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Springer Undergraduate Mathematics Series

From Natural Numbers to Quaternions

Authors: Kramer, Jürg, von Pippich, Anna-Maria

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  • Provides a self-contained introduction to the construction of integers, rationals, reals, complex numbers and Hamilton's quaternions
  • Develops the basic prerequisites in group and ring theory as well as elementary number theory
  • Contains appendices to each chapter highlighting the ubiquity of the material
  • Includes more than 100 exercises with solutions
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eBook $34.99
price for USA in USD (gross)
  • ISBN 978-3-319-69429-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $44.99
price for USA in USD
  • ISBN 978-3-319-69427-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

This textbook offers an invitation to modern algebra through number systems of increasing complexity, beginning with the natural numbers and culminating with Hamilton's quaternions.

Along the way, the authors carefully develop the necessary concepts and methods from abstract algebra: monoids, groups, rings, fields, and skew fields. Each chapter ends with an appendix discussing related topics from algebra and number theory, including recent developments reflecting the relevance of the material to current research.

The present volume is intended for undergraduate courses in abstract algebra or elementary number theory. The inclusion of exercises with solutions also makes it suitable for self-study and accessible to anyone with an interest in modern algebra and number theory.

About the authors

Jürg Kramer is Professor of Mathematics at the Humboldt-Universität zu Berlin, Germany. His research focuses on arithmetic geometry, in particular on Arakelov geometry, and the theory of modular and automorphic forms. He is also interested in questions about the teaching of mathematics at university level.

Anna-Maria von Pippich is Junior Professor of Algebra and Number Theory at the Technische Universität Darmstadt, Germany. She is working in number theory, in particular in the theory of automorphic forms, and Arakelov geometry.

Table of contents (6 chapters)

Table of contents (6 chapters)

Buy this book

eBook $34.99
price for USA in USD (gross)
  • ISBN 978-3-319-69429-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $44.99
price for USA in USD
  • ISBN 978-3-319-69427-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
From Natural Numbers to Quaternions
Authors
Series Title
Springer Undergraduate Mathematics Series
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-69429-0
DOI
10.1007/978-3-319-69429-0
Softcover ISBN
978-3-319-69427-6
Series ISSN
1615-2085
Edition Number
1
Number of Pages
XVIII, 277
Number of Illustrations
4 b/w illustrations, 6 illustrations in colour
Additional Information
Original German edition published by Springer Spektrum, Wiesbaden, 2013
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