LEADER 03157nam 22005415 450 001 9910254095503321 005 20200704065305.0 010 $a981-10-1789-1 024 7 $a10.1007/978-981-10-1789-6 035 $a(CKB)3710000000837592 035 $a(DE-He213)978-981-10-1789-6 035 $a(MiAaPQ)EBC6314896 035 $a(MiAaPQ)EBC5555641 035 $a(Au-PeEL)EBL5555641 035 $a(OCoLC)959934072 035 $a(PPN)19480254X 035 $a(EXLCZ)993710000000837592 100 $a20160829d2016 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAnalysis I$b[electronic resource] $eThird Edition /$fby Terence Tao 205 $a1st ed. 2016. 210 1$aSingapore :$cSpringer Singapore :$cImprint: Springer,$d2016. 215 $a1 online resource (XIX, 350 p.) 225 1 $aTexts and Readings in Mathematics,$x2366-8717 ;$v37 300 $aIncludes index. 311 $a981-10-1788-3 327 $aChapter 1. Introduction -- Chapter 2. Starting at the beginning: the natural numbers -- Chapter 3. Set theory -- Chapter 4. Integers and rationals -- Chapter 5. The real numbers -- Chapter 6. Limits of sequences -- Chapter 7. Series -- Chapter 8. Infinite sets -- Chapter 9. Continuous functions on R -- Chapter 10. Differentiation of functions -- Chapter 11. The Riemann integral. . 330 $aThis is part one of a two-volume book on real analysis and is intended for senior undergraduate students of mathematics who have already been exposed to calculus. The emphasis is on rigour and foundations of analysis. Beginning with the construction of the number systems and set theory, the book discusses the basics of analysis (limits, series, continuity, differentiation, Riemann integration), through to power series, several variable calculus and Fourier analysis, and then finally the Lebesgue integral. These are almost entirely set in the concrete setting of the real line and Euclidean spaces, although there is some material on abstract metric and topological spaces. The book also has appendices on mathematical logic and the decimal system. The entire text (omitting some less central topics) can be taught in two quarters of 25?30 lectures each. The course material is deeply intertwined with the exercises, as it is intended that the student actively learn the material (and practice thinking and writing rigorously) by proving several of the key results in the theory. . 410 0$aTexts and Readings in Mathematics,$x2366-8717 ;$v37 606 $aMathematical analysis 606 $aAnalysis (Mathematics) 606 $aAnalysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12007 615 0$aMathematical analysis. 615 0$aAnalysis (Mathematics). 615 14$aAnalysis. 676 $a515 700 $aTao$b Terence$4aut$4http://id.loc.gov/vocabulary/relators/aut$0477043 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254095503321 996 $aAnalysis I$91523142 997 $aUNINA