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History of Mathematics Subseries

What is the Genus?

Authors: Popescu-Pampu, Patrick

  • Presents, through the works of the pioneers, the sophisticated evolution of one of the most important notions of geometry and topology
  • Features many illustrations which aid the understanding of the more complicated constructions
  • Excepting M. Audin's novel La formule de Stokes, there are no similar books
  • Explains many connections between analysis, algebra, number theory, geometry and topology
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eBook $44.99
price for USA in USD (gross)
  • ISBN 978-3-319-42312-8
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.99
price for USA in USD
  • ISBN 978-3-319-42311-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

Exploring several of the evolutionary branches of the mathematical notion of genus, this book traces the idea from its prehistory in problems of integration, through algebraic curves and their associated Riemann surfaces, into algebraic surfaces, and finally into higher dimensions. Its importance in analysis, algebraic geometry, number theory and topology is emphasized through many theorems. Almost every chapter is organized around excerpts from a research paper in which a new perspective was brought on the genus or on one of the objects to which this notion applies. The author was motivated by the belief that a subject may best be understood and communicated by studying its broad lines of development, feeling the way one arrives at the definitions of its fundamental notions, and appreciating the amount of effort spent in order to explore its phenomena.

Reviews

“This book provides a fascinating—yet technically quite demanding—tour of the ideas and generalizations that feed into our modern conception of the genus. It should therefore serve as a useful starting point for historical and even philosophical investigations into past mathematical practice of forming and shaping concepts. It may also be useful in teaching advanced mathematical content with a view to historical development … .” (Henrik Kragh Sørensen, ISIS, Vol. 109 (2), June, 2018)
“This book is addressed to any person with a little knowledge of mathematics (such as an undergraduate student) who wants to get an idea of some of the most important concepts that arose in geometry and topology in the last couple of centuries: the author has made a commendable effort to explain all the more advanced concepts almost from scratch (but obviously this was not possible for the last chapter).” (Pietro De Poi, Mathematical Reviews, July, 2017)

“This clear book thoroughly covers the metamorphosis and theoretical significance of the genus by using several historical approaches that incorporate discussions related to analysis, algebraic geometry, number theory, and topology. … The book contains 20 figures and concludes with a list of 200 references and an index, which will help those who wish to delve into deeper studies. Summing Up: Recommended. Upper-division undergraduates and above; faculty and professionals.” (D. P. Turner, Choice, Vol. 54 (9), May, 2017)


Table of contents (46 chapters)

  • The γ 𝜀 ́ ν o ς $$\gamma \acute{\varepsilon }\nu o\varsigma$$ According to Aristotle

    Popescu-Pampu, Patrick

    Pages 1-1

  • Descartes and the New World of Curves

    Popescu-Pampu, Patrick

    Pages 5-6

  • Newton and the Classification of Curves

    Popescu-Pampu, Patrick

    Pages 7-8

  • When Integrals Hide Curves

    Popescu-Pampu, Patrick

    Pages 9-10

  • Jakob Bernoulli and the Construction of Curves

    Popescu-Pampu, Patrick

    Pages 11-13

Buy this book

eBook $44.99
price for USA in USD (gross)
  • ISBN 978-3-319-42312-8
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.99
price for USA in USD
  • ISBN 978-3-319-42311-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
What is the Genus?
Authors
Series Title
History of Mathematics Subseries
Series Volume
2162
Copyright
2016
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-42312-8
DOI
10.1007/978-3-319-42312-8
Softcover ISBN
978-3-319-42311-1
Series ISSN
2193-1771
Edition Number
1
Number of Pages
XVII, 184
Number of Illustrations and Tables
20 b/w illustrations
Topics