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abstract algebra: an introduction, 3rd Edition thomas hungerford [pdf] abstract algebra: 3rd Edition thomas hungerford [pdf] mathschool

Abstract Algebra: An Introduction (3rd Edition) by Thomas W. Hungerford

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Abstract Algebra: An Introduction (3rd Edition) written by Thomas W. Hungerford, Saint Louis University . The flexible design of the text makes it suitable for courses of various lengths and different levels of mathematical sophistication flavor. The emphasis of this text is on clarity of exposition. The chapters are organized around three themes: arithmetic, congruence, and abstract structures. The interconnections of the basic areas of algebra are frequently pointed out in the text and in the Thematic Table of Contents.

Abstract Algebra: An Introduction (3rd Edition) written by Thomas W. Hungerford cover the following topics.

• Preface
To the Instructor
To the Student

• Part 1. The Core Course

• 1. Arithmetic inZRevisited
1.1 The Division Algorithm
1.2 Divisibility
1.3 Primes and Unique Factorization

• 2. Conuruence inZandModularArithmetic
2.1 Congruence and Congruence Classes
2.2 Modular Arithmetic
2.3 The Structure of Z,, (p Prime) and Zn

• 3. Rings
3.1 Definition and Examples of Rings
3.2 Basic Properties of Rings
3.3 Isomorphisms and Homomorphisms

• 4. Arithmetic in f[x]
4.1 Polynomial Arithmetic and the Division Algorithm
4.2 Divisibility in f[x]
4.3 lrreducibles and Unique Factorization
4.4 Polynomial Functi ons, Roots, and Reducibility
4.5* lrreducibillty in O[x]
4.6* lrreducibillty in IR[x] and C[x]

• 5. Congruence in f[x] and Congruence-Glass Arithmetic
5.1 Congruence in F[x] and Congruence Classes
5.2 Congruence-Class Arithmetic
5.3 The Structure of F{x]/(p(x)) When p(x) Is Irreducible

• 6. Ideals and Quotient Rings
6.1 Ideals and Congruence
6.2 Quotient Rings and Homomorphisms
6.3* The Structure of Rf /When /Is Prime or Maximal

• 7. Groups
7.1 Definition and Examples of Groups
7.1.A Definition and Examples of Groups
7.2 Basic Properties of Groups
7.3 Subgroups
7.4 Isomorphisms and Homomorphisms
7.5* The Symmetric and Alternating Groups

• 8. Normal Subgroups and Quotient Groups
8.1 Congruence and Lagrange
s Theorem
8.2 Normal Subgroups
8.3 Quotient Groups
8.4 Quotient Groups and Homomorphisms
8.5* The Simplicity of An

• 9. Topics in Group Theory
9.1 Direct Products
9.2 Finite Abelian Groups
9.3 The Sylow Theorems
9.4 Conjugacy and the Proof of the Sylow Theorems
9.5 The Structure of Finite Groups

• 1O. Arithmetic in Integral Domains
10.1 Euclidean Domains
10.2 Principal Ideal Domains and Unique Factorization Domains
10.4 The Field of Quotients of an Integral Domain
10.5 Unique Factorization in Polynomial Domains

• 11. Field Extensions
11.1 Vector Spaces
11.2 Simple Extensions
11.3 Algebraic Extensions
11.4 Splitting Fields
11.5 Separability
11.6 Finite Fields

• 12. GaloisTheory
12.1 The Galois Group
12.2 The Fundamental Theorem of Galois Theory

• Part 3 Excursions and Applications

• 13. Public-Key Cryptography
Prerequisite: Section 2.3

• 14. The Chinese RemainderTheorem
14.1 Proof of the Chinese Remainder Theorem Prerequisites: Section 2.1, Appendix C
14.2 Applications of the Chinese Remainder Theorem Prerequisite: Section 3.1
14.3 The Chinese Remainder Theorem for Rings Prerequisite: Section 6.2

• 15. Geometric Constructions
Prerequisites: Sections 4.1, 4.4, and 4.5

• 16. Algebraic CodingTheory
16.1 Linear Codes, Prerequisites: Section 7.4, Appendix F
16.2 DecodingTechniques, Prerequisite; Section 8.4
16.3 BCH Codes, Prerequisite: Section 11.6

• 4. Appendices
A. Logic and Proof
B. Sets and Functions
C.Well Ordering And Induction
D.Equivalence Relations
E. The Binomial Theorem
F.Matrix Algebra
Bibliography
Answers and Suggestions for Selected Odd-Numbered
Exercises
Index

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