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First Course in Abstract Algebra, A

Paperback Engels 2005 9780131862678
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Samenvatting

This text introduces students to the algebraic concepts of group and rings, providing a comprehensive discussion of theory as well as a significant number of applications for each.

Specificaties

ISBN13:9780131862678
Taal:Engels
Bindwijze:Paperback

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Inhoudsopgave

Chapter 1: Number Theory <p style="MARGIN: 0in 0in 0pt; LINE-HEIGHT: 150%; mso-pagination: none; mso-layout-grid-align: none" sonormal="">Induction </p> <p style="MARGIN: 0in 0in 0pt; LINE-HEIGHT: 150%; mso-pagination: none; mso-layout-grid-align: none" sonormal="">Binomial Coefficients </p> <p style="MARGIN: 0in 0in 0pt; LINE-HEIGHT: 150%; mso-pagination: none; mso-layout-grid-align: none" sonormal="">Greatest Common Divisors </p> <p style="MARGIN: 0in 0in 0pt; LINE-HEIGHT: 150%; mso-pagination: none; mso-layout-grid-align: none" sonormal="">The Fundamental Theorem of Arithmetic </p> <p style="MARGIN: 0in 0in 0pt; LINE-HEIGHT: 150%; mso-pagination: none; mso-layout-grid-align: none" sonormal="">Congruences </p> <p style="MARGIN: 0in 0in 0pt; LINE-HEIGHT: 150%; mso-pagination: none; mso-layout-grid-align: none" sonormal="">Dates and Days </p> <p style="MARGIN: 0in 0in 0pt; LINE-HEIGHT: 150%; mso-pagination: none; mso-layout-grid-align: none" sonormal="">&nbsp; </p> Chapter 2: Groups I <p style="MARGIN: 0in 0in 0pt; LINE-HEIGHT: 150%; mso-pagination: none; mso-layout-grid-align: none" sonormal="">Some Set Theory </p> <p style="MARGIN: 0in 0in 0pt; LINE-HEIGHT: 150%; mso-pagination: none; mso-layout-grid-align: none" sonormal="">Permutations </p> <p style="MARGIN: 0in 0in 0pt; LINE-HEIGHT: 150%; mso-pagination: none; mso-layout-grid-align: none" sonormal="">Groups </p> <p style="MARGIN: 0in 0in 0pt; LINE-HEIGHT: 150%; mso-pagination: none; mso-layout-grid-align: none" sonormal="">Subgroups and Lagrange's Theorem </p> <p style="MARGIN: 0in 0in 0pt; LINE-HEIGHT: 150%; mso-pagination: none; mso-layout-grid-align: none" sonormal="">Homomorphisms </p> <p style="MARGIN: 0in 0in 0pt; LINE-HEIGHT: 150%; mso-pagination: none; mso-layout-grid-align: none" sonormal="">Quotient Groups </p> <p style="MARGIN: 0in 0in 0pt; LINE-HEIGHT: 150%; mso-pagination: none; mso-layout-grid-align: none" sonormal="">Group Actions </p> <p style="MARGIN: 0in 0in 0pt; LINE-HEIGHT: 150%; mso-pagination: none; mso-layout-grid-align: none" sonormal="">Counting with Groups </p> <p style="MARGIN: 0in 0in 0pt; LINE-HEIGHT: 150%; mso-pagination: none; mso-layout-grid-align: none" sonormal="">&nbsp; </p> Chapter 3: Commutative Rings I <p style="MARGIN: 0in 0in 0pt; LINE-HEIGHT: 150%; mso-pagination: none; mso-layout-grid-align: none" sonormal="">First Properties </p> <p style="MARGIN: 0in 0in 0pt; LINE-HEIGHT: 150%; mso-pagination: none; mso-layout-grid-align: none" sonormal="">Fields </p> <p style="MARGIN: 0in 0in 0pt; LINE-HEIGHT: 150%; mso-pagination: none; mso-layout-grid-align: none" sonormal="">Polynomials </p> <p style="MARGIN: 0in 0in 0pt; LINE-HEIGHT: 150%; mso-pagination: none; mso-layout-grid-align: none" sonormal="">Homomorphisms </p> <p style="MARGIN: 0in 0in 0pt; LINE-HEIGHT: 150%; mso-pagination: none; mso-layout-grid-align: none" sonormal="">Greatest Common Divisors </p> <p style="MARGIN: 0in 0in 0pt; LINE-HEIGHT: 150%; mso-pagination: none; mso-layout-grid-align: none" sonormal="">Unique Factorization </p> <p style="MARGIN: 0in 0in 0pt; LINE-HEIGHT: 150%; mso-pagination: none; mso-layout-grid-align: none" sonormal="">Irreducibility </p> <p style="MARGIN: 0in 0in 0pt; LINE-HEIGHT: 150%; mso-pagination: none; mso-layout-grid-align: none" sonormal="">Quotient Rings and Finite Fields </p> <p style="MARGIN: 0in 0in 0pt; LINE-HEIGHT: 150%; mso-pagination: none; mso-layout-grid-align: none" sonormal="">Officers, Magic, Fertilizer, and Horizons </p> <p style="MARGIN: 0in 0in 0pt; LINE-HEIGHT: 150%; mso-pagination: none; mso-layout-grid-align: none" sonormal="">&nbsp; </p> Chapter 4: Linear Algebra <p style="MARGIN: 0in 0in 0pt; LINE-HEIGHT: 150%; mso-pagination: none; mso-layout-grid-align: none" sonormal="">Vector Spaces </p> <p style="MARGIN: 0in 0in 0pt; LINE-HEIGHT: 150%; mso-pagination: none; mso-layout-grid-align: none" sonormal="">Euclidean Constructions </p> <p style="MARGIN: 0in 0in 0pt; LINE-HEIGHT: 150%; mso-pagination: none; mso-layout-grid-align: none" sonormal="">Linear Transformations </p> <p style="MARGIN: 0in 0in 0pt; LINE-HEIGHT: 150%; mso-pagination: none; mso-layout-grid-align: none" sonormal="">Determinants </p> <p style="MARGIN: 0in 0in 0pt; LINE-HEIGHT: 150%; mso-pagination: none; mso-layout-grid-align: none" sonormal="">Codes </p> <p style="MARGIN: 0in 0in 0pt; LINE-HEIGHT: 150%; mso-pagination: none; mso-layout-grid-align: none" sonormal="">Canonical Forms </p> <p style="MARGIN: 0in 0in 0pt; LINE-HEIGHT: 150%; mso-pagination: none; mso-layout-grid-align: none" sonormal="">&nbsp; </p> Chapter 5: Fields <p style="MARGIN: 0in 0in 0pt; LINE-HEIGHT: 150%; mso-pagination: none; mso-layout-grid-align: none" sonormal="">Classical Formulas </p> <p style="MARGIN: 0in 0in 0pt; LINE-HEIGHT: 150%; mso-pagination: none; mso-layout-grid-align: none" sonormal="">Insolvability of the General Quintic </p> <p style="MARGIN: 0in 0in 0pt; LINE-HEIGHT: 150%; mso-pagination: none; mso-layout-grid-align: none" sonormal="">Epilog </p> <p style="MARGIN: 0in 0in 0pt; LINE-HEIGHT: 150%; mso-pagination: none; mso-layout-grid-align: none" sonormal="">&nbsp; </p> Chapter 6: Groups II <p style="MARGIN: 0in 0in 0pt; LINE-HEIGHT: 150%; mso-pagination: none; mso-layout-grid-align: none" sonormal="">Finite Abelian Groups </p> <p style="MARGIN: 0in 0in 0pt; LINE-HEIGHT: 150%; mso-pagination: none; mso-layout-grid-align: none" sonormal="">The Sylow Theorems </p> <p style="MARGIN: 0in 0in 0pt; LINE-HEIGHT: 150%; mso-pagination: none; mso-layout-grid-align: none" sonormal="">Ornamental Symmetry </p> <p style="MARGIN: 0in 0in 0pt; LINE-HEIGHT: 150%; mso-pagination: none; mso-layout-grid-align: none" sonormal="">&nbsp; </p> Chapter 7: Commutative Rings III <p style="MARGIN: 0in 0in 0pt; LINE-HEIGHT: 150%; mso-pagination: none; mso-layout-grid-align: none" sonormal="">Prime Ideals and Maximal Ideals </p> <p style="MARGIN: 0in 0in 0pt; LINE-HEIGHT: 150%; mso-pagination: none; mso-layout-grid-align: none" sonormal="">Unique Factorization </p> <p style="MARGIN: 0in 0in 0pt; LINE-HEIGHT: 150%; mso-pagination: none; mso-layout-grid-align: none" sonormal="">Noetherian Rings </p> <p style="MARGIN: 0in 0in 0pt; LINE-HEIGHT: 150%; mso-pagination: none; mso-layout-grid-align: none" sonormal="">Varieties </p> <p style="MARGIN: 0in 0in 0pt; LINE-HEIGHT: 150%; mso-pagination: none; mso-layout-grid-align: none" sonormal="">Grobner Bases </p> <p style="MARGIN: 0in 0in 0pt; LINE-HEIGHT: 150%; mso-pagination: none; mso-layout-grid-align: none" sonormal="">&nbsp; </p> <p style="MARGIN: 0in 0in 0pt; LINE-HEIGHT: 150%; mso-pagination: none; mso-layout-grid-align: none" sonormal="">Hints for Selected Exercises </p> <p style="MARGIN: 0in 0in 0pt; LINE-HEIGHT: 150%; mso-pagination: none; mso-layout-grid-align: none" sonormal="">Bibliography </p> <p style="MARGIN: 0in 0in 0pt; LINE-HEIGHT: 150%; mso-pagination: none; mso-layout-grid-align: none" sonormal="">Index </p>

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        First Course in Abstract Algebra, A