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. A strong emphasis on congruence classes leads in a natural way to finite groups and f...
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oai:112.137.131.14:VNU_123-302072020-06-19T08:54:35Z A Concrete Introduction to Higher Algebra Childs, Lindsay N. Mathematics Statistics 512 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. 2017-04-18T01:15:13Z 2017-04-18T01:15:13Z 2009 Book 978-0-387-74527-5 http://repository.vnu.edu.vn/handle/VNU_123/30207 en 592 p. application/pdf Springer |
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Vietnam National University, Hanoi |
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Mathematics Statistics 512 |
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Mathematics Statistics 512 Childs, Lindsay N. A Concrete Introduction to Higher Algebra |
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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. |
format |
Book |
author |
Childs, Lindsay N. |
author_facet |
Childs, Lindsay N. |
author_sort |
Childs, Lindsay N. |
title |
A Concrete Introduction to Higher Algebra |
title_short |
A Concrete Introduction to Higher Algebra |
title_full |
A Concrete Introduction to Higher Algebra |
title_fullStr |
A Concrete Introduction to Higher Algebra |
title_full_unstemmed |
A Concrete Introduction to Higher Algebra |
title_sort |
concrete introduction to higher algebra |
publisher |
Springer |
publishDate |
2017 |
url |
http://repository.vnu.edu.vn/handle/VNU_123/30207 |
_version_ |
1680963737549275136 |