Concrete Introduction to Higher Algebra (eBook)

Lindsay N. Childs (Autor)

eBook Download: PDF

2008 | 3. Auflage
617 Seiten
Springer New York (Verlag)
978-0-387-74725-5 (ISBN)

Infos

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, 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, 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. “At every stage, a wide variety of applications is presented...The user-friendly exposition is appropriate for the intended audience.” T.W. Hungerford The new edition will contain topics such as Luhn's formula, homomorphisms, detaching coefficients, and more.

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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.

Produkt-Details

• Erscheint lt. Verlag: 5.12.2008
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Technik
• ISBN-10: 0-387-74725-7 / 0387747257
• ISBN-13: 978-0-387-74725-5 / 9780387747255