E-Book Overview
A clear, efficient exposition of this topic with complete proofs and exercises, covering cubic and quartic formulas; fundamental theory of Galois theory; insolvability of the quintic; Galoiss Great Theorem; and computation of Galois groups of cubics and quartics. Suitable for first-year graduate students, either as a text for a course or for study outside the classroom, this new edition has been completely rewritten in an attempt to make proofs clearer by providing more details. It now begins with a short section on symmetry groups of polygons in the plane, for there is an analogy between polygons and their symmetry groups and polynomials and their Galois groups - an analogy which serves to help readers organise the various field theoretic definitions and constructions. The text is rounded off by appendices on group theory, ruler-compass constructions, and the early history of Galois Theory. The exposition has been redesigned so that the discussion of solvability by radicals now appears later and several new theorems not found in the first edition are included.
E-Book Content
Joseph Rotman GADS THEORY SECOND EDITION Springer Universitext Editorial Board (North America): S. Axler F.W. Gehring K.A. Ribet pnnger Springer New York Berlin Heidelberg Barcelona Budapest Hong Kong London Milan Paris Singapore Tokyo Universitext Editors (North America): S. Axler, F.W. Gehring, and K.A. Ribet Aksoy/Khamsi: Nonstandard Methods in Fixed Point Theory Andersson: Topics in Complex Analysis Aupetit: A Primer on Spectral Theory Berberian: Fundamentals of Real Analysis Booss/Bleecker: Topology and Analysis Borkar: Probability Theory - An Advanced Course Carleson/Gamelin: Complex Dynamics Cecil: Lie Sphere Geometry: With Applications to Submanifolds Chae: Lebesgue Integration (2nd ed.) Charlap: Bieberbach Groups and Flat Manifolds Chern: Complex Manifolds Without Potential Theory Cohn: A Classical Invitation to Algebraic Numbers and Class Fields Curtis: Abstract Linear Algebra Curtis: Matrix Groups DiBenedetto: Degenerate Parabolic Equations Dimca: Singularities and Topology of Hypersurfaces Edwards: A Formal Background to Mathematics I a/b Edwards: A Formal Background to Mathematics H afb FouIds: Graph Theory Applications Friedman: Algebraic Surfaces and Holomorphic Vector Bundles Fuhrmann: A Polynomial Approach to Linear Algebra Gardiner: A First Course in Group Theory Garding/Tambour: Algebra for Computer Science Goldblatt: Orthogonality and Spacetime Geometry Gustafson/Rao: Numerical Range - The Field of Values of Linear Operatol and Matrices Hahn: Quadratic Algebras, Clifford Algebras, and Arithmetic Witt Groups Holmgren: A First Course in Discrete Dynamical Systems Howe/Tan: Non-Abelian Harmonic Analysis: Applications of SL(2, R) Howes: Modern Analysis and Topology Humi/Miller: Second Course in Ordinary Differential Equations Hurwitz/Kritikos: Lectures on Number Theory Jennings: Modern Geometry with Applications Jones/Morris/Pearson: Abstract Algebra and Famous Impossibilities Kannan/Krueger: Advanced Analysis Kelly/Matthews: The Non-Euclidean Hyperbolic Plane Kostrikin: Introduction to Algebra Luecking/Rubel: Complex Analysis. A Functional Analysis Approach MacLane/Moerdijk: Sheaves in Geometry and Logic Marcus: Number Fields McCarthy: Introduction to Arithmetical Functions Meyer: Essential Mathematics for Applied Fields Mines/Richman/Ruitenburg: A Course in Constructive Algebra Moise: Introductory Problems Course in Analysis and Topology Morris: Introduction to Game Theory Polster: A Geometrical Picture Book Porter/Woods: Extensions and Absolutes of Hausdorff Spaces Ramsay/Richtmyer: Introduction to Hyperbolic Geometry Reisel: Elementary Theory of Metric Spaces Rickart: Natural Function Algebras Joseph Rotman Galois Theory Second Edition Springer Joseph