A Concrete Introduction To Higher Algebra

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9780387745275: A Concrete Introduction To Higher Algebra

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.

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Book Description:

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)

Dalla quarta di copertina:

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. A strong emphasis on congruence classes leads in a natural way to finite groups and finite fields. The new examples and theory are built in a well-motivated fashion and made relevant by many applications - to cryptography, error correction, integration, and especially to elementary and computational number theory. The later chapters include expositions of Rabin's probabilistic primality test, quadratic reciprocity, the classification of finite fields, and factoring polynomials over the integers. Over 1000 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.

The new edition includes topics such as Luhn's formula, Karatsuba multiplication, quotient groups and homomorphisms, Blum-Blum-Shub pseudorandom numbers, root bounds for polynomials, Montgomery multiplication, and more.

"At every stage, a wide variety of applications is presented...The user-friendly exposition is appropriate for the intended audience"

- T.W. Hungerford, Mathematical Reviews

"The style is leisurely and informal, a guided tour through the foothills, the guide unable to resist numerous side paths and return visits to favorite spots..."

- Michael Rosen, American Mathematical Monthly

Le informazioni nella sezione "Su questo libro" possono far riferimento a edizioni diverse di questo titolo.

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Childs, Lindsay N.
Editore: Springer-Verlag New York Inc., United States (2008)
ISBN 10: 0387745270 ISBN 13: 9780387745275
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Descrizione libro Springer-Verlag New York Inc., United States, 2008. Hardback. Condizione libro: New. 3rd ed. 2009. 236 x 158 mm. Language: English . Brand New 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. 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. Codice libro della libreria LIB9780387745275

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Descrizione libro Springer, 2008. Condizione libro: New. Codice libro della libreria L9780387745275

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Childs, Lindsay N.
Editore: Springer-Verlag New York Inc., United States (2008)
ISBN 10: 0387745270 ISBN 13: 9780387745275
Nuovi Rilegato Quantità: 10
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The Book Depository US
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[?]

Descrizione libro Springer-Verlag New York Inc., United States, 2008. Hardback. Condizione libro: New. 3rd ed. 2009. 236 x 158 mm. Language: English . Brand New 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. 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. Codice libro della libreria LIB9780387745275

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Descrizione libro Springer, 2008. Hardback. Condizione libro: NEW. 9780387745275 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. Codice libro della libreria HTANDREE0274258

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ISBN 10: 0387745270 ISBN 13: 9780387745275
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Descrizione libro Springer-Verlag Gmbh Dez 2008, 2008. Buch. Condizione libro: Neu. 244x165x43 mm. Neuware - 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. 603 pp. Englisch. Codice libro della libreria 9780387745275

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Descrizione libro Springer-Verlag New York Inc., 2008. HRD. Condizione libro: New. New Book. Shipped from US within 10 to 14 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Codice libro della libreria I1-9780387745275

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Descrizione libro Springer, 2016. Paperback. Condizione libro: New. PRINT ON DEMAND Book; New; Publication Year 2016; Not Signed; Fast Shipping from the UK. No. book. Codice libro della libreria ria9780387745275_lsuk

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Descrizione libro Springer-Verlag Gmbh Dez 2008, 2008. Buch. Condizione libro: Neu. 244x165x43 mm. Neuware - 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. 603 pp. Englisch. Codice libro della libreria 9780387745275

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Childs, Lindsay N.
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Descrizione libro Springer-Verlag Gmbh Dez 2008, 2008. Buch. Condizione libro: Neu. 244x165x43 mm. Neuware - 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. 603 pp. Englisch. Codice libro della libreria 9780387745275

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Descrizione libro Springer-Verlag New York Inc., 2008. HRD. Condizione libro: New. New Book. Delivered from our US warehouse in 10 to 14 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Codice libro della libreria I1-9780387745275

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