Elementary Galois Theory A Constructive Approach /
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 con...
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| Format: | Electronic eBook |
| Language: | English |
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Berlin, Heidelberg :
Springer Berlin Heidelberg : Imprint: Springer,
2024.
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| Edition: | 1st ed. 2024. |
| Series: | Mathematics Study Resources,
3 |
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| Online Access: | https://doi.org/10.1007/978-3-662-66643-2 |
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| 100 | 1 | |a Nieper-Wißkirchen, Marc. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Elementary Galois Theory |h [electronic resource] : |b A Constructive Approach / |c by Marc Nieper-Wißkirchen. |
| 250 | |a 1st ed. 2024. | ||
| 264 | 1 | |a Berlin, Heidelberg : |b Springer Berlin Heidelberg : |b Imprint: Springer, |c 2024. | |
| 300 | |a 1 online resource (XVII, 301 p. 31 illus.). |b 15 illus. in color. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 341 | 0 | |b Table of contents navigation |2 onix | |
| 341 | 0 | |b Single logical reading order |2 onix | |
| 341 | 0 | |b Short alternative textual descriptions |2 onix | |
| 341 | 0 | |b Use of colour is Not sole means of conveying information |2 onix | |
| 341 | 0 | |b Use of high contrast between text and background colour |2 onix | |
| 341 | 0 | |b Next / Previous structural navigation |2 onix | |
| 341 | 0 | |b All Non-decorative content supports reading without sight |2 onix | |
| 347 | |a text file |b PDF |2 rda | ||
| 490 | 1 | |a Mathematics Study Resources, |x 2731-3832 ; |v 3 | |
| 505 | 0 | |a 1. introduction -- 2. the fundamental theorem of algebra -- 3. impossibility of squaring the circle -- 4. impossibility of cube doubling and angle division -- 5. on the constructability of regular n-corners -- 6. on the solvability of polynomial equations -- A constructive mathematics -- B linear algebra -- C analysis. | |
| 520 | |a 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. 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. The translation was done with the help of artificial intelligence. A subsequent human revision was done primarily in terms of content. | ||
| 532 | 8 | |a Accessibility summary: This PDF does Not fully comply with PDF/UA standards but does include limited screen reader support, descriptions for Non-text content (such as images and graphs), bookmarks for easy navigation, and searchable, selectable text. Users of assistive technologies may experience difficulty navigating or interpreting content in this document. We recognise the importance of accessibility and welcome queries about accessibility for any of our products. If you have a question or an access need, please get in touch with us via https://www.springernature.com/gp/info/accessibility | |
| 532 | 8 | |a Inaccessible, or known limited accessibility | |
| 532 | 8 | |a No reading system accessibility options actively disabled | |
| 532 | 8 | |a Publisher contact for further accessibility information: accessibilitysupport@springernature.com | |
| 588 | |a Print version record. | ||
| 650 | 0 | |a Algebra. | |
| 650 | 1 | 4 | |a Algebra. |
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| 773 | 0 | |t Springer Nature eBook | |
| 776 | 0 | 8 | |i Printed edition: |z 9783662666425 |
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| 830 | 0 | |a Mathematics Study Resources, |x 2731-3832 ; |v 3 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-3-662-66643-2 |
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| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||