LEADER 03516nam 22005895 450 001 9910254074303321 005 20200630040006.0 010 $a3-319-30967-6 024 7 $a10.1007/978-3-319-30967-5 035 $a(CKB)3710000000717746 035 $a(DE-He213)978-3-319-30967-5 035 $a(MiAaPQ)EBC6311719 035 $a(MiAaPQ)EBC5578372 035 $a(Au-PeEL)EBL5578372 035 $a(OCoLC)951425440 035 $a(PPN)194079228 035 $a(EXLCZ)993710000000717746 100 $a20160528d2016 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aWriting Proofs in Analysis /$fby Jonathan M. Kane 205 $a1st ed. 2016. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2016. 215 $a1 online resource (XX, 347 p. 79 illus., 4 illus. in color.) 300 $aIncludes Index. 311 $a3-319-30965-X 327 $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 . 330 $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. 606 $aFunctional analysis 606 $aFourier analysis 606 $aMathematical logic 606 $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066 606 $aFourier Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12058 606 $aMathematical Logic and Foundations$3https://scigraph.springernature.com/ontologies/product-market-codes/M24005 615 0$aFunctional analysis. 615 0$aFourier analysis. 615 0$aMathematical logic. 615 14$aFunctional Analysis. 615 24$aFourier Analysis. 615 24$aMathematical Logic and Foundations. 676 $a511.36 700 $aKane$b Jonathan M$4aut$4http://id.loc.gov/vocabulary/relators/aut$0756126 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254074303321 996 $aWriting proofs in analysis$91523721 997 $aUNINA