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Galois Theory 4th edition [Pehme köide]

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  • Formaat: Paperback / softback, 344 pages, kõrgus x laius: 234x156 mm, kaal: 640 g, 2 Tables, black and white; 29 Illustrations, black and white
  • Ilmumisaeg: 06-Mar-2015
  • Kirjastus: Apple Academic Press Inc.
  • ISBN-10: 1482245825
  • ISBN-13: 9781482245820
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Galois Theory 4th editionSuurem pilt
  • Formaat: Paperback / softback, 344 pages, kõrgus x laius: 234x156 mm, kaal: 640 g, 2 Tables, black and white; 29 Illustrations, black and white
  • Ilmumisaeg: 06-Mar-2015
  • Kirjastus: Apple Academic Press Inc.
  • ISBN-10: 1482245825
  • ISBN-13: 9781482245820
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Teised raamatud sellest sooduspakkumisest: Taylor & Francis teadusraamatud International Student Editions hindadega
Püsilink: https://www.kriso.ee/db/9781482245820.html
Märksõnad:
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 todays 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.

Arvustused

" 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 Stewarts 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 Newsletter

Acknowledgements xi
Preface to the First Edition xiii
Preface to the Second Edition xv
Preface to the Third Edition xvii
Preface to the Fourth Edition xxi
Historical Introduction 1(16)
1 Classical Algebra
17(18)
1.1 Complex Numbers
18(1)
1.2 Subfields and Subrings of the Complex Numbers
18(4)
1.3 Solving Equations
22(2)
1.4 Solution by Radicals
24(11)
2 The Fundamental Theorem of Algebra
35(12)
2.1 Polynomials
35(4)
2.2 Fundamental Theorem of Algebra
39(3)
2.3 Implications
42(5)
3 Factorisation of Polynomials
47(16)
3.1 The Euclidean Algorithm
47(4)
3.2 Irreducibility
51(3)
3.3 Gauss's Lemma
54(1)
3.4 Eisenstein's Criterion
55(2)
3.5 Reduction Modulo p
57(1)
3.6 Zeros of Polynomials
58(5)
4 Field Extensions
63(8)
4.1 Field Extensions
63(3)
4.2 Rational Expressions
66(1)
4.3 Simple Extensions
67(4)
5 Simple Extensions
71(8)
5.1 Algebraic and Transcendental Extensions
71(1)
5.2 The Minimal Polynomial
72(1)
5.3 Simple Algebraic Extensions
73(2)
5.4 Classifying Simple Extensions
75(4)
6 The Degree of an Extension
79(8)
6.1 Definition of the Degree
79(1)
6.2 The Tower Law
80(7)
7 Ruler-and-Compass Constructions
87(20)
7.1 Approximate Constructions and More General Instruments
89(1)
7.2 Constructions in C
90(4)
7.3 Specific Constructions
94(5)
7.4 Impossibility Proofs
99(2)
7.5 Construction From a Given Set of Points
101(6)
8 The Idea Behind Galois Theory
107(22)
8.1 A First Look at Galois Theory
108(1)
8.2 Galois Groups According to Galois
108(2)
8.3 How to Use the Galois Group
110(1)
8.4 The Abstract Setting
111(1)
8.5 Polynomials and Extensions
112(2)
8.6 The Galois Correspondence
114(2)
8.7 Diet Galois
116(5)
8.8 Natural Irrationalities
121(8)
9 Normality and Separability
129(8)
9.1 Splitting Fields
129(3)
9.2 Normality
132(1)
9.3 Separability
133(4)
10 Counting Principles
137(8)
10.1 Linear Independence of Monomorphisms
137(8)
11 Field Automorphisms
145(6)
11.1 K-Monomorphisms
145(1)
11.2 Normal Closures
146(5)
12 The Galois Correspondence
151(4)
12.1 The Fundamental Theorem of Galois Theory
151(4)
13 A Worked Example
155(6)
14 Solubility and Simplicity
161(10)
14.1 Soluble Groups
161(3)
14.2 Simple Groups
164(2)
14.3 Cauchy's Theorem
166(5)
15 Solution by Radicals
171(10)
15.1 Radical Extensions
171(5)
15.2 An Insoluble Quintic
176(2)
15.3 Other Methods
178(3)
16 Abstract Rings and Fields
181(12)
16.1 Rings and Fields
181(3)
16.2 General Properties of Rings and Fields
184(2)
16.3 Polynomials Over General Rings
186(1)
16.4 The Characteristic of a Field
187(1)
16.5 Integral Domains
188(5)
17 Abstract Field Extensions
193(12)
17.1 Minimal Polynomials
193(1)
17.2 Simple Algebraic Extensions
194(1)
17.3 Splitting Fields
195(2)
17.4 Normality
197(1)
17.5 Separability
197(5)
17.6 Galois Theory for Abstract Fields
202(3)
18 The General Polynomial Equation
205(16)
18.1 Transcendence Degree
205(3)
18.2 Elementary Symmetric Polynomials
208(1)
18.3 The General Polynomial
209(2)
18.4 Cyclic Extensions
211(3)
18.5 Solving Equations of Degree Four or Less
214(7)
19 Finite Fields
221(6)
19.1 Structure of Finite Fields
221(1)
19.2 The Multiplicative Group
222(2)
19.3 Application to Solitaire
224(3)
20 Regular Polygons
227(16)
20.1 What Euclid Knew
227(3)
20.2 Which Constructions are Possible?
230(1)
20.3 Regular Polygons
231(4)
20.4 Fermat Numbers
235(1)
20.5 How to Draw a Regular 17-gon
235(8)
21 Circle Division
243(24)
21.1 Genuine Radicals
244(2)
21.2 Fifth Roots Revisited
246(3)
21.3 Vandermonde Revisited
249(1)
21.4 The General Case
250(3)
21.5 Cyclotomic Polynomials
253(2)
21.6 Galois Group of Q(ζ): Q
255(1)
21.7 The Technical Lemma
256(1)
21.8 More on Cyclotomic Polynomials
257(2)
21.9 Constructions Using a Trisector
259(8)
22 Calculating Galois Groups
267(10)
22.1 Transitive Subgroups
267(1)
22.2 Bare Hands on the Cubic
268(3)
22.3 The Discriminant
271(1)
22.4 General Algorithm for the Galois Group
272(5)
23 Algebraically Closed Fields
277(8)
23.1 Ordered Fields and Their Extensions
277(2)
23.2 Sylow's Theorem
279(2)
23.3 The Algebraic Proof
281(4)
24 Transcendental Numbers
285(10)
24.1 Irrationality
286(2)
24.2 Transcendence of e
288(1)
24.3 Transcendence of π
289(6)
25 What Did Galois Do or Know?
295(14)
25.1 List of the Relevant Material
296(1)
25.2 The First Memoir
296(1)
25.3 What Galois Proved
297(2)
25.4 What is Galois Up To?
299(2)
25.5 Alternating Groups, Especially A5
301(1)
25.6 Simple Groups Known to Galois
302(1)
25.7 Speculations about Proofs
303(6)
References 309(6)
Index 315
Ian Stewart is an emeritus professor of mathematics at the University of Warwick and a fellow of the Royal Society. Dr. Stewart has been a recipient of many honors, including the Royal Societys Faraday Medal, the IMA Gold Medal, the AAAS Public Understanding of Science and Technology Award, and the LMS/IMA Zeeman Medal. He has published more than 180 scientific papers and numerous books, including several bestsellers co-authored with Terry Pratchett and Jack Cohen that combine fantasy with nonfiction.