03881nam a22004335i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003500137050001400172072001600186072002300202072001500225100009400240245011000334250001800444264008200462300006600544336002600610337002600636338003600662347002400698490004900722505032500771520203301096650001903129650001903148710003403167773002603201776003603227776003603263830005603299856004603355912001403401912001503415999001703430978-3-662-66643-2DE-He21320251030113310.0cr nn 008mamaa241113s2024    gw |    s    |||| 0|eng d  a97836626664329978-3-662-66643-27 a10.1007/978-3-662-66643-22doi 4aQA150-272 7aPBF2bicssc 7aMAT0020002bisacsh 7aPBF2thema1 aNieper-Wißkirchen, Marc.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut98742310aElementary Galois Theoryh[electronic resource] :bA Constructive Approach /cby Marc Nieper-Wißkirchen.  a1st ed. 2024. 1aBerlin, Heidelberg :bSpringer Berlin Heidelberg :bImprint: Springer,c2024.  aXVII, 301 p. 31 illus., 15 illus. in color.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aMathematics Study Resources,x2731-3832 ;v30 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.  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. 0aAlgebra.9150114aAlgebra.915012 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978366266642508iPrinted edition:z9783662666449 0aMathematics Study Resources,x2731-3832 ;v398115340uhttps://doi.org/10.1007/978-3-662-66643-2  aZDB-2-SMA  aZDB-2-SXMS  c64915d64915