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"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."--Jacket.
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Previews available in: English
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1
A concrete introduction to higher algebra
2009, Springer
in English
- 3rd ed.
0387745270 9780387745275
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2
A concrete introduction to higher algebra
2009, Springer
in English
- 3rd ed.
0387745270 9780387745275
|
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3
A concrete introduction to higher algebra
1995, Springer
in English
- 2nd ed.
0387944842 9780387944845
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4
A concrete introduction to higher algebra
1983, Springer
in English
- Corr. 2nd print.
038790333X 9780387903330
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Book Details
Edition Notes
Includes bibliographical references (p. 595-598) and index.
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