國立虎尾科技大學 |

A Brief History of Analysis = With Emphasis on Philosophy, Concepts, and Numbers, Including Weierstraß' Real Numbers /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	A Brief History of Analysis/ by Detlef D. Spalt.
其他題名:	With Emphasis on Philosophy, Concepts, and Numbers, Including Weierstraß' Real Numbers /
作者:	Spalt, Detlef D.
面頁冊數:	XXIII, 254 p. 23 illus.online resource. :
Contained By:	Springer Nature eBook
標題:	Analysis. -
電子資源:	https://doi.org/10.1007/978-3-031-00650-0
ISBN:	9783031006500

A Brief History of Analysis = With Emphasis on Philosophy, Concepts, and Numbers, Including Weierstraß' Real Numbers /
Spalt, Detlef D.

A Brief History of AnalysisWith Emphasis on Philosophy, Concepts, and Numbers, Including Weierstraß' Real Numbers /[electronic resource] :by Detlef D. Spalt. - 1st ed. 2022. - XXIII, 254 p. 23 illus.online resource.

The Invention of the Mathematical Formula -- Numbers, Distances, Points, but No Crooked Lines -- Lines and Variables -- Individual: An Old Term, or What Does the Continuum Consist of? -- Are There Infinite Numbers? - An Unresolved Argument Between Leibniz and Johann Bernoulli -- Johann Bernoulli's Rules of Differential -- What Does "Equal" Mean? -- Euler Absolutizes Formal Arithmetic -- Accents in Algebraic Analysis, According to Euler -- Bolzano: The Republican Revolutionary of Analysis -- Cauchy: The Bourgeois Revolutionary as a Restorer -- The Interregnum: Analysis on Swampy Ground -- Weierstrass: The Last Attempt at a Substantial Analysis -- The Detachment of Analysis from Reality, and the Introduction of Actual Infinity into the Fundamentals of Mathematics -- Analysis With or Without Paradoxes.

This book explores the origins of mathematical analysis in an accessible, clear, and precise manner. Concepts such as function, continuity, and convergence are presented with a unique historical point of view. In part, this is accomplished by investigating the impact of and connections between famous figures, like Newton, Leibniz, Johann Bernoulli, Euler, and more. Of particular note is the treatment of Karl Weierstraß, whose concept of real numbers has been frequently overlooked until now. By providing such a broad yet detailed survey, this book examines how analysis was formed, how it has changed over time, and how it continues to evolve today. A Brief History of Analysis will appeal to a wide audience of students, instructors, and researchers who are interested in discovering new historical perspectives on otherwise familiar mathematical ideas.

ISBN: 9783031006500

Standard No.: 10.1007/978-3-031-00650-0doiSubjects--Topical Terms:

669490
Analysis.

LC Class. No.: QA21-27

Dewey Class. No.: 510.9

A Brief History of Analysis = With Emphasis on Philosophy, Concepts, and Numbers, Including Weierstraß' Real Numbers /
LDR:03271nam a22004455i 4500 001 1089260
003 DE-He213
005 20220802190850.0
007 cr nn 008mamaa
008 221228s2022 sz | s |||| 0|eng d
020 $a 9783031006500 $9 978-3-031-00650-0
024 7 $a 10.1007/978-3-031-00650-0 $2 doi
035 $a 978-3-031-00650-0
050 4 $a QA21-27
072 7 $a PBX $2 bicssc
072 7 $a MAT015000 $2 bisacsh
072 7 $a PBX $2 thema
082 0 4 $a 510.9 $2 23
100 1 $a Spalt, Detlef D. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1306531
245 1 2 $a A Brief History of Analysis $h [electronic resource] : $b With Emphasis on Philosophy, Concepts, and Numbers, Including Weierstraß' Real Numbers / $c by Detlef D. Spalt.
250 $a 1st ed. 2022.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Birkhäuser, $c 2022.
300 $a XXIII, 254 p. 23 illus. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
505 0 $a The Invention of the Mathematical Formula -- Numbers, Distances, Points, but No Crooked Lines -- Lines and Variables -- Individual: An Old Term, or What Does the Continuum Consist of? -- Are There Infinite Numbers? - An Unresolved Argument Between Leibniz and Johann Bernoulli -- Johann Bernoulli's Rules of Differential -- What Does "Equal" Mean? -- Euler Absolutizes Formal Arithmetic -- Accents in Algebraic Analysis, According to Euler -- Bolzano: The Republican Revolutionary of Analysis -- Cauchy: The Bourgeois Revolutionary as a Restorer -- The Interregnum: Analysis on Swampy Ground -- Weierstrass: The Last Attempt at a Substantial Analysis -- The Detachment of Analysis from Reality, and the Introduction of Actual Infinity into the Fundamentals of Mathematics -- Analysis With or Without Paradoxes.
520 $a This book explores the origins of mathematical analysis in an accessible, clear, and precise manner. Concepts such as function, continuity, and convergence are presented with a unique historical point of view. In part, this is accomplished by investigating the impact of and connections between famous figures, like Newton, Leibniz, Johann Bernoulli, Euler, and more. Of particular note is the treatment of Karl Weierstraß, whose concept of real numbers has been frequently overlooked until now. By providing such a broad yet detailed survey, this book examines how analysis was formed, how it has changed over time, and how it continues to evolve today. A Brief History of Analysis will appeal to a wide audience of students, instructors, and researchers who are interested in discovering new historical perspectives on otherwise familiar mathematical ideas.
650 2 4 $a Analysis. $3 669490
650 1 4 $a History of Mathematical Sciences. $3 785417
650 0 $a Mathematical analysis. $3 527926
650 0 $a History. $3 669538
650 0 $a Mathematics. $3 527692
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783031006494
776 0 8 $i Printed edition: $z 9783031006517
776 0 8 $i Printed edition: $z 9783031006524
776 0 8 $i Printed edition: $z 9783031029080
776 0 8 $i Printed edition: $z 9783031029073
776 0 8 $i Printed edition: $z 9783031029066
776 0 8 $i Printed edition: $z 9783031029059
856 4 0 $u https://doi.org/10.1007/978-3-031-00650-0
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)