9780534402648

Elements Of Modern Algebra

by ;
  • ISBN13:

    9780534402648

  • ISBN10:

    053440264X

  • Edition: 6th
  • Format: Hardcover
  • Copyright: 8/10/2004
  • Publisher: Brooks Cole
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Summary

Succeed in modern algebra with ELEMENTS OF MODERN ALGEBRA! With a user-friendly format, this mathematics text provides you with the tools you need to get a good grade. Strategy boxes give you guidance and explanations about techniques and enable you to become more proficient at constructing proofs. A summary of key words and phrases at the end of each chapter help you master the material. A reference section, symbolic marginal notes, an appendix, and numerous examples help you develop your problem solving skills.

Table of Contents

Preface ix
Fundamentals
1(56)
Sets
2(10)
Mappings
12(10)
Properties of Composite Mappings (Optional)
22(5)
Binary Operations
27(5)
Permutations and Inverses
32(5)
Matrices
37(11)
Relations
48(9)
Key Words and Phrases
54(1)
A Pioneer in Mathematics
55(2)
Arthur Cayley
The Integers
57(60)
Postulates for the Integers (Optional)
58(5)
Mathematical Induction
63(7)
Divisibility
70(5)
Prime Factors and Greatest Common Divisor
75(8)
Congruence of Integers
83(6)
Congruence Classes
89(7)
Introduction to Coding Theory (Optional)
96(8)
Introduction to Cryptography (Optional)
104(13)
Key Words and Phrases
114(1)
A Pioneer in Mathematics
115(2)
Blaise Pascal
Groups
117(46)
Definition of a Group
118(13)
Subgroups
131(10)
Cyclic Groups
141(9)
Isomorphisms
150(7)
Homomorphisms
157(6)
Key Words and Phrases
162(1)
A Pioneer in Mathematics
162(1)
Niels Henrik Abel
More on Groups
163(58)
Finite Permutation Groups
164(12)
Cayley's Theorem
176(3)
Permutation Groups in Science and Art (Optional)
179(5)
Normal Subgroups
184(12)
Quotient Groups
196(9)
Direct Sums (Optional)
205(6)
Some Results on Finite Abelian Groups (Optional)
211(10)
Key Words and Phrases
219(1)
A Pioneer in Mathematics
220(1)
Augustin Louis Cauchy
Rings, Integral Domains, and Fields
221(32)
Definition of a Ring
222(11)
Integral Domains and Fields
233(5)
The Field of Quotients of an Integral Domain
238(7)
Ordered Integral Domains
245(8)
Key Words and Phrases
252(1)
A Pioneer in Mathematics
252(1)
Richard Dedekind
More on Rings
253(30)
Ideals and Quotient Rings
254(8)
Ring Homomorphisms
262(9)
The Characteristic of a Ring
271(5)
Maximal Ideals (Optional)
276(7)
Key Words and Phrases
280(1)
A Pioneer in Mathematics
280(3)
Amalie Emmy Noether
Real and Complex Numbers
283(26)
The Field of Real Numbers
284(7)
Complex Numbers and Quaternions
291(8)
De Moivre's Theorem and Roots of Complex Numbers
299(10)
Key Words and Phrases
308(1)
A Pioneer in Mathematics
308(1)
William Rowan Hamilton
Polynomials
309(56)
Polynomials over a Ring
310(10)
Divisibility and Greatest Common Divisor
320(7)
Factorization in F[x]
327(7)
Zeros of a Polynomial
334(9)
Solutions of Cubic and Quartic Equations by Formulas (Optional)
343(9)
Algebraic Extensions of a Field
352(13)
Key Words and Phrases
362(1)
A Pioneer in Mathematics
363(2)
Carl Friedrich Gauss
Appendix: The Basics of Logic 365(11)
Answers to Selected Computational Exercises 376(47)
Bibliography 423(3)
Index 426

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