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Contemporary Abstract Algebra 9th edition [Hardback]

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(University of Minnesota, Duluth)
  • Formāts: Hardback, 656 pages, height x width x depth: 27x165x233 mm, weight: 952 g
  • Izdošanas datums: 01-Jan-2016
  • Izdevniecība: Brooks/Cole
  • ISBN-10: 1305657969
  • ISBN-13: 9781305657960
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Contemporary Abstract Algebra 9th editionPalielināt
  • Formāts: Hardback, 656 pages, height x width x depth: 27x165x233 mm, weight: 952 g
  • Izdošanas datums: 01-Jan-2016
  • Izdevniecība: Brooks/Cole
  • ISBN-10: 1305657969
  • ISBN-13: 9781305657960
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9781305657960.html
Keywords:
CONTEMPORARY ABSTRACT ALGEBRA, NINTH EDITION is primarily intended for an abstract algebra course whose main purpose is to enable students to do computations and write proofs. Gallian's text stresses the importance of obtaining a solid introduction to the traditional topics of abstract algebra, while at the same time presenting it as a contemporary and very much an active subject which is currently being used by working physicists, chemists, and computer scientists.
Preface xv
PART 1 Integers and Equivalence Relations
1(28)
Preliminaries
3(1)
Properties of Integers
3(3)
Modular Arithmetic
6(7)
Complex Numbers
13(2)
Mathematical Induction
15(3)
Equivalence Relations
18(2)
Functions (Mappings)
20(3)
Exercises
23(6)
PART 2 Groups
29(196)
1 Introduction to Groups
31(11)
Symmetries of a Square
31(3)
The Dihedral Groups
34(3)
Exercises
37(4)
Biography of Niels Abel
41(1)
2 Groups
42(18)
Definition and Examples of Groups
42(7)
Elementary Properties of Groups
49(3)
Historical Note
52(2)
Exercises
54(6)
3 Finite Groups; Subgroups
60(15)
Terminology and Notation
60(2)
Subgroup Tests
62(3)
Examples of Subgroups
65(3)
Exercises
68(7)
4 Cyclic Groups
75(18)
Properties of Cyclic Groups
75(6)
Classification of Subgroups of Cyclic Groups
81(4)
Exercises
85(6)
Biography of James Joseph Sylvester
91(2)
5 Permutation Groups
93(27)
Definition and Notation
93(3)
Cycle Notation
96(2)
Properties of Permutations
98(11)
A Check-Digit Scheme Based on D5
109(3)
Exercises
112(6)
Biography of Augustin Cauchy
118(1)
Biography of Alan Turing
119(1)
6 Isomorphisms
120(18)
Motivation
120(1)
Definition and Examples
120(4)
Cayley's Theorem
124(1)
Properties of Isomorphisms
125(3)
Automorphisms
128(4)
Exercises
132(5)
Biography of Arthur Cayley
137(1)
7 Cosets and Lagrange's Theorem
138(18)
Properties of Cosets
138(4)
Lagrange's Theorem and Consequences
142(4)
An Application of Cosets to Permutation Groups
146(1)
The Rotation Group of a Cube and a Soccer Ball
147(3)
An Application of Cosets to the Rubik's Cube
150(1)
Exercises
150(5)
Biography of Joseph Lagrange
155(1)
8 External Direct Products
156(18)
Definition and Examples
156(2)
Properties of External Direct Products
158(2)
The Group of Units Modulo n as an External Direct Product
160(2)
Applications
162(5)
Exercises
167(6)
Biography of Leonard Adleman
173(1)
9 Normal Subgroups and Factor Groups
174(20)
Normal Subgroups
174(2)
Factor Groups
176(4)
Applications of Factor Groups
180(3)
Internal Direct Products
183(4)
Exercises
187(6)
Biography of Evariste Galois
193(1)
10 Group Homomorphisms
194(18)
Definition and Examples
194(2)
Properties of Homomorphisms
196(4)
The First Isomorphism Theorem
200(5)
Exercises
205(6)
Biography of Camille Jordan
211(1)
11 Fundamental Theorem of Finite Abelian Groups
212(13)
The Fundamental Theorem
212(1)
The Isomorphism Classes of Abelian Groups
213(4)
Proof of the Fundamental Theorem
217(3)
Exercises
220(5)
PART 3 Rings
225(102)
12 Introduction to Rings
227(10)
Motivation and Definition
227(1)
Examples of Rings
228(1)
Properties of Rings
229(1)
Subrings
230(2)
Exercises
232(4)
Biography of I. N. Herstein
236(1)
13 Integral Domains
237(12)
Definition and Examples
237(1)
Fields
238(2)
Characteristic of a Ring
240(3)
Exercises
243(5)
Biography of Nathan Jacobson
248(1)
14 Ideals and Factor Rings
249(14)
Ideals
249(1)
Factor Rings
250(3)
Prime Ideals and Maximal Ideals
253(3)
Exercises
256(5)
Biography of Richard Dedekind
261(1)
Biography of Emmy Noether
262(1)
15 Ring Homomorphisms
263(13)
Definition and Examples
263(3)
Properties of Ring Homomorphisms
266(2)
The Field of Quotients
268(2)
Exercises
270(5)
Biography of Irving Kaplansky
275(1)
16 Polynomial Rings
276(13)
Notation and Terminology
276(3)
The Division Algorithm and Consequences
279(4)
Exercises
283(5)
Biography of Saunders Mac Lane
288(1)
17 Factorization of Polynomials
289(17)
Reducibility Tests
289(3)
Irreducibility Tests
292(5)
Unique Factorization in Z[ x]
297(1)
Weird Dice: An Application of Unique Factorization
298(2)
Exercises
300(5)
Biography of Serge Lang
305(1)
18 Divisibility in Integral Domains
306(21)
Irreducibles, Primes
306(3)
Historical Discussion of Fermat's Last Theorem
309(3)
Unique Factorization Domains
312(3)
Euclidean Domains
315(3)
Exercises
318(5)
Biography of Sophie Germain
323(1)
Biography of Andrew Wiles
324(1)
Biography of Pierre de Fermat
325(2)
PART 4 Fields
327(58)
19 Vector Spaces
329(9)
Definition and Examples
329(1)
Subspaces
330(1)
Linear Independence
331(2)
Exercises
333(3)
Biography of Emil Artin
336(1)
Biography of Olga Taussky-Todd
337(1)
20 Extension Fields
338(16)
The Fundamental Theorem of Field Theory
338(2)
Splitting Fields
340(6)
Zeros of an Irreducible Polynomial
346(4)
Exercises
350(3)
Biography of Leopold Kronecker
353(1)
21 Algebraic Extensions
354(13)
Characterization of Extensions
354(2)
Finite Extensions
356(4)
Properties of Algebraic Extensions
360(2)
Exercises
362(4)
Biography of Ernst Steinitz
366(1)
22 Finite Fields
367(11)
Classification of Finite Fields
367(1)
Structure of Finite Fields
368(4)
Subfields of a Finite Field
372(2)
Exercises
374(3)
Biography of L. E. Dickson
377(1)
23 Geometric Constructions
378(7)
Historical Discussion of Geometric Constructions
378(1)
Constructible Numbers
379(2)
Angle-Trisectors and Circle-Squarers
381(1)
Exercises
381(4)
PART 5 Special Topics
385
24 Sylow Theorems
387(17)
Conjugacy Classes
387(1)
The Class Equation
388(1)
The Sylow Theorems
389(6)
Applications of Sylow Theorems
395(3)
Exercises
398(5)
Biography of Oslo Ludwig Sylow
403(1)
25 Finite Simple Groups
404(18)
Historical Background
404(5)
Nonsimplicity Tests
409(4)
The Simplicity of A5
413(1)
The Fields Medal
414(1)
The Cole Prize
415(1)
Exercises
415(4)
Biography of Michael Aschbacher
419(1)
Biography of Daniel Gorenstein
420(1)
Biography of John Thompson
421(1)
26 Generators and Relations
422(16)
Motivation
422(1)
Definitions and Notation
423(1)
Free Group
424(1)
Generators and Relations
425(4)
Classification of Groups of Order Up to 15
429(2)
Characterization of Dihedral Groups
431(1)
Realizing the Dihedral Groups with Mirrors
432(2)
Exercises
434(3)
Biography of Marshall Hall, Jr.
437(1)
27 Symmetry Groups
438(8)
Isometries
438(2)
Classification of Finite Plane Symmetry Groups
440(1)
Classification of Finite Groups of Rotations in R3
441(2)
Exercises
443(3)
28 Frieze Groups and Crystallographic Groups
446(26)
The Frieze Groups
446(6)
The Crystallographic Groups
452(6)
Identification of Plane Periodic Patterns
458(6)
Exercises
464(5)
Biography of M. C. Escher
469(1)
Biography of George Poly a
470(1)
Biography of John H. Conway
471(1)
29 Symmetry and Counting
472(10)
Motivation
472(1)
Burnside's Theorem
473(2)
Applications
475(3)
Group Action
478(1)
Exercises
479(2)
Biography of William Burnside
481(1)
30 Cayley Digraphs of Groups
482(21)
Motivation
482(1)
The Cayley Digraph of a Group
482(4)
Hamiltonian Circuits and Paths
486(6)
Some Applications
492(3)
Exercises
495(6)
Biography of William Rowan Hamilton
501(1)
Biography of Paul Erdos
502(1)
31 Introduction to Algebraic Coding Theory
503(27)
Motivation
503(5)
Linear Codes
508(5)
Parity-Check Matrix Decoding
513(3)
Coset Decoding
516(4)
Historical Note: The Ubiquitous Reed-Solomon Codes
520(2)
Exercises
522(5)
Biography of Richard W. Hamming
527(1)
Biography of Jessie MacWilliams
528(1)
Biography of Vera Pless
529(1)
32 An Introduction to Galois Theory
530(17)
Fundamental Theorem of Galois Theory
530(7)
Solvability of Polynomials by Radicals
537(4)
Insolvability of a Quintic
541(1)
Exercises
542(4)
Biography of Philip Hall
546(1)
33 Cyclotomic Extensions
547
Motivation
547(1)
Cyclotomic Polynomials
548(4)
The Constructible Regular n-gons
552(2)
Exercises
554(2)
Biography of Carl Friedrich Gauss
556(1)
Biography of Manjul Bhargava
557
Selected Answers 1(32)
Index of Mathematicians 33(4)
Index of Terms 37
Joseph Gallian earned his PhD from Notre Dame. In addition to receiving numerous awards for his teaching and exposition, he served, first, as the Second Vice President, and, then, as the President of the MAA. He has served on 40 national committees, chairing ten of them. He has published over 100 articles and authored six books. Numerous articles about his work have appeared in the national news outlets, including the New York Times, the Washington Post, the Boston Globe, and Newsweek, among many others.