9780534373511

Elements of Modern Algebra

by ;
  • ISBN13:

    9780534373511

  • ISBN10:

    0534373518

  • Format: Hardcover
  • Copyright: 9/10/1999
  • 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

Fundamentals
1(52)
Sets
2(9)
Mappings
11(11)
Properties of Composite Mappings (Optional)
22(4)
Binary Operations
26(10)
Matrices
36(10)
Relations
46(7)
Key Words and Phrases
51(1)
A Pioneer in Mathematics: Arthur Cayley
52(1)
The Integers
53(56)
Postulates for the Integers (Optional)
54(4)
Mathematical Induction
58(8)
Divisibility
66(4)
Prime Factors and Greatest Common Divisor
70(7)
Congruence of Integers
77(6)
Congruence Classes
83(7)
Introduction to Coding Theory (Optional)
90(8)
Introduction to Cryptography (Optional)
98(11)
Key Words and Phrases
107(1)
A Pioneer in Mathematics: Blaise Pascal
108(1)
Groups
109(44)
Definition of a Group
110(12)
Subgroups
122(9)
Cyclic Groups
131(9)
Isomorphisms
140(7)
Homomorphisms
147(6)
Key Words and Phrases
151(1)
A Pioneer in Mathematics: Niels Henrik Abel
152(1)
More on Groups
153(54)
Finite Permutation Groups
154(11)
Cayley's Theorem
165(3)
Permutation Groups in Science and Art (Optional)
168(5)
Normal Subgroups
173(11)
Quotient Groups
184(8)
Direct Sums (Optional)
192(5)
Some Results on Finite Abelian Groups (Optional)
197(10)
Key Words and Phrases
205(1)
A Pioneer in Mathematics: Augustin Louis Cauchy
206(1)
Rings, Integral Domains, and Fields
207(31)
Definition of a Ring
208(10)
Integral Domains and Fields
218(5)
The Field of Quotients of an Integral Domain
223(7)
Ordered Integral Domains
230(8)
Key Words and Phrases
236(1)
A Pioneer in Mathematics: Richard Dedekind
237(1)
More on Rings
238(27)
Ideals and Quotient Rings
239(7)
Ring Homomorphisms
246(9)
The Characteristic of a Ring
255(5)
Maximal Ideals (Optional)
260(5)
Key Words and Phrases
263(1)
A Pioneer in Mathematics: Amalie Emmy Noether
264(1)
Real and Complex Numbers
265(25)
The Field of Real Numbers
266(7)
Complex Numbers and Quaternions
273(8)
De Moivre's Theorem and Roots of Complex Numbers
281(9)
Key Words and Phrases
289(1)
A Pioneer in Mathematics: William Rowan Hamilton
289(1)
Polynomials
290(45)
Polynomials over a Ring
291(9)
Divisibility and Greatest Common Divisor
300(7)
Factorization in F[x]
307(7)
Zeros of a Polynomial
314(9)
Algebraic Extensions of a Field
323(12)
Key Words and Phrases
333(1)
A Pioneer in Mathematics: Carl Friedrich Gauss
334(1)
Appendix: The Basics of Logic 335(11)
Bibliography 346(3)
Answers to Selected Computational Exercises 349(39)
Index 388

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