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Cover: 9780387985411 | Galois Theory | Joseph Rotman | Taschenbuch | Universitext | Paperback
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Galois Theory
Taschenbuch von Joseph Rotman
Sprache: Englisch

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Beschreibung
The first edition aimed to give a geodesic path to the Fundamental Theorem of Galois Theory, and I still think its brevity is valuable. Alas, the book is now a bit longer, but I feel that the changes are worthwhile. I began by rewriting almost all the text, trying to make proofs clearer, and often giving more details than before. Since many students find the road to the Fundamental Theorem an intricate one, the book now begins with a short section on symmetry groups of polygons in the plane; an analogy of polygons and their symmetry groups with polynomials and their Galois groups can serve as a guide by helping readers organize the various definitions and constructions. The exposition has been reorganized so that the discussion of solvability by radicals now appears later; this makes the proof of the Abel-Ruffini theo rem easier to digest. I have also included several theorems not in the first edition. For example, the Casus Irreducibilis is now proved, in keeping with a historical interest lurking in these pages.
The first edition aimed to give a geodesic path to the Fundamental Theorem of Galois Theory, and I still think its brevity is valuable. Alas, the book is now a bit longer, but I feel that the changes are worthwhile. I began by rewriting almost all the text, trying to make proofs clearer, and often giving more details than before. Since many students find the road to the Fundamental Theorem an intricate one, the book now begins with a short section on symmetry groups of polygons in the plane; an analogy of polygons and their symmetry groups with polynomials and their Galois groups can serve as a guide by helping readers organize the various definitions and constructions. The exposition has been reorganized so that the discussion of solvability by radicals now appears later; this makes the proof of the Abel-Ruffini theo rem easier to digest. I have also included several theorems not in the first edition. For example, the Casus Irreducibilis is now proved, in keeping with a historical interest lurking in these pages.
Zusammenfassung
This text offers a clear, efficient exposition of Galois Theory with complete proofs and exercises. Topics include: cubic and quartic formulas; Fundamental Theory of Galois Theory; insolvability of the quintic; Galois's Great Theorem (solvability by radicals of a polynomial is equivalent to solvability of its Galois Group); and computation of Galois groups of cubics and quartics. There are appendices on group theory, ruler-compass constructions, and the early history of Galois Theory.
Inhaltsverzeichnis
Symmetry.- Rings.- Domains and Fields.- Homomorphisms and Ideals.- Quotient Rings.- Polynomial Rings over Fields.- Prime Ideals and Maximal Ideals.- Irreducible Polynomials.- Classical Formulas.- Splitting Fields.- The Galois Group.- Roots of Unity.- Solvability by Radicals.- Independence of Characters.- Galois Extensions.- The Fundamental Theorem of Galois Theory.- Applications.- Galois's Great Theorem.- Discriminants.- Galois Groups of Quadratics, Cubics, and Quartics.- Epilogue.- Appendix A: Group Theory Dictionary.- Appendix B: Group Theory Used in the Text.- Appendix C: Ruler-Compass Constructions.- Appendix D: Old-fashioned Galois Theory.- References.
Details
Erscheinungsjahr: 1998
Fachbereich: Arithmetik & Algebra
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 176
Reihe: Universitext
Inhalt: xiv
176 S.
9 s/w Illustr.
9 s/w Zeichng.
ISBN-13: 9780387985411
ISBN-10: 0387985417
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Rotman, Joseph
Auflage: 2nd ed. 1998
Hersteller: Springer US
Springer New York
Universitext
Maße: 235 x 155 x 10 mm
Von/Mit: Joseph Rotman
Erscheinungsdatum: 01.10.1998
Gewicht: 0,277 kg
preigu-id: 104625564
Zusammenfassung
This text offers a clear, efficient exposition of Galois Theory with complete proofs and exercises. Topics include: cubic and quartic formulas; Fundamental Theory of Galois Theory; insolvability of the quintic; Galois's Great Theorem (solvability by radicals of a polynomial is equivalent to solvability of its Galois Group); and computation of Galois groups of cubics and quartics. There are appendices on group theory, ruler-compass constructions, and the early history of Galois Theory.
Inhaltsverzeichnis
Symmetry.- Rings.- Domains and Fields.- Homomorphisms and Ideals.- Quotient Rings.- Polynomial Rings over Fields.- Prime Ideals and Maximal Ideals.- Irreducible Polynomials.- Classical Formulas.- Splitting Fields.- The Galois Group.- Roots of Unity.- Solvability by Radicals.- Independence of Characters.- Galois Extensions.- The Fundamental Theorem of Galois Theory.- Applications.- Galois's Great Theorem.- Discriminants.- Galois Groups of Quadratics, Cubics, and Quartics.- Epilogue.- Appendix A: Group Theory Dictionary.- Appendix B: Group Theory Used in the Text.- Appendix C: Ruler-Compass Constructions.- Appendix D: Old-fashioned Galois Theory.- References.
Details
Erscheinungsjahr: 1998
Fachbereich: Arithmetik & Algebra
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 176
Reihe: Universitext
Inhalt: xiv
176 S.
9 s/w Illustr.
9 s/w Zeichng.
ISBN-13: 9780387985411
ISBN-10: 0387985417
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Rotman, Joseph
Auflage: 2nd ed. 1998
Hersteller: Springer US
Springer New York
Universitext
Maße: 235 x 155 x 10 mm
Von/Mit: Joseph Rotman
Erscheinungsdatum: 01.10.1998
Gewicht: 0,277 kg
preigu-id: 104625564
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