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Modern Algebra Paperback Seth Warner

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Book Title
Modern Algebra Paperback Seth Warner
ISBN
9780486663418

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Product Identifiers

Publisher
Dover Publications, Incorporated
ISBN-10
0486663418
ISBN-13
9780486663418
eBay Product ID (ePID)
762320

Product Key Features

Number of Pages
832 Pages
Language
English
Publication Name
Modern Algebra
Publication Year
1990
Subject
Algebra / Intermediate, Algebra / General
Type
Textbook
Subject Area
Mathematics
Author
Seth Warner
Series
Dover Books on Mathematics Ser.
Format
Trade Paperback

Dimensions

Item Weight
34.5 Oz
Item Length
8.5 in
Item Width
5.3 in

Additional Product Features

Intended Audience
College Audience
LCCN
89-025870
Dewey Edition
20
Illustrated
Yes
Dewey Decimal
512.8
Table Of Content
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 GroupsChapter 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 SpacesChapter III. The Natural Numbers 14. Orderings 15. Ordered Semigroups 16. The Natural Numbers 17. Finite Sets 18. Induced N-ary Operations 19. Combinatorial AnalysisChapter 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 TheoremChapter 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 OperatorsChapter 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 IndeterminatesChapter 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 QuaternionsChapter 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 RadicalsChapter IX. Linear Operators 54. Diagonalizable Operators 55. Primary and Torsion-free Modules 56. Finitely Generated Modules 57. Decompositions of Linear Operators 58. DeterminantsChapter X. Inner Product Spaces 59. Inner Products 60. Orthonormal Bases 61. Adjoints 62. The Spectral Theorem 63. Linear Operators on Inner Product SpacesChapter XI. The Axiom of Choice 64. The Axiom of Choice 65. Zorn's Lemma 66. Algebraic ClosuresList of Symbols, Index
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., 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., 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.
LC Classification Number
QA251.W36 1990

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