Advanced Algebra : Along with a companion volume Basic Algebra
Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together, the two books give the reader a global view of algebra and its role in mathematics as a whole. Key topics and fea...
Enregistré dans:
| Auteur principal: | |
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| Format: | Livre numérique |
| Langue: | Anglais |
| Publié: |
Boston, MA :
Birkhäuser Boston : Imprint: Birkhäuser
[20..].
Cham : Springer Nature |
| Collection: | Cornerstones
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| Sujets: | |
| Accès en ligne: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Note: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) Numérisation de l'édition de Boston ; Basel ; Berlin : Springer , cop. 2007 |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Advanced algebra, along with a companion volume Basic Algebra, Anthony W. Knapp, 2007, Boston, Birkhäuser, 1 vol. (XXIV-730 p.), Cornerstones, 978-0-8176-4522-9 • Advanced algebra, along with a companion volume Basic algebra, Anthony W. Knapp, Corrected at 2nd printing, 2015, Boston, Birkhäuser, 1 vol. (XXIV-730 p.), Cornerstones, 978-0-8176-4522-9 |
| Résumé: | Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together, the two books give the reader a global view of algebra and its role in mathematics as a whole. Key topics and features of Advanced Algebra: *Topics build upon the linear algebra, group theory, factorization of ideals, structure of fields, Galois theory, and elementary theory of modules as developed in Basic Algebra *Chapters treat various topics in commutative and noncommutative algebra, providing introductions to the theory of associative algebras, homological algebra, algebraic number theory, and algebraic geometry *Sections in two chapters relate the theory to the subject of Gröbner bases, the foundation for handling systems of polynomial equations in computer applications *Text emphasizes connections between algebra and other branches of mathematics, particularly topology and complex analysis *Book carries on two prominent themes recurring in Basic Algebra: the analogy between integers and polynomials in one variable over a field, and the relationship between number theory and geometry *Many examples and hundreds of problems are included, along with hints or complete solutions for most of the problems *The exposition proceeds from the particular to the general, often providing examples well before a theory that incorporates them; it includes blocks of problems that illuminate aspects of the text and introduce additional topics Advanced Algebra presents its subject matter in a forward-looking way that takes into account the historical development of the subject. It is suitable as a text for the more advanced parts of a two-semester first-year graduate sequence in algebra. It requires of the reader only a familiarity with the topics developed in Basic Algebra |
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| Description: | Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) Numérisation de l'édition de Boston ; Basel ; Berlin : Springer , cop. 2007 |
| ISBN: | 9780817646134 |
| Accès: | Accès en ligne pour les établissements français bénéficiaires des licences nationales Accès soumis à abonnement pour tout autre établissement Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 |