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000827155 019__ $$a1030459915$$a1030600577$$a1030767067$$a1033666620$$a1034555138
000827155 020__ $$a9783319723266$$q(electronic book)
000827155 020__ $$a331972326X$$q(electronic book)
000827155 020__ $$z9783319723259
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000827155 0247_ $$a10.1007/978-3-319-72326-6$$2doi
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000827155 1001_ $$aBrzeziński, Juliusz,$$eauthor.
000827155 24510 $$aGalois theory through exercises /$$cJuliusz Brzeziński.
000827155 264_1 $$aCham, Switzerland :$$bSpringer,$$c2018.
000827155 300__ $$a1 online resource (xvii, 293 pages) :$$billustrations.
000827155 336__ $$atext$$btxt$$2rdacontent
000827155 337__ $$acomputer$$bc$$2rdamedia
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000827155 347__ $$atext file$$bPDF$$2rda
000827155 4901_ $$aSpringer undergraduate mathematics series,$$x1615-2085
000827155 504__ $$aIncludes bibliographical references and index.
000827155 5050_ $$a1 Solving algebraic equations -- 2 Field extensions -- 3 Polynomials and irreducibility -- 4 Algebraic extensions -- 5 Splitting fields -- 6 Automorphism groups of fields -- 7 Normal extensions -- 8 Separable extensions -- 9 Galois extensions -- 10 Cyclotomic extensions -- 11 Galois modules -- 12 Solvable groups -- 13 Solvability of equations -- 14 Geometric constructions -- 15 Computing Galois groups -- 16 Supplementary problems -- 17 Proofs of the theorems -- 18 Hints and answers -- 19 Examples and selected solutions -- Appendix: Groups, rings and fields -- References -- List of notations -- Index.
000827155 506__ $$aAccess limited to authorized users.
000827155 520__ $$aThis textbook offers a unique introduction to classical Galois theory through many concrete examples and exercises of varying difficulty (including computer-assisted exercises). In addition to covering standard material, the book explores topics related to classical problems such as Galois’ theorem on solvable groups of polynomial equations of prime degrees, Nagell's proof of non-solvability by radicals of quintic equations, Tschirnhausen's transformations, lunes of Hippocrates, and Galois' resolvents. Topics related to open conjectures are also discussed, including exercises related to the inverse Galois problem and cyclotomic fields. The author presents proofs of theorems, historical comments and useful references alongside the exercises, providing readers with a well-rounded introduction to the subject and a gateway to further reading. A valuable reference and a rich source of exercises with sample solutions, this book will be useful to both students and lecturers. Its original concept makes it particularly suitable for self-study.--$$cProvided by publisher.
000827155 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed March 27, 2018).
000827155 650_0 $$aGalois theory$$vProblems, exercises, etc.
000827155 77608 $$iPrint version: $$z3319723251$$z9783319723259$$w(OCoLC)1011212949
000827155 830_0 $$aSpringer undergraduate mathematics series.
000827155 852__ $$bebk
000827155 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-3-319-72326-6$$zOnline Access$$91397441.1
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