Opis: Galois Theory - Ian Nicholas Stewart

Since 1973, Galois Theory has been educating undergraduate students on Galois groups and classical Galois theory. In Galois Theory, Fourth Edition, mathematician and popular science author Ian Stewart updates this well-established textbook for today's algebra students. New to the Fourth Edition * The replacement of the topological proof of the fundamental theorem of algebra with a simple and plausible result from point-set topology and estimates that will be familiar to anyone who has taken a first course in analysis * Revised chapter on ruler-and-compass constructions that results in a more elegant theory and simpler proofs * A section on constructions using an angle-trisector since it is an intriguing and direct application of the methods developed * A new chapter that takes a retrospective look at what Galois actually did compared to what many assume he did * Updated references This bestseller continues to deliver a rigorous yet engaging treatment of the subject while keeping pace with current educational requirements. More than 200 exercises and a wealth of historical notes augment the proofs, formulas, and theorems. "... this book remains a highly recommended introduction to Galois theory along the more classical lines. It contains many exercises and a wealth of examples, including a pretty application of finite fields to the game solitaire. ... provides readers with insight and historical perspective; it is written for readers who would like to understand this central part of basic algebra rather than for those whose only aim is collecting credit points." -Zentralblatt MATH 1322 Praise for the Third Edition: "This edition preserves and even extends one of the most popular features of the original edition: the historical introduction and the story of the fatal duel of Evariste Galois. ... These historical notes should be of interest to students as well as mathematicians in general. ... after more than 30 years, Ian Stewart's Galois Theory remains a valuable textbook for algebra undergraduate students." -Zentralblatt MATH, 1049 "The penultimate chapter is about algebraically closed fields and the last chapter, on transcendental numbers, contains 'what-every-mathematician-should-see-at-least-once,' the proof of transcendence of pi. ... The book is designed for second- and third-year undergraduate courses. I will certainly use it." -EMS NewsletterClassical Algebra Complex Numbers Subfields and Subrings of the Complex Numbers Solving Equations Solution by Radicals The Fundamental Theorem of Algebra Polynomials Fundamental Theorem of Algebra Implications Factorisation of Polynomials The Euclidean Algorithm Irreducibility Gauss's Lemma Eisenstein's Criterion Reduction Modulo p Zeros of Polynomials Field Extensions Field Extensions Rational Expressions Simple Extensions Simple Extensions Algebraic and Transcendental Extensions The Minimal Polynomial Simple Algebraic Extensions Classifying Simple Extensions The Degree of an Extension Definition of the Degree The Tower Law Ruler-and-Compass Constructions Approximate Constructions and More General Instruments Constructions in C Specific Constructions Impossibility Proofs Construction from a Given Set of Points The Idea behind Galois Theory A First Look at Galois Theory Galois Groups According to Galois How to Use the Galois Group The Abstract Setting Polynomials and Extensions The Galois Correspondence Diet Galois Natural Irrationalities Normality and Separability Splitting Fields Normality Separability Counting Principles Linear Independence of Monomorphisms Field Automorphisms K-Monomorphisms Normal Closures The Galois Correspondence The Fundamental Theorem of Galois Theory A Worked Example Solubility and Simplicity Soluble Groups Simple Groups Cauchy's Theorem Solution by Radicals Radical Extensions An Insoluble Quintic Other Methods Abstract Rings and Fields Rings and Fields General Properties of Rings and Fields Polynomials over General Rings The Characteristic of a Field Integral Domains Abstract Field Extensions Minimal Polynomials Simple Algebraic Extensions . Splitting Fields Normality Separability Galois Theory for Abstract Fields The General Polynomial Equation Transcendence Degree Elementary Symmetric Polynomials The General Polynomial Cyclic Extensions Solving Equations of Degree Four or Less Finite Fields Structure of Finite Fields The Multiplicative Group Application to Solitaire Regular Polygons What Euclid Knew Which Constructions Are Possible? Regular Polygons Fermat Numbers How to Draw a Regular 17-gon Circle Division Genuine Radicals Fifth Roots Revisited Vandermonde Revisited The General Case Cyclotomic Polynomials Galois Group of Q(zeta) : Q The Technical Lemma More on Cyclotomic Polynomials Constructions Using a Trisector Calculating Galois Groups Transitive Subgroups Bare Hands on the Cubic The Discriminant General Algorithm for the Galois Group Algebraically Closed Fields Ordered Fields and Their Extensions Sylow's Theorem The Algebraic Proof Transcendental Numbers Irrationality Transcendence of e Transcendence of pi What Did Galois Do or Know? List of the Relevant Material The First Memoir What Galois Proved What Is Galois up to? Alternating Groups, Especially A5 Simple Groups Known to Galois Speculations about Proofs References Index

Szczegóły: Galois Theory - Ian Nicholas Stewart

Tytuł: Galois Theory
Autor: Ian Nicholas Stewart
Wydawnictwo: Apple
ISBN: 9781482245820
Rok wydania: 2015
Ilość stron: 344
Oprawa: Miękka
Waga: 0.48 kg

Recenzje: Galois Theory - Ian Nicholas Stewart