04094nam a22004815i 4500 978-3-662-66643-2 DE-He213 20251030113310.0 cr nn 008mamaa 241113s2024 gw | s |||| 0|eng d 9783662666432 978-3-662-66643-2 10.1007/978-3-662-66643-2 doi QA150-272 PBF bicssc MAT002000 bisacsh PBF thema Nieper-Wißkirchen, Marc. author. aut http://id.loc.gov/vocabulary/relators/aut 87423 Elementary Galois Theory [electronic resource] : A Constructive Approach / by Marc Nieper-Wißkirchen. 1st ed. 2024. Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2024. XVII, 301 p. 31 illus., 15 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Mathematics Study Resources, 2731-3832 ; 3 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. 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. Algebra. 1501 Algebra. 1501 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783662666425 Printed edition: 9783662666449 Mathematics Study Resources, 2731-3832 ; 3 81153 https://doi.org/10.1007/978-3-662-66643-2 ZDB-2-SMA ZDB-2-SXMS 64915 64915