Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra (Undergraduate Texts in Mathematics)

Hello. I got this book as a student and it reads fairly well.You need some algebra background although the book inserts some quick algebra in there. Example it explains what rings are, fields, ideals, etc. Basic ring theory. So dont expect anything too fancy.After that, the book introduces the topic with every now and then backtracks to algebra for review. Example, it presents ideal properties, radical ideal properties before it introduces a definition from alg geo that includes them in there.Essesntial, you work with fields, and polynomial rings, and affine space. So expect all the proofs to be focused on that, even though they may be true for any ring, not just polynomial rings. True for some not all.Other than that, it is a good read, nothing fancy, pretty concrete and for self learning its pretty good. Check it out.

I recently completed my honour's degree in mathematics, my research subject was Groebner bases, this text was my bible throughout the process

good

This book explains the concepts well and the proofs are written carefully and clearly. This is a math book, so you should expect the usual Definition-Theorem-Proof format, but the exposition is progressive, and the material is very well motivated. I had to implement an algorithm for the computation of Groebner bases, and I borrowed this book from the University library to learn about the Buchberger algorithm and related topics, and thanks to this book I was able to understand this algorithm and its correctness proof without the help of anyone. Of course Buchberger's algorithm is only a small part of this book, and you can find a lot of important topics in it.Finally, note that the second part of Madhu Sudan's Algebra and Computation course at MIT follows this book closely. So at least one top expert in the field seems to have a good opinion of the book.

This is the 3rd edition of a popular reference on the subject. There was some production error with earlier version of the book. Even with the latest version, the authors have provided 14-page worth of corrections for the 1st printing of the 3rd edition. See [...]So buyers may be better off waiting for a corrected later version from the publisher.

This is simply the best book I ever read on the subject. Either your want a computational treatment of the subject or you want a more theoretical approach this is the right book.

Habe mir dieses Buch zu einer Vorlesung gekauft, die ich während des Bachelor-Studiums gehört habe. Der Schreibstil ist einfach und gut nachzuvollziehen, die Beweisführung dem Niveau angemessen und die Aufgaben am Ende jedes Kapitels lassen genug Platz für eigene Ideen. Insgesamt bin ich sehr zufrieden mit dem Buch, habe es auch nach der Vorlesung noch ein paar Mal durchgestöbert, weil mich dieses Gebiet der Mathematik wirklich interessiert.