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...
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Livre numérique |
| Lenguaje: | Anglais |
| Publicado: |
New York, NY :
Springer New York
[20..].
Cham : Springer Nature |
| Edición: | 3rd ed. 2009. |
| Colección: | Undergraduate Texts in Mathematics
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| Materias: | |
| Acceso en línea: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Nota: |
Description d'après consultation du 07 juillet 2011 Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • A concrete introduction to higher algebra, Lindsay N. Childs, 3rd edition, New York, Springer, 2008, 1 vol. (603 p.), Undergraduate texts in mathematics, 978-0-387-74527-5 |
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| 084 | |a 12-01. 2010 | ||
| 100 | 1 | |a Childs, Lindsay, |d 1940- | |
| 245 | 1 | 0 | |a A Concrete introduction to higher algebra |c edited by Lindsay N. Childs. |
| 250 | |a 3rd ed. 2009. | ||
| 260 | |a New York, NY : |b Springer New York. | ||
| 260 | |a Cham : |b Springer Nature, |c [20..]. | ||
| 490 | 1 | |a Undergraduate Texts in Mathematics |x 2197-5604 | |
| 500 | |a Description d'après consultation du 07 juillet 2011 | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 504 | |a Bibliogr. Index | ||
| 505 | 1 | |a Numbers Numbers Induction Euclid's Algorithm Unique Factorization Congruence Congruence classes and rings Congruence Classes Rings and Fields Matrices and Codes Congruences and Groups Fermat's and Euler's Theorems Applications of Euler's Theorem Groups The Chinese Remainder Theorem Polynomials Polynomials Unique Factorization The Fundamental Theorem of Algebra Polynomials in ?[x] Congruences and the Chinese Remainder Theorem Fast Polynomial Multiplication Primitive Roots Cyclic Groups and Cryptography Carmichael Numbers Quadratic Reciprocity Quadratic Applications Finite Fields Congruence Classes Modulo a Polynomial Homomorphisms and Finite Fields BCH Codes Factoring Polynomials Factoring in ?[x] Irreducible Polynomials | |
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 520 | |a 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 | ||
| 650 | |a Théorie des nombres |x Problèmes et exercices | ||
| 700 | 1 | |a Childs, Lindsay, |d 1940- |4 edt | |
| 776 | 0 | |0 130515477 |t A concrete introduction to higher algebra |f Lindsay N. Childs |e 3rd edition |c New York |n Springer |d 2008 |p 1 vol. (603 p.) |s Undergraduate texts in mathematics |z 978-0-387-74527-5 | |
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