A Concrete Introduction to Higher Algebra (Undergraduate Texts in Mathematics)

Childs, Lindsay N.

ISBN 10: 1441925619 / ISBN 13: 9781441925619

Verlag: Springer (edition Softcover reprint of hardcover 3rd ed. 2009), 2010

It's a preowned item in good condition and includes all the pages. It may have some general signs of wear and tear, such as markings, highlighting, slight damage to the cover, minimal wear to the binding, etc., but they will not affect the overall reading experience. Softcover reprint of hardcover 3rd ed. 2009. Bestandsnummer des Verkäufers 1441925619-11-1

Inhaltsangabe:

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.

Von der hinteren Coverseite: <p>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.</p><p>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.</p><p>"At every stage, a wide variety of applications is presented...The user-friendly exposition is appropriate for the intended audience"</p><p>- T.W. Hungerford, Mathematical Reviews</p><p>"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..."</p><p></p><p>- Michael Rosen, American Mathematical Monthly</p>

Bibliografische Details

Titel: A Concrete Introduction to Higher Algebra (...
Verlag: Springer (edition Softcover reprint of hardcover 3rd ed. 2009)
Erscheinungsdatum: 2010
Einband: Paperback
Zustand: Good