Basic Algebra I

Um classico.

Il migliore libro di algebra astratta che abbia mai letto. A distanza di anni dal primo utilizzo, continua a tornarmi utile per “rispolverare” certi argomenti. La peculiarità che mi porta a consigliare questo testo piuttosto che altri, è l’ordine con cui gli argomenti vengono introdotti: credo che non esista modo migliore per farlo.

Les deux tomes Basic Algebra I et II constituent un cours complet d'algèbre couvrant (largement) tous les sujets étudiés jusqu'en première année de Master. Toutes les notions importantes sont traitées en profondeur et le tout est agrémenté d'un grand nombre d'exemples, d'exercices et de commentaires historiques. Un ouvrage vivement recommandé pour tous les étudiants en mathématiques.

In the 1980's when the first edition of this text appeared I visited the Boston Museum of Science and Technology. At a mathematics exhibit I found a timeline of great mathematicians in which Jacobson was identified as "the father of modern algebra." This book, now in its second edition is still widely used at many universities. I read it while I was a student at Yale in the 80's, and discovered that I missed a lot of material, having originally studied algebra from Herstein and linear algebra from Hoffman and Kunze as an undergrad at Cornell. Jacobson covers a lot more ground and his exercises are more challenging. I love this book, and it is a standard reference for elementary mathematics in my home library.