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| 001 | 978-3-662-66643-2 | ||
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| 005 | 20251030113310.0 | ||
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_a9783662666432 _9978-3-662-66643-2 |
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_a10.1007/978-3-662-66643-2 _2doi |
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_aNieper-Wißkirchen, Marc. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut _987423 |
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| 245 | 1 | 0 |
_aElementary Galois Theory _h[electronic resource] : _bA Constructive Approach / _cby Marc Nieper-Wißkirchen. |
| 250 | _a1st ed. 2024. | ||
| 264 | 1 |
_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg : _bImprint: Springer, _c2024. |
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| 300 |
_aXVII, 301 p. 31 illus., 15 illus. in color. _bonline resource. |
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| 336 |
_atext _btxt _2rdacontent |
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| 337 |
_acomputer _bc _2rdamedia |
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| 338 |
_aonline resource _bcr _2rdacarrier |
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| 347 |
_atext file _bPDF _2rda |
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| 490 | 1 |
_aMathematics Study Resources, _x2731-3832 ; _v3 |
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| 505 | 0 | _a1. 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 | _aWhy 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. | ||
| 650 | 0 |
_aAlgebra. _91501 |
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| 650 | 1 | 4 |
_aAlgebra. _91501 |
| 710 | 2 | _aSpringerLink (Online service) | |
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_iPrinted edition: _z9783662666425 |
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_iPrinted edition: _z9783662666449 |
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_aMathematics Study Resources, _x2731-3832 ; _v3 _981153 |
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| 856 | 4 | 0 | _uhttps://doi.org/10.1007/978-3-662-66643-2 |
| 912 | _aZDB-2-SMA | ||
| 912 | _aZDB-2-SXMS | ||
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