LEADER 03161nam 22004695 450 001 9910682550003321 005 20230526100906.0 010 $a3-031-19738-0 024 7 $a10.1007/978-3-031-19738-3 035 $a(CKB)5580000000524083 035 $a(DE-He213)978-3-031-19738-3 035 $a(EXLCZ)995580000000524083 100 $a20230315d2022 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 12$aA Circle-Line Study of Mathematical Analysis$b[electronic resource] /$fby Simone Secchi 205 $a1st ed. 2022. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2022. 215 $a1 online resource (XIX, 469 p. 1 illus.) 225 1 $aLa Matematica per il 3+2,$x2038-5757 ;$v141 311 $a3-031-19737-2 327 $aPart I First half of the journey -- 1 An appetizer of propositional logic -- 2 Sets, relations, functions in a naïve way -- 3 Numbers -- 4 Elementary cardinality -- 5 Distance, topology and sequences on the set of real numbers -- 6 Series -- 7 Limits: from sequences to functions of a real variable -- 8 Continuous functions of a real variable -- 9 Derivatives and differentiability- 10 Riemann?s integral -- 11 Elementary functions -- Part II Second half of the journey -- 12 Return to Set Theory -- 13 Neighbors again: topological spaces -- 14 Differentiating again: linearization in normed spaces -- 15 A functional approach to Lebesgue integration theory -- 16 Measures before integrals. 330 $aThe book addresses the rigorous foundations of mathematical analysis. The first part presents a complete discussion of the fundamental topics: a review of naive set theory, the structure of real numbers, the topology of R, sequences, series, limits, differentiation and integration according to Riemann. The second part provides a more mature return to these topics: a possible axiomatization of set theory, an introduction to general topology with a particular attention to convergence in abstract spaces, a construction of the abstract Lebesgue integral in the spirit of Daniell, and the discussion of differentiation in normed linear spaces. The book can be used for graduate courses in real and abstract analysis and can also be useful as a self-study for students who begin a Ph.D. program in Analysis. The first part of the book may also be suggested as a second reading for undergraduate students with a strong interest in mathematical analysis. 410 0$aLa Matematica per il 3+2,$x2038-5757 ;$v141 606 $aMathematical analysis 606 $aAnalysis 606 $aAnàlisi matemàtica$2thub 606 $aTeoria de conjunts$2thub 608 $aLlibres electrònics$2thub 615 0$aMathematical analysis. 615 14$aAnalysis. 615 7$aAnàlisi matemàtica 615 7$aTeoria de conjunts 676 $a515 700 $aSecchi$b Simone$4aut$4http://id.loc.gov/vocabulary/relators/aut$08582 906 $aBOOK 912 $a9910682550003321 996 $aA Circle-Line Study of Mathematical Analysis$93091289 997 $aUNINA