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Bernhard Riemann, 1826-1866 : turning points in the conception of mathematics

Author: Detlef Laugwitz
Publisher: Boston : Birkhäuser, ©1999.
Edition/Format:   Print book : Biography : EnglishView all editions and formats
Database:WorldCat
Summary:
This book, originally written in German and presented here in an English-language translation, is the first attempt to examine Riemann's scientific work from a single unifying perspective. Laugwitz describes Riemann's development of a conceptual approach to mathematics at a time when conventional algorithmic thinking dictated that formulas and figures, rigid constructs, and transformations of terms were the only  Read more...
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Genre/Form: Biography
History
Named Person: Bernhard Riemann; Bernhard Riemann; Bernhard Riemann; Bernhard Riemann
Material Type: Biography
Document Type: Book
All Authors / Contributors: Detlef Laugwitz
ISBN: 0817640401 9780817640408 3764340401 9783764340407
OCLC Number: 38992931
Description: xvi, 357 pages : illustrations ; 25 cm
Contents: 0. Introduction --
1. Complex Analysis --
1.1. The genesis of complex analysis up to Riemann's time --
1.2. The dissertation of 1851 --
1.3. The elaborations --
1.4. The zeta function and the distribution of primes --
2. Real Analysis --
2.1. Foundations of real analysis --
2.2. Trigonometric series before Riemann --
2.3. Riemann's results --
2.4. Trigonometric series after Riemann --
2.5. A self-contained chapter: Gauss, Riemann, and the Gottingen atmosphere --
3. Geometry; Physics; Philosophy --
3.1. Geometry --
3.2. Physics --
3.3. On philosophy --
4. Turning Points in the Conception of Mathematics --
4.1. The historians' search for revolutions in mathematics --
4.2. Turning point in the conception of the infinite in mathematics --
4.3. Turning point in the method: Thinking instead of computing --
4.4. Turning point in the ontology: Mathematics as thinking in concepts --
4.5. The ontology and methodology of mathematics after Riemann --
4.6. Concluding remarks.
Other Titles: Bernhard Riemann, 1826-1866.
Responsibility: Detlef Laugwitz ; translated by Abe Shenitzer with the editorial assistance of the author, Hardy Grant, and Sarah Shenitzer.

Abstract:

This is an examination of Bernhard Riemann's scientific work from a unifying perspective. His development of a conceptual approach to maths at a time when conventional algorithmic thinking dictated  Read more...

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"Laugwitz's 1996 book in German is an excellent place to begin a study of [Riemann's] life, work, and influence. The 1999 translation...into English is especially welcome... There is excellent Read more...

 
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