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Solution Manual for Abstract Algebra: An Introduction, 3rd Edition Thomas W. Hungerford

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This is completed downloadable of Solution Manual for Abstract Algebra: An Introduction, 3rd Edition Thomas W. Hungerford

 

Product Details:

  • ISBN-10 ‏ : ‎ 1111569622
  • ISBN-13 ‏ : ‎ 978-1111569624
  • Author:  Thomas W. Hungerford
  • ABSTRACT ALGEBRA: AN INTRODUCTION is intended for a first undergraduate course in modern abstract algebra. Its flexible design makes it suitable for courses of various lengths and different levels of mathematical sophistication, ranging from a traditional abstract algebra course to one with a more applied flavor.  The book is organized around two themes: arithmetic and congruence. Each theme is developed first for the integers, then for polynomials, and finally for rings and groups, so students can see where many abstract concepts come from, why they are important, and how they relate to one another.  New Features: 
  • A groups-first option that enables those who want to cover groups before rings to do so easily. 
    • Proofs for beginners in the early chapters, which are broken into steps, each of which is explained and proved in detail.  
    • In the core course (chapters 1-8), there are 35% more examples and 13% more exercises.

 

Table of Content:

  1. Part 1: The Core Course
  2. Ch 1: Arithmetic in Z Revisited
  3. Introduction
  4. 1.1 The Division Algorithm
  5. 1.2 Divisibility
  6. 1.3 Primes and Unique Factorization
  7. Ch 2: Congruence in Z and Modular Arithmetic
  8. Introduction
  9. 2.1 Congruence and Congruence Classes
  10. 2.2 Modular Arithmetic
  11. 2.3 The Structure of Zp (p Prime) and Zn
  12. Ch 3: Rings
  13. Introduction
  14. 3.1 Definition and Examples of Rings
  15. 3.2 Basic Properties of Rings
  16. 3.3 Isomorphisms and Homomorphisms
  17. Ch 4: Arithmetic in F[x]
  18. Introduction
  19. 4.1 Polynomial Arithmetic and the Division Algorithm
  20. 4.2 Divisibility in F[x]
  21. 4.3 Irreducibles and Unique Factorization
  22. 4.4 Polynomial Functions, Roots, and Reducibility
  23. 4.5 Irreducibility in Q[x]
  24. 4.6 Irreducibility in R[x] and C[x]
  25. Ch 5: Congruence in F[x] and Congruence-Class Arithmetic
  26. Introduction
  27. 5.1 Congruence in F[x] and Congruence Classes
  28. 5.2 Congruence-Class Arithmetic
  29. 5.3 The Structure of F[x]/(p(x)) When p(x) Is Irreducible
  30. Ch 6: Ideals and Quotient Rings
  31. Introduction
  32. 6.1 Ideals and Congruence
  33. 6.2 Quotient Rings and Homomorphisms
  34. 6.3 The Structure of R/I When I Is Prime or Maximal
  35. Ch 7: Groups
  36. Introduction
  37. 7.1 Definition and Examples of Groups
  38. 7.1.A Definition and Examples of Groups
  39. 7.2 Basic Properties of Groups
  40. 7.3 Subgroups
  41. 7.4 Isomorphisms and Homomorphisms
  42. 7.5 The Symmetric and Alternating Groups
  43. Ch 8: Normal Subgroups and Quotient Groups
  44. Introduction
  45. 8.1 Congruence and Lagrange’s Theorem
  46. 8.2 Normal Subgroups
  47. 8.3 Quotient Groups
  48. 8.4 Quotient Groups and Homomorphisms
  49. 8.5 The Simplicity of An
  50. Part 2: Advanced Topics
  51. Ch 9: Topics in Group Theory
  52. Introduction
  53. 9.1 Direct Products
  54. 9.2 Finite Abelian Groups
  55. 9.3 The Sylow Theorems
  56. 9.4 Conjugacy and the Proof of the Sylow Theorems
  57. 9.5 The Structure of Finite Groups
  58. Ch 10: Arithmetic in Integral Domains
  59. Introduction
  60. 10.1 Euclidean Domains
  61. 10.2 Principal Ideal Domains and Unique Factorization Domains
  62. 10.3 Factorization of Quadratic Integers
  63. 10.4 The Field of Quotients of an Integral Domain
  64. 10.5 Unique Factorization in Polynomial Domains
  65. Ch 11: Field Extensions
  66. Introduction
  67. 11.1 Vector Spaces
  68. 11.2 Simple Extensions
  69. 11.3 Algebraic Extensions
  70. 11.4 Splitting Fields
  71. 11.5 Separability
  72. 11.6 Finite Fields
  73. Ch 12: Galois Theory
  74. Introduction
  75. 12.1 The Galois Group
  76. 12.2 The Fundamental Theorem of Galois Theory
  77. 12.3 Solvability by Radicals
  78. Part 3: Excursions and Applications
  79. Ch 13: Public-Key Cryptography
  80. Introduction
  81. Ch 14: The Chinese Remainder Theorem
  82. Introduction
  83. 14.1 Proof of the Chinese Remainder Theorem
  84. 14.2 Applications of the Chinese Remainder Theorem
  85. 14.3 The Chinese Remainder Theorem for Rings
  86. Ch 15: Geometric Constructions
  87. Introduction
  88. Ch 16: Algebraic Coding Theory
  89. Introduction
  90. 16.1 Linear Codes
  91. 16.2 Decoding Techniques
  92. 16.3 BCH Codes
  93. Part 4: Appendices
  94. Appendix A: Logic and Proof
  95. Appendix B: Sets and Functions
  96. Appendix C: Well Ordering and Induction
  97. Appendix D: Equivalence Relations
  98. Appendix E: The Binomial Theorem
  99. Appendix F: Matrix Algebra
  100. Appendix G: Polynomials
  101. Bibliography
  102. Answers and Suggestions for Selected Odd-Numbered Exercises
  103. Index
  104. EP3
  105. EP4

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