Springer Undergraduate Mathematics Series

The Real and the Complex: A History of Analysis in the 19th Century

Authors: Gray, Jeremy

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  • Introduces key ideas in real and complex analysis in the manner they were discovered
  • Motivates and explains many related developments in neighbouring fields, including number theory, elliptic function theory, and potential theory
  • Displays many examples illustrating the merits of rigorous analysis
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eBook $34.99
price for USA in USD (gross)
  • ISBN 978-3-319-23715-2
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $44.99
price for USA in USD
  • ISBN 978-3-319-23714-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

This book contains a history of real and complex analysis in the nineteenth century, from the work of Lagrange and Fourier to the origins of set theory and the modern foundations of analysis. It studies the works of many contributors including Gauss, Cauchy, Riemann, and Weierstrass.

This book is unique owing to the treatment of real and complex analysis as overlapping, inter-related subjects, in keeping with how they were seen at the time. It is suitable as a course in the history of mathematics for students who have studied an introductory course in analysis, and will enrich any course in undergraduate real or complex analysis.

About the authors

Jeremy Gray is the author or co-author of ten books, most recently Hidden Harmony – Geometric Fantasies: the rise of complex function theory (Springer 2013) with Umberto Bottazzini (Milan), upon which this book is based. He is also the author of Henri Poincaré: a scientific biography (Princeton U.P. 2012) and Plato’s Ghost: The Modernist Transformation of Mathematics (Princeton U.P. 2008). In 2009 he was awarded the Albert Leon Whiteman Memorial Prize of the American Mathematical Society for his work in the history of mathematics, and he was elected an inaugural Fellow of the American Mathematical Society in 2012.

Reviews

“The Real and the Complex originated in a course Jeremy Gray gave to upper-level mathematics students and is part of a Springer series on undergraduate mathematics. An important aim of the book is to help the student understand how any given part of mathematics first arises and comes to fruition. … for those readers with some university-level background in mathematics who are interested in the technical contours of nineteenth-century science, Gray’s book will repay careful study and is highly recommended.” (Craig Fraser, Isis, Vol. 108 (2), June, 2017)

“I view it as an extremely valuable addition to my library and a book that I am sure I will consult frequently in the future: this is a text that should serve well as a desk reference for a faculty member teaching either analysis (real or complex) or the history of mathematics. Certainly, no good university library should be without it.” (Mark Hunacek, MAA Reviews, maa.org, January, 2017)

“Gray’s 29 chapters take us on quite a ride through the ideas, results, and difficulties of the major figures of nineteenth-century analysis. …  Any mathematician who would like to know how analysis developed should find it interesting. Those who teach analysis can gain much insight from seeing the blind alleys as well as the great ideas … . The writing style is clear and unpretentious, as well as marked by immense learning. … I strongly recommend … .” (Judith V. Grabiner, Notices of the AMS, Vol. 64 (11), 2017)

“The Real and the Complex … develops the subject of analysis by reviewing the works of some of the prominent mathematicians of the 19th century. … Summing Up: Recommended. Upper-division undergraduates, graduate students, researchers/faculty, professionals/practitioners.” (M. D. Sanford, Choice, Vol. 53 (9), May, 2016)

“This is a history book on the development of mathematics in the 19th century. Each chapter is built up around one or a few mathematicians. … this book is not only an interesting read for the students who (have to) study it, but equally valuable for professional mathematicians.” (Adhemar Bultheel, European Mathematical Society, euro-math-soc.eu, February, 2016)


Table of contents (30 chapters)

Table of contents (30 chapters)

Buy this book

eBook $34.99
price for USA in USD (gross)
  • ISBN 978-3-319-23715-2
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $44.99
price for USA in USD
  • ISBN 978-3-319-23714-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
The Real and the Complex: A History of Analysis in the 19th Century
Authors
Series Title
Springer Undergraduate Mathematics Series
Copyright
2015
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-23715-2
DOI
10.1007/978-3-319-23715-2
Softcover ISBN
978-3-319-23714-5
Series ISSN
1615-2085
Edition Number
1
Number of Pages
XVI, 350
Number of Illustrations
71 b/w illustrations
Topics