|dAS
041 0 eng
050 4 QA9.54
082 04 511.36|223
100 1 Kane, Jonathan M.,|eauthor
245 10 Writing proofs in analysis /|cby Jonathan M. Kane
264 1 Cham :|bSpringer International Publishing :|bImprint:
Springer,|c2016
300 1 online resource (xx, 347 pages) :|billustrations,
digital ;|c24 cm
336 text|btxt|2rdacontent
337 computer|bc|2rdamedia
338 online resource|bcr|2rdacarrier
347 text file|bPDF|2rda
505 0 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
520 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
650 0 Proof theory
650 0 Mathematical analysis
650 14 Mathematics
650 24 Functional Analysis
650 24 Fourier Analysis
650 24 Mathematical Logic and Foundations
710 2 SpringerLink (Online service)
773 0 |tSpringer eBooks
856 40 |uhttp://dx.doi.org/10.1007/978-3-319-30967-5
|zeBook(Springerlink)