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A Concrete Introduction to Higher Algebra (Undergraduate Texts in Mathe 3rd Edi
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eBay-Artikelnr.:388959444525
Artikelmerkmale
- Artikelzustand
- Brand
- Unbranded
- Book Title
- A Concrete Introduction to Higher Algebra (Undergraduate Texts i
- MPN
- Does not apply
- ISBN
- 9780387745275
Über dieses Produkt
Product Identifiers
Publisher
Springer New York
ISBN-10
0387745270
ISBN-13
9780387745275
eBay Product ID (ePID)
63179298
Product Key Features
Number of Pages
Xiv, 604 Pages
Publication Name
Concrete Introduction to Higher Algebra
Language
English
Subject
Algebra / General
Publication Year
2008
Type
Textbook
Subject Area
Mathematics
Series
Undergraduate Texts in Mathematics Ser.
Format
Hardcover
Dimensions
Item Weight
80.8 Oz
Item Length
9.3 in
Item Width
6.1 in
Additional Product Features
Edition Number
3
Intended Audience
Scholarly & Professional
LCCN
2008-939988
Reviews
From the reviews:"The user-friendly exposition is appropriate for the intended audience. Exercises often appear in the text at the point they are relevant, as well as at the end of the section or chapter. Hints for selected exercises are given at the end of the book. There is sufficient material for a two-semester course and various suggestions for one-semester courses are provided. Although the overall organization remains the same in the second edition Changes include the following: greater emphasis on finite groups, more explicit use of homomorphisms, increased use of the Chinese remainder theorem, coverage of cubic and quartic polynomial equations, and applications which use the discrete Fourier transform." MATHEMATICAL REVIEWSFrom the reviews of the third edition:"This book can serve as both an introduction to number theory and abstract algebra, sacrifices have to be made with respect to its algebraic content. the book has been written with a high degree of rigor and accuracy and I definitely recommend it for consideration as the basis of an alternative route into abstract algebra and its applications." (The Mathematical Association of America, April, 2009)"The target audience remains students requiring a substantial introduction to the elements of university-level algebra. the text proceeds throughout on a foundation built from the students " familiarity with integers and polynomials over fields. Great care is taken to proceed to abstract concepts by way of familiar examples, and a great many exercises are provided throughout the text. A noteworthy feature of the book is the inclusion of extensive material on applications, to such topics as cryptography and factoring polynomials." (Kenneth A. Brown, Mathematical Reviews, Issue 2009 i), From the reviews: "The user-friendly exposition is appropriate for the intended audience. Exercises often appear in the text at the point they are relevant, as well as at the end of the section or chapter. Hints for selected exercises are given at the end of the book. There is sufficient material for a two-semester course and various suggestions for one-semester courses are provided. Although the overall organization remains the same in the second edition¿Changes include the following: greater emphasis on finite groups, more explicit use of homomorphisms, increased use of the Chinese remainder theorem, coverage of cubic and quartic polynomial equations, and applications which use the discrete Fourier transform." MATHEMATICAL REVIEWS From the reviews of the third edition: "This book is an introduction to abstract algebra. ... it has enough material to give the instructor flexibility in the course. It is a good book for the serious student to have in his/her library. ... I would recommend this especially for self-study, as the book reads exactly as a good teacher talks to a class." (Philosophy, Religion and Science Book Reviews, bookinspections.wordpress.com, October, 2013) "This book can serve as both an introduction to number theory and abstract algebra, sacrifices have to be made with respect to its algebraic content. ... the book has been written with a high degree of rigor and accuracy and I definitely recommend it for consideration as the basis of an alternative route into abstract algebra and its applications." (The Mathematical Association of America, April, 2009) "The target audience remains students requiring a substantial introduction to the elements of university-level algebra. ... the text proceeds throughout on a foundation built from the students' familiarity with integers and polynomials over fields. Great care is taken to proceed to abstract concepts by way of familiar examples, and agreat many exercises are provided throughout the text. ... A noteworthy feature of the book is the inclusion of extensive material on applications, to such topics as cryptography and factoring polynomials." (Kenneth A. Brown, Mathematical Reviews, Issue 2009 i), From the reviews: "The user-friendly exposition is appropriate for the intended audience. Exercises often appear in the text at the point they are relevant, as well as at the end of the section or chapter. Hints for selected exercises are given at the end of the book. There is sufficient material for a two-semester course and various suggestions for one-semester courses are provided. Although the overall organization remains the same in the second edition¿Changes include the following: greater emphasis on finite groups, more explicit use of homomorphisms, increased use of the Chinese remainder theorem, coverage of cubic and quartic polynomial equations, and applications which use the discrete Fourier transform." MATHEMATICAL REVIEWS From the reviews of the third edition: "This book can serve as both an introduction to number theory and abstract algebra, sacrifices have to be made with respect to its algebraic content. ... the book has been written with a high degree of rigor and accuracy and I definitely recommend it for consideration as the basis of an alternative route into abstract algebra and its applications." (The Mathematical Association of America, April, 2009) "The target audience remains students requiring a substantial introduction to the elements of university-level algebra. ... the text proceeds throughout on a foundation built from the students' familiarity with integers and polynomials over fields. Great care is taken to proceed to abstract concepts by way of familiar examples, and a great many exercises are provided throughout the text. ... A noteworthy feature of the book is the inclusion of extensive material on applications, to such topics as cryptography and factoring polynomials." (Kenneth A. Brown, Mathematical Reviews, Issue 2009 i), From the reviews: "The user-friendly exposition is appropriate for the intended audience. Exercises often appear in the text at the point they are relevant, as well as at the end of the section or chapter. Hints for selected exercises are given at the end of the book. There is sufficient material for a two-semester course and various suggestions for one-semester courses are provided. Although the overall organization remains the same in the second edition¿Changes include the following: greater emphasis on finite groups, more explicit use of homomorphisms, increased use of the Chinese remainder theorem, coverage of cubic and quartic polynomial equations, and applications which use the discrete Fourier transform." MATHEMATICAL REVIEWS From the reviews of the third edition: "This book is an introduction to abstract algebra. ... it has enough material to give the instructor flexibility in the course. It is a good book for the serious student to have in his/her library. ... I would recommend this especially for self-study, as the book reads exactly as a good teacher talks to a class." (Philosophy, Religion and Science Book Reviews, bookinspections.wordpress.com, October, 2013) "This book can serve as both an introduction to number theory and abstract algebra, sacrifices have to be made with respect to its algebraic content. ... the book has been written with a high degree of rigor and accuracy and I definitely recommend it for consideration as the basis of an alternative route into abstract algebra and its applications." (The Mathematical Association of America, April, 2009) "The target audience remains students requiring a substantial introduction to the elements of university-level algebra. ... the text proceeds throughout on a foundation built from the students' familiarity with integers and polynomials over fields. Great care is taken to proceed to abstract concepts by way of familiar examples, and a great many exercises are provided throughout the text. ... A noteworthy feature of the book is the inclusion of extensive material on applications, to such topics as cryptography and factoring polynomials." (Kenneth A. Brown, Mathematical Reviews, Issue 2009 i)
Dewey Edition
21
TitleLeading
A
Number of Volumes
1 vol.
Illustrated
Yes
Dewey Decimal
512.7/4
Table Of Content
Numbers.- Numbers.- Induction.- Euclid's Algorithm.- Unique Factorization.- Congruence.- Congruence classes and rings.- Congruence Classes.- Rings and Fields.- Matrices and Codes.- Congruences and Groups.- Fermat's and Euler's Theorems.- Applications of Euler's Theorem.- Groups.- The Chinese Remainder Theorem.- Polynomials.- Polynomials.- Unique Factorization.- The Fundamental Theorem of Algebra.- Polynomials in ?[x].- Congruences and the Chinese Remainder Theorem.- Fast Polynomial Multiplication.- Primitive Roots.- Cyclic Groups and Cryptography.- Carmichael Numbers.- Quadratic Reciprocity.- Quadratic Applications.- Finite Fields.- Congruence Classes Modulo a Polynomial.- Homomorphisms and Finite Fields.- BCH Codes.- Factoring Polynomials.- Factoring in ?[x].- Irreducible Polynomials.
Synopsis
This book is an introduction to higher algebra for students with a background of a year of calculus. The ?rst edition of this book emerged from a set of notes written in the 1970's for a sophomore-juniorlevel undergraduatecourse at the University at Albany entitled "Classical Algebra". The objective of the course, and the book, is to offer students a highly motivated introduction to the basic concepts of abstract algebra--rings and ?elds, groups, homomorphisms--by developing the algebraic theory of the familiar examples of integers and polynomials, and introducing the abstract concepts as needed to help illuminate the theory. By building the algebra out of numbers and polynomials, the booktakesmaximaladvantageof the student'spriorexperiencein algebraandari- metic from secondary school and calculus. The new concepts of abstract algebra arise in a familiar context. An ultimate goal of the presentation is to reach a substantial result in abstract algebra, namely, the classi'cation of ?nite ?elds. But while heading generally - wardsthat goal, motivationis maintainedbymanyapplicationsof the new concepts. The student can see throughout that the concepts of abstract algebra help illuminate more concrete mathematics, as well as lead to substantial theoretical results. Thus a student who asks, "Why am I learning this?" will ?nd answers usually within a chapter or two., This book is written as an introduction to higher algebra for students with a background of a year of calculus. It has been used as a successful undergraduate text for more than 20 years. The objective of the book is to give students enough experience in the algebraic theory of the integers and polynomials to appreciate the basic concepts of abstract algebra. New sections on Luhn's formula, Cosets and equations, and detaching coefficients are included. The later chapters include expositions of Rabiin's probabilistic primality test, quadratic reciprocity, and the classification of finite fields. Over 900 exercises, ranging from routine examples to extensions of theory, are found throughout the book; hints and answers for many of them are included in an appendix., This book is an informal and readable introduction to higher algebra at the post-calculus level. The concepts of ring and field are introduced through study of the familiar examples of the integers and polynomials. The new examples and theory are built in a well-motivated fashion and made relevant by many applications - to cryptography, coding, integration, history of mathematics, and especially to elementary and computational number theory. The later chapters include expositions of Rabiin's probabilistic primality test, quadratic reciprocity, and the classification of finite fields. Over 900 exercises are found throughout the book., This book is an informal and readable introduction to higher algebra at the post-calculus level. The concepts of ring and field are introduced through study of the familiar examples of the integers and polynomials. Over 900 exercises are found throughout the book.
LC Classification Number
QA150-272
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