I used this book in a course that was offered to upper year undergraduates and 1st year graduate students at Queen's University.
The material is fun to teach and the books is excellent to teach from (and the students enjoyed the course a great deal!). I could easily let the students read things I didn't have time to finish in class, as the book is easy to follow, contains all the necessary proofs, and is remarkably free of errors.
For the teacher, the tutorials are a real bonus. They allowed me to tailor the extra work I gave to the students in a way that took into account their background -- easy tutorials, or pieces of tutorials for the undergraduate students and more demanding tutorials for the graduate students. I have to admit that I enjoyed the tutorials myself as they took me to places I hadn't visited before!
I would strongly recommend this book to anyone contemplating teaching this material and I would strongly urge that this material become part of every undergraduate's training.
Anthony V. Geramita
I covered the book in a course for graduate students at Purdue during the Fall semester of 2000. I enjoyed going through the material, which is concrete, important and interesting--and the students did too.
The book is written with great care: all the details can be followed, the notation is a model of consistency, and there are almost no misprints.
The problems and tutorials were not only interesting, but fun, as was working with CoCoA (except when it tended to crash too often on my Macintosh, until I learned how to avoid certain pitfalls). All in all, it was a very nice educational experience for all concerned.
Joseph Lipman
The book by Kreuzer and Robbiano provides an excellent hands-on introduction to the field of Computational Commutative Algebra.
I am currently teaching a course "Topics in Applied Mathematics" at UC Berkeley with emphasis on Solving Polynomial Equations, and the book "Computational Commutative Algebra 1" was at the top of reading list I gave to my students. It provides them with a solid foundation for more advanced study and research in algorithms for algebraic geometry.
Bernd Sturmfels
"A Beautiful Mind" ha appena vinto 4 premi Oscar, ma rimane più che mai attuale la frase di Gian-Carlo Rota
"It is difficult to imagine a more imminent danger to survival of mathematics than the present ignorance of mathematics, coupled with widespread hostility against mathematics and mathematicians. In these days of triumphant P.R., when the obsessive repetition of simplistic slogans has become a condition sine qua non for survival, the ineptness of the mathematical community in making the message of mathematics heard beyond their narrow confines is a forerunner of doom".
C'è bisogno di libri di matematica come questo che, a sfogliarli, facciano venir voglia di leggerli, anche se chi li sfoglia è un informatico, come me, o un qualsiasi altro non-matematico. Come non apprezzare l'inconsueta verve del capitolo 0 o le citazioni a inizio paragrafo (come si fa a trovarne tante, tutte spiritose e pertinenti)? Come non essere intrigati dal polinomio col quadrato "ristretto" del paragrafo 0.10 e del tutorial 42? Come non apprezzare (e magari copiare) l'idea stessa dei tutorial, specie se capita addirittura di trovarci spunti per i propri argomenti di ricerca, com'è capitato a me? Peccato che non ci sia un riferimento per approfondire l'argomento, ma a questo si può rimediare scrivendo agli autori, che così si spaventano e mettono i riferimenti in rete, o nel secondo volume, o nella seconda edizione.
Peccato che il libro sia in inglese: almeno il commento, lasciatemelo scrivere in italiano (antiglobal?)!
Il libro è consigliato per il corso di Algebra Computazionale, complementare per Informatica e Matematica all'Università di Milano, docente Stefania De Stefano, mia moglie. Peccato che il corso abbia solo tre studenti, e uno sono io. Questa non è una battuta, e ci riporta all'inizio.
Mauro Torelli