Overview
- Suitable for first-year students in Bachelor's and teacher training programmes
- Consistently constructive approach facilitates understanding
- Core statements and essential arguments are summarised
Part of the book series: Mathematics Study Resources (MSR, volume 3)
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Keywords
- Galois theory
- Resolvability of polynomial equations
- Constructability of regular n-corners
- Impossibility of cube doubling and angle division
- Impossibility of squaring the circle
- Fundamental theorem of algebra
- Constructive mathematics
- Intuitionistic logic
About this book
Why is the squaring of the circle, why is the division of angles with compass and ruler impossible? Why are there general solution formulas for polynomial equations of degree 2, 3 and 4, but not for degree 5 or higher?
This textbook deals with such classical questions in an elementary way in the context of Galois theory. It thus provides a classical introduction and at the same time deals with applications. The point of view of a constructive mathematician is consistently adopted: To prove the existence of a mathematical object, an algorithmic construction of that object is always given. Some statements are therefore formulated somewhat more cautiously than is classically customary; some proofs are more elaborately conducted, but are clearer and more comprehensible. Abstract theories and definitions are derived from concrete problems and solutions and can thus be better understood and appreciated.
The material in this volume can be covered in a one-semester lecture on algebra right at the beginning of mathematics studies and is equally suitable for first-year students at the Bachelor's level and for teachers.
The central statements are already summarised and concisely presented within the text, so the reader is encouraged to pause and reflect and can repeat content in a targeted manner. In addition, there is a short summary at the end of each chapter, with which the essential arguments can be comprehended step by step, as well as numerous exercises with an increasing degree of difficulty.
Authors and Affiliations
About the author
Marc Nieper-Wißkirchen studied mathematics and physics in Cologne and earned his doctorate there in algebraic geometry. He was then a junior professor in Mainz. Since 2008, he has held the Chair of Algebra and Number Theory at the University of Augsburg. He is also interested in computer science, especially in algorithmic implementations of mathematical procedures.
Bibliographic Information
Book Title: Elementary Galois Theory
Book Subtitle: A Constructive Approach
Authors: Marc Nieper-Wißkirchen
Series Title: Mathematics Study Resources
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer-Verlag GmbH, DE, part of Springer Nature 2024
Softcover ISBN: 978-3-662-66642-5Due: 26 November 2024
eBook ISBN: 978-3-662-66643-2Due: 26 November 2024
Series ISSN: 2731-3824
Series E-ISSN: 2731-3832
Edition Number: 1
Number of Pages: XV, 269
Number of Illustrations: 24 b/w illustrations, 15 illustrations in colour
Additional Information: ...