Authors:
- 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
- Includes supplementary material: sn.pub/extras
Part of the book series: Springer Undergraduate Mathematics Series (SUMS)
Buy it now
Buying options
Tax calculation will be finalised at checkout
Other ways to access
This is a preview of subscription content, log in via an institution to check for access.
Table of contents (6 chapters)
-
Front Matter
-
Back Matter
About this book
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.
Keywords
- MSC (2010): 08–01, 11–01, 12–01, 20–01
- integers construction
- rational numbers construction
- real numbers construction
- complex numbers construction
- Hamiltonian quaternions construction
- group theory elements
- ring theory elements
- complex numbers algebraicity
- proof transcendence Euler number e
- Associative Rings and Algebras
- Commutative Rings and Algebras
- Field Theory and Polynomials
- Group Theory and Generalizations
- Number Theory
Authors and Affiliations
-
Department of Mathematics, Humboldt-Universität zu Berlin, Berlin, Germany
Jürg Kramer
-
Department of Mathematics, Technische Universität Darmstadt, Darmstadt, Germany
Anna-Maria von Pippich
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.
Bibliographic Information
Book Title: From Natural Numbers to Quaternions
Authors: Jürg Kramer, Anna-Maria von Pippich
Series Title: Springer Undergraduate Mathematics Series
DOI: https://doi.org/10.1007/978-3-319-69429-0
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG 2017
Softcover ISBN: 978-3-319-69427-6Published: 23 November 2017
eBook ISBN: 978-3-319-69429-0Published: 15 November 2017
Series ISSN: 1615-2085
Series E-ISSN: 2197-4144
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
Topics: Algebra, Number Theory