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

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Review

“In each of the new editions the authors' were interested to incorporate new developments, simplifications of arguments as well as further applications. Thanks to the authors' this is also the case in the present fourth edition. … Thanks to the continuously updating the textbook will remain an excellent source for the computational Commutative Algebra for students as well as for researchers interested in learning the subject.” (Peter Schenzel, zbMATH 1335.13001, 2016)

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From the Back Cover

This text covers topics in algebraic geometry and commutative algebra with a strong perspective toward practical and computational aspects. The first four chapters form the core of the book. A comprehensive chart in the preface illustrates a variety of ways to proceed with the material once these chapters are covered. In addition to the fundamentals of algebraic geometry―the elimination theorem, the extension theorem, the closure theorem, and the Nullstellensatz―this new edition incorporates several substantial changes, all of which are listed in the Preface. The largest revision incorporates a new chapter (ten), which presents some of the essentials of progress made over the last decades in computing Gröbner bases. The book also includes current computer algebra material in Appendix C and updated independent projects (Appendix D). The book may serve as a first or second course in undergraduate abstract algebra and, with some supplementation perhaps, for beginning graduate level courses in algebraic geometry or computational algebra. Prerequisites for the reader include linear algebra and a proof-oriented course. It is assumed that the reader has access to a computer algebra system. Appendix C describes features of Maple™, Mathematica®, and Sage, as well as other systems that are most relevant to the text. Pseudocode is used in the text; Appendix B carefully describes the pseudocode used.From the reviews of previous editions:“…The book gives an introduction to Buchberger’s algorithm with applications to syzygies, Hilbert polynomials, primary decompositions. There is an introduction to classical algebraic geometry with applications to the ideal membership problem, solving polynomial equations, and elimination theory. …The book is well-written. …The reviewer is sure that it will be an excellent guide to introduce further undergraduates in the algorithmic aspect of commutative algebra and algebraic geometry.” ―Peter Schenzel, zbMATH, 2007“I consider the book to be wonderful. ... The exposition is very clear, there are many helpful pictures, and there are a great many instructive exercises, some quite challenging ... offers the heart and soul of modern commutative and algebraic geometry.” ―The American Mathematical Monthly

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Product details

Series: Undergraduate Texts in Mathematics

Hardcover: 646 pages

Publisher: Springer; 4th ed. 2015 edition (April 30, 2015)

Language: English

ISBN-10: 3319167200

ISBN-13: 978-3319167206

Product Dimensions:

6.1 x 1.4 x 9.2 inches

Shipping Weight: 2.2 pounds (View shipping rates and policies)

Average Customer Review:

4.8 out of 5 stars

14 customer reviews

Amazon Best Sellers Rank:

#152,517 in Books (See Top 100 in Books)

I used this text as a supplemental text for a course for one term. It was excellent as a supplement, but I was glad I was not using it as my main text for the course.This text is very clear and well-written, has tons of examples and develops geometric intuition for the subject quite well. Overall I think it is a great text for its target audience of undergraduate students with basically no background in abstract algebra. Unfortunately for a student who has had a course in abstract algebra the text goes too slowly, develops a lot of concepts they should already know in it and the explanations can be rather long at times.I highly recommend this text for its intended audience or as a supplement to a more advanced text for a reader who wants more examples, clearer statements, a more thorough development or a good source for geometric intuition about the subject.

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.

This book explains and illustrates the algorithms used by symbolic math packages such as Mathematica, Maple, CoCoA, MatLab, MuPAD,... to solve problems involving polynomials in many variables, and along the way teaches the elements of real algebraic geometry-- most mathematics texts concentrate on the complex-variable version. It is not just for undergraduates; electrical engineers, for instance, should see it. Lots of pictures!

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

Certainly will take you from a novice to a high level of understanding. If you are already a professional mathematician, you will need to skim parts (the authors repeat things a lot, which is a very useful pedagogical device, but can be annoying if you are reading the book sequentially.

great book. I use it for introducting to abstract algebra.

Filled with great information about its subject (see title). Its my second copy. I ruined the first copy by working it so hard.

good

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

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

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

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