000 03402nam a22004935i 4500
001 978-3-319-30967-5
003 DE-He213
005 20181204134231.0
007 cr nn 008mamaa
008 160528s2016 gw | s |||| 0|eng d
020 _a9783319309675
_9978-3-319-30967-5
024 7 _a10.1007/978-3-319-30967-5
_2doi
040 _aISI Library, Kolkata
050 4 _aQA319-329.9
072 7 _aPBKF
_2bicssc
072 7 _aMAT037000
_2bisacsh
072 7 _aPBKF
_2thema
082 0 4 _a515.7
_223
100 1 _aKane, Jonathan M.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aWriting Proofs in Analysis
_h[electronic resource] /
_cby Jonathan M. Kane.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2016.
300 _aXX, 347 p. 79 illus., 4 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
505 0 _aWhat 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 _aThis 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 _aFunctional analysis.
650 0 _aFourier analysis.
650 0 _aLogic, Symbolic and mathematical.
650 1 4 _aFunctional Analysis.
_0http://scigraph.springernature.com/things/product-market-codes/M12066
650 2 4 _aFourier Analysis.
_0http://scigraph.springernature.com/things/product-market-codes/M12058
650 2 4 _aMathematical Logic and Foundations.
_0http://scigraph.springernature.com/things/product-market-codes/M24005
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783319309651
776 0 8 _iPrinted edition:
_z9783319309668
776 0 8 _iPrinted edition:
_z9783319809311
856 4 0 _uhttps://doi.org/10.1007/978-3-319-30967-5
912 _aZDB-2-SMA
942 _cEB
950 _aMathematics and Statistics (Springer-11649)
999 _c426632
_d426632