LEADER 03382nam 22005295 450 001 9910279756303321 005 20200706181651.0 010 $a1-4939-6795-9 024 7 $a10.1007/978-1-4939-6795-7 035 $a(CKB)4100000004243399 035 $a(DE-He213)978-1-4939-6795-7 035 $a(MiAaPQ)EBC6315391 035 $a(PPN)227400127 035 $a(EXLCZ)994100000004243399 100 $a20180511d2017 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAmazing and Aesthetic Aspects of Analysis$b[electronic resource] /$fby Paul Loya 205 $a1st ed. 2017. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d2017. 215 $a1 online resource (XV, 722 p. 122 illus.) 225 1 $aUndergraduate texts in mathematics 311 $a1-4939-6793-2 320 $aIncludes bibliographical references and index. 327 $aPreface -- Some of the most beautiful formulæ in the world -- Part 1. Some standard curriculum -- 1. Very naive set theory, functions, and proofs -- 2. Numbers, numbers, and more numbers -- 3. Infinite sequences of real and complex numbers -- 4. Limits, continuity, and elementary functions -- 5. Some of the most beautiful formulæ in the world I-III -- Part 2. Extracurricular activities -- 6. Advanced theory of infinite series -- 7. More on the infinite: Products and partial fractions -- 8. Infinite continued fractions -- Bibliography -- Index . 330 $aLively prose and imaginative exercises draw the reader into this unique introductory real analysis textbook. Motivating the fundamental ideas and theorems that underpin real analysis with historical remarks and well-chosen quotes, the author shares his enthusiasm for the subject throughout. A student reading this book is invited not only to acquire proficiency in the fundamentals of analysis, but to develop an appreciation for abstraction and the language of its expression. In studying this book, students will encounter: the interconnections between set theory and mathematical statements and proofs; the fundamental axioms of the natural, integer, and real numbers; rigorous ?-N and ?-? definitions; convergence and properties of an infinite series, product, or continued fraction; series, product, and continued fraction formulæ for the various elementary functions and constants. Instructors will appreciate this engaging perspective, showcasing the beauty of these fundamental results. 410 0$aUndergraduate texts in mathematics. 606 $aSequences (Mathematics) 606 $aFunctions of real variables 606 $aSequences, Series, Summability$3https://scigraph.springernature.com/ontologies/product-market-codes/M1218X 606 $aReal Functions$3https://scigraph.springernature.com/ontologies/product-market-codes/M12171 615 0$aSequences (Mathematics). 615 0$aFunctions of real variables. 615 14$aSequences, Series, Summability. 615 24$aReal Functions. 676 $a515 700 $aLoya$b Paul$4aut$4http://id.loc.gov/vocabulary/relators/aut$0767657 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910279756303321 996 $aAmazing and Aesthetic Aspects of Analysis$91563129 997 $aUNINA