Modern Algebra

Name: Modern Algebra
Price: 38.25 USD
Availability: InStock
ISBN: 9780471321477

ISBN-10: 0471321478

ISBN-13: 9780471321477

Edition: 4th 2000

Authors: John R. Durbin

List price: $110.95

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The author has written this book with two main goals in mind: to introduce the most important kinds of algebraic structures, and to help students improve their ability to understand and work with abstract ideas.

Book details

List price: $110.95
Edition: 4th
Copyright year: 2000
Publisher: John Wiley & Sons, Incorporated
Publication date: 9/3/1999
Binding: Hardcover
Pages: 352
Size: 7.17" wide x 10.20" long x 0.78" tall
Weight: 1.628
Language: English



Introduction



Mappings and Operations



Mappings



Composition


Invertible Mappings



Operations



Composition as an Operation



Introduction to Groups



Definition and Examples



Permutations



Subgroups



Groups and Symmetry



Equivalence. Congruence. Divisibility



Equivalence Relations



Congruence


The Division Algorithm



Integers Modulon



Greatest Common Divisors


The Euclidean Algorithm



Factorization


Euler's Phi-Function



Groups



Elementary Properties



Generators


Direct Products



Cosets



Lagrange's Theorem



Isomorphism



More on Isomorphism



Cayley's Theorem



Group Homomorphisms



Homomorphisms of Groups


Kernels



Quotient Groups



The Fundamental Homomorphism Theorem



Introduction to Rings



Definition and Examples



Integral Domains


Subrings



Fields



Isomorphism


Characteristic



The Familiar Number Systems



Ordered Integral Domains



The Integers



Field of Quotients


The Field of Rational Number



Ordered Fields


The Field of Real Numbers



The Field of Complex Numbers



Complex Roots of Unity



Polynomials



Definition and Elementary Properties



The Division Algorithm



Factorization of Polynomials



Unique Factorization Domains



Quotient Rings



Homomorphisms of Rings


Ideals



Quotient Rings



Quotient Rings off[X]



Factorization and Ideals



Field Extensions



Simple Extensions



Degrees of Extensions



Splitting Fields



Finite Fields



Galois Theory



Galois Groups



Separability and Normality



Fundamental Theorem of Galois Theory



Solvability by Radicals



Geometric Constructions



Three Famous Problems



Constructible Numbers



Impossible Constructions



Applications of Permutation Groups



Groups Acting on Sets



Burnside's Counting Theorem



Sylow's Theorem



Symmetry



Finite Symmetry Groups



Infinite Two-dimensional Symmetry Groups



On Crystallographic Groups



The Euclidean Group



Cryptography and Algebraic Coding



RSA Algorithm



Introduction to Algebraic Coding



Linear Codes



Standard Decoding



Error Probability



Lattices and Boolean Algebras



Partially Ordered Sets



Lattices



Boolean Algebras



Finite Boolean Algebras



Switching



Sets



Proofs



Mathematical Induction



Linear Algebra



Solutions to Selected Problems


Photo Credit List


Index of Notation


Index