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Modern Algebra 2 Volumes Bound As One

by

Modern Algebra 2 Volumes Bound As One Cover

 

Synopses & Reviews

Publisher Comments:

This standard text, written for junior and senior undergraduates, is unusual in that its presentation is accessible enough for the beginner, yet its thoroughness and mathematical rigor provide the more advanced student with an exceptionally comprehensive treatment of every aspect of modern algebra. It especially lends itself to use by beginning graduate students unprepared in modern algebra.

The presentation opens with a study of algebraic structures in general; the first part then carries the development from natural numbers through rings and fields, vector spaces, and polynomials. The second part (originally published as a separate volume) is made up of five chapters on the real and complex number fields, algebraic extensions of fields, linear operations, inner product spaces, and the axiom of choice.

For the benefit of the beginner who can best absorb the principles of algebra by solving problems, the author has provided over 1300 carefully selected exercises. "There is a vast amount of material in these books and a great deal is either new or presented in a new form." — Mathematical Reviews. Preface. List of Symbols. Exercises. Index. 28 black-and-white line illustrations.

Synopsis:

Standard text provides an exceptionally comprehensive treatment of every aspect of modern algebra. Explores algebraic structures, rings and fields, vector spaces, polynomials, linear operators, much more. Over 1,300 exercises. 1965 edition.

Synopsis:

Beginning with algebraic structures in general, the author covers natural numbers, rings and fields, vector spaces, polynomials, real and complex number fields, linear operators, many other topics. Includes over 1,300 carefully selected exercises. 1965 edition. List of Symbols.

Table of Contents

Chapter I. Algebraic Structures

  1. The Language of Set Theory

  2. Compositions

  3. Unions and Intersections of Sets

  4. Neutral Elements and Inverses

  5. Composites and Inverses of Functions

  6. Isomorphisms of Algebraic Structures

  7. Semigroups and Groups

Chapter II. New Structures from Old

  8. Compositions Induced on Subsets

  9. Compositions Induced on the Set of All Subsets

  10. Equivalence Relations

  11. Quotient Structures

  12. Homomorphisms

  13. Compositions Induced on Cartesian Products and Function Spaces

Chapter III. The Natural Numbers

  14. Orderings

  15. Ordered Semigroups

  16. The Natural Numbers

  17. Finite Sets

  18. Induced N-ary Operations

  19. Combinatorial Analysis

Chapter IV. Rings and Fields

  20. The Integers

  21. Rings and Integral Domains

  22. New Rings from Old

  23. The Field of Rational Numbers

  24. The Division Algorithm

  25. Cyclic Groups and Lagrange's Theorem

Chapter V. Vector Spaces

  26. Vector Spaces and Modules

  27. Subspaces and Bases

  28. Linear Transformations

  29. Matrices

  30. Linear Equations

  31. Direct Sums and Quotient Spaces

  32. Rings of Linear Operators

Chapter VI. Polynomials

  33. Algebras

  34. The Algebra of Polynomials

  35. Principal Ideal Domains

  36. Substitution

  37. Irreducibility Criteria

  38. Adjoining Roots

  39. Finite Fields and Division Rings

  40. Polynomials in Several Indeterminates

Chapter VII. The Real and Complex Number Fields

  41. Dedekind and Archimedian Ordered Fields

  42. The Construction of a Dedekind Ordered Field

  43. Isomorphisms of Archimedian Ordered Groups

  44. The field of Complex Numbers

  45. The Algebra of Quaternions

Chapter VIII. Algebraic Extensions of Fields

  46. Algebraic Extensions

  47. Constructions by Ruler and Compass

  48. Galois Theory

  49. Separable and Normal Extensions

  50. Roots of Unity

  51. Solving Quadratics, Cubics, and Quartics

  52. Permutation Groups

  53. Solving Polynomials by Radicals

Chapter IX. Linear Operators

  54. Diagonalizable Operators

  55. Primary and Torsion-free Modules

  56. Finitely Generated Modules

  57. Decompositions of Linear Operators

  58. Determinants

Chapter X. Inner Product Spaces

  59. Inner Products

  60. Orthonormal Bases

  61. Adjoints

  62. The Spectral Theorem

  63. Linear Operators on Inner Product Spaces

Chapter XI. The Axiom of Choice

  64. The Axiom of Choice

  65. Zorn's Lemma

  66. Algebraic Closures

List of Symbols, Index

Product Details

ISBN:
9780486663418
Author:
Warner, Seth
Publisher:
Dover Publications
Author:
Warner
Author:
Mathematics
Location:
New York :
Subject:
Mathematics
Subject:
Algebra
Subject:
Algebra - General
Subject:
General Mathematics
Subject:
Algebra - Intermediate
Subject:
Mathematics - Algebra
Copyright:
Edition Description:
Trade Paper
Series:
Dover Books on Mathematics
Series Volume:
v. 4
Publication Date:
19900631
Binding:
TRADE PAPER
Language:
English
Illustrations:
Yes
Pages:
832
Dimensions:
8.5 x 5.38 in 1.8 lb

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Related Subjects


Science and Mathematics » Mathematics » Algebra » Abstract Algebra
Science and Mathematics » Mathematics » Algebra » General
Science and Mathematics » Mathematics » Algebra » Other
Science and Mathematics » Mathematics » General
Science and Mathematics » Physics » General

Modern Algebra 2 Volumes Bound As One New Trade Paper
0 stars - 0 reviews
$34.95 In Stock
Product details 832 pages Dover Publications - English 9780486663418 Reviews:
"Synopsis" by ,
Standard text provides an exceptionally comprehensive treatment of every aspect of modern algebra. Explores algebraic structures, rings and fields, vector spaces, polynomials, linear operators, much more. Over 1,300 exercises. 1965 edition.

"Synopsis" by ,
Beginning with algebraic structures in general, the author covers natural numbers, rings and fields, vector spaces, polynomials, real and complex number fields, linear operators, many other topics. Includes over 1,300 carefully selected exercises. 1965 edition. List of Symbols.

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