LEADER 03096oam 2200517 450 001 996466568603316 005 20210708224430.0 010 $a3-030-64701-3 024 7 $a10.1007/978-3-030-64701-8 035 $a(CKB)4100000011772832 035 $a(DE-He213)978-3-030-64701-8 035 $a(MiAaPQ)EBC6480698 035 $a(PPN)253859115 035 $a(EXLCZ)994100000011772832 100 $a20210708d2021 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aReal analysis $efoundations /$fSergeĭ Ovchinnikov 205 $a1st ed. 2021. 210 1$aCham, Switzerland :$cSpringer,$d[2021] 210 4$d©2021 215 $a1 online resource (XII, 178 p. 13 illus.) 225 1 $aUniversitext 311 $a3-030-64700-5 320 $aIncludes bibliographical references and index. 327 $a1 Rational Numbers -- 2 Real Numbers -- 3 Continuous Functions -- 4 Differentiation -- 5 Integration -- 6 Infinite Series -- A Natural Numbers and Integers -- B Dedekind's Construction of Real Numbers. C A Panorama of Ordered Fields. 330 $aThis textbook explores the foundations of real analysis using the framework of general ordered fields, demonstrating the multifaceted nature of the area. Focusing on the logical structure of real analysis, the definitions and interrelations between core concepts are illustrated with the use of numerous examples and counterexamples. Readers will learn of the equivalence between various theorems and the completeness property of the underlying ordered field. These equivalences emphasize the fundamental role of real numbers in analysis. Comprising six chapters, the book opens with a rigorous presentation of the theories of rational and real numbers in the framework of ordered fields. This is followed by an accessible exploration of standard topics of elementary real analysis, including continuous functions, differentiation, integration, and infinite series. Readers will find this text conveniently self-contained, with three appendices included after the main text, covering an overview of natural numbers and integers, Dedekind's construction of real numbers, historical notes, and selected topics in algebra. Real Analysis: Foundations is ideal for students at the upper-undergraduate or beginning graduate level who are interested in the logical underpinnings of real analysis. With over 130 exercises, it is suitable for a one-semester course on elementary real analysis, as well as independent study. 410 0$aUniversitext. 606 $aMathematical analysis 606 $aFunctions of real variables 606 $aOrdered fields 615 0$aMathematical analysis. 615 0$aFunctions of real variables. 615 0$aOrdered fields. 676 $a515.8 700 $aOvchinnikov$b Sergeĭ$01221216 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bUtOrBLW 906 $aBOOK 912 $a996466568603316 996 $aReal analysis$92831828 997 $aUNISA