This book details the heart and soul of modern commutative and algebraic geometry. It covers such topics as the Hilbert Basis Theorem, the Nullstellensatz, invariant theory, projective geometry, and dimension theory. In addition to enhancing the text of the second edition, with over 200 pages reflecting changes to enhance clarity and correctness, this third edition of Ideals, Varieties and Algorithms includes: a significantly updated section on Maple; updated information on AXIOM, CoCoA, Macaulay 2, Magma, Mathematica and SINGULAR; and presents a shorter proof of the Extension Theorem.
Ideals, Varieties, and Algorithms
and over one million other books are available for Amazon Kindle.
Learn more
FREE Two-Day Shipping for Students. Learn more |
| ||||||||||||||||||
 Sell Back Your Copy for $18.00
Whether you buy it used on Amazon for $30.00 or somewhere else, you can sell it back through our Book Trade-In Program at the current price of $18.00.
Used Price$30.00
Trade-in Price$18.00
Price after
Trade-in$12.00 |
Book Description
Special Offers and Product Promotions
- Buy $50 in qualifying physical textbooks, get $5 in Amazon MP3 Credit. Here's how (restrictions apply)
Frequently Bought Together
Editorial Reviews
Review
From the reviews of the third edition:
"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 a excellent guide to introduce further undergraduates in the algorithmic aspect of commutative algebra and algebraic geometry." (Peter Schenzel, Zentralblatt MATH, Vol. 1118 (20), 2007)
From the Back Cover
Algebraic Geometry is the study of systems of polynomial equations in one or more variables, asking such questions as: Does the system have finitely many solutions, and if so how can one find them? And if there are infinitely many solutions, how can they be described and manipulated?
The solutions of a system of polynomial equations form a geometric object called a variety; the corresponding algebraic object is an ideal. There is a close relationship between ideals and varieties which reveals the intimate link between algebra and geometry. Written at a level appropriate to undergraduates, this book covers such topics as the Hilbert Basis Theorem, the Nullstellensatz, invariant theory, projective geometry, and dimension theory.
The algorithms to answer questions such as those posed above are an important part of algebraic geometry. Although the algorithmic roots of algebraic geometry are old, it is only in the last forty years that computational methods have regained their earlier prominence. New algorithms, coupled with the power of fast computers, have led to both theoretical advances and interesting applications, for example in robotics and in geometric theorem proving.
In addition to enhancing the text of the second edition, with over 200 pages reflecting changes to enhance clarity and correctness, this third edition of Ideals, Varieties and Algorithms includes:
A significantly updated section on Maple in Appendix C
Updated information on AXIOM, CoCoA, Macaulay 2, Magma, Mathematica and SINGULAR
A shorter proof of the Extension Theorem presented in Section 6 of Chapter 3
From the 2nd Edition:
"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
Product Details
Would you like to update product info or give feedback on images?
|
More About the Author
Discover books, learn about writers, read author blogs, and more.
Customer Reviews
|
Share your thoughts with other customers:
|
||||||||||||||||||||||
|
Most Helpful Customer Reviews
10 of 12 people found the following review helpful:
4.0 out of 5 stars
Careful about production error,
By Random Thoughts (Maryland) - See all my reviews
This review is from: Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra (Undergraduate Texts in Mathematics) (Hardcover)
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 www.cs.amherst.edu/~dac/iva/3ed1.pdf.
So buyers may be better off waiting for a corrected later version from the publisher.
7 of 8 people found the following review helpful:
5.0 out of 5 stars
Very clearly written.,
This review is from: Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra (Undergraduate Texts in Mathematics) (Hardcover)
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.
2 of 12 people found the following review helpful:
3.0 out of 5 stars
Good book (for Math people),
By
Amazon Verified Purchase(What's this?)
This review is from: Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra (Undergraduate Texts in Mathematics) (Hardcover)
I actually haven't gone through the entire book, but the parts that I did go through were interesting. The book was (I thought) a little confusing to understand, but that may just be because it is for higher level abstract math. Lost of proofs and interesting things if your interested in abstract math!
Share your thoughts with other customers: Create your own review
|
|
Inside This Book
(learn more)
Key Phrases - Statistically Improbable Phrases (SIPs):
(learn more)
projective algebraic geometry, elimination theory, circle theorem, first elimination ideal, ideal description problem, grlex order, cyclic matrix group, using lex order, finite matrix group, many homogeneous invariants, grevlex order, reduced row echelon matrices, monomial ideal, implicitization problem, monomial order, reduced row echelon matrix, intermediate dividend, using elimination theory, ideal membership problem, polynomial parametrization, affine variety, coordinate subspace, most computer algebra systems, smallest variety containing, projective closure Key Phrases - Capitalized Phrases (CAPs): (learn more)
Extension Theorem, Use Exercise, Bezout's Theorem, Hilbert Basis Theorem, Closure Theorem, Euclidean Algorithm, Weak Nullstellensatz, Prove Proposition, The Algebra-Geometry Dictionary, Use Theorem, Hilbert's Nullstellensatz, Elimination Theorem, Invariant Theory of Finite Groups, Pappus's Theorem, The Geometry of Quadric Hypersurfaces, Parametrizations of Affine Varieties, Rational Functions, Dickson's Lemma, Use Definition, Quotients of Polynomial Rings, Algorithmic Computations, Polynomials of One Variable, Intersections of Ideals, Repeat Exercise, Use Corollary Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
projective algebraic geometry, elimination theory, circle theorem, first elimination ideal, ideal description problem, grlex order, cyclic matrix group, using lex order, finite matrix group, many homogeneous invariants, grevlex order, reduced row echelon matrices, monomial ideal, implicitization problem, monomial order, reduced row echelon matrix, intermediate dividend, using elimination theory, ideal membership problem, polynomial parametrization, affine variety, coordinate subspace, most computer algebra systems, smallest variety containing, projective closure Key Phrases - Capitalized Phrases (CAPs): (learn more)
Extension Theorem, Use Exercise, Bezout's Theorem, Hilbert Basis Theorem, Closure Theorem, Euclidean Algorithm, Weak Nullstellensatz, Prove Proposition, The Algebra-Geometry Dictionary, Use Theorem, Hilbert's Nullstellensatz, Elimination Theorem, Invariant Theory of Finite Groups, Pappus's Theorem, The Geometry of Quadric Hypersurfaces, Parametrizations of Affine Varieties, Rational Functions, Dickson's Lemma, Use Definition, Quotients of Polynomial Rings, Algorithmic Computations, Polynomials of One Variable, Intersections of Ideals, Repeat Exercise, Use Corollary Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
What Other Items Do Customers Buy After Viewing This Item?
Tags Customers Associate with This Product(What's this?)Click on a tag to find related items, discussions, and people.
|
Customer Discussions
|
This product's forum
Active discussions in related forums
Search Customer Discussions
|
Related forums
|
Listmania!
|
|
So You'd Like to...
|
|
Look for Similar Items by Category
- Books > Computers & Technology > Programming > Algorithms
- Books > Computers & Technology > Software
- Books > New & Used Textbooks > Computer Science
- Books > New & Used Textbooks > Science & Mathematics > Mathematics > Algebra & Trigonometry
- Books > New & Used Textbooks > Science & Mathematics > Mathematics > Geometry
- Books > Science & Math > Mathematics
