applications undergraduate computational combinatorics

books:

Steps in Commutative Algebra (London Mathematical Society Student Texts)
Rodney Y. Sharp

Cambridge University Press, 2001

This introductory account of commutative algebra is aimed at students with a background only in basic algebra. Professor Sharp's book provides a good foundation from which the reader can proceed to more advanced works in commutative algebra or algebraic geometry. This new edition contains additional chapters on regular sequences and on Cohen-Macaulay rings.

Commutative Ring Theory (Cambridge Studies in Advanced Mathematics)

2 reviews
H. Matsumura

Cambridge University Press, 1989

Truly Beautiful
Matsumura has achieved a great success with this book. The first nine chapters contain all of the algebra used in Hartshorne's _Algebraic Geometry_, and a reader who masters all of that material will be well on the way to a solid understanding of algebraic geometry. At the same time, the writing is clear and concise, and the exercises (which the reader should of course do!) are enlightening. ...

Commutative Algebra, Vol 2

1 review
O. Zariski, Pierre Samuel

Springer, 1976

Not much to say, really.
I bought this to have a matching set with my Volume II. Decent enough for reference, but that's about it. Yeah...that's about it.

Computational Commutative Algebra 1
Martin Kreuzer, Lorenzo Robbiano

Springer, 2008

This is a book about Gröbner bases and their applications. It contains 3 chapters, 20 sections, 44 tutorials, 165 exercises, and numerous further amusements. It is going to help you bridge the gap between theoretical computer algebra and actual computation. We hope you will have as much fun reading it as the authors had writing it! From the reviews: "This is one of the most refreshing mathematical books I have ever held in my hands. This ...

Undergraduate Commutative Algebra (London Mathematical Society Student Texts)

1 review
Miles Reid

Cambridge University Press, 1996

"Undergraduate" in the best way
The material in this book is not usually considered "undergraduate": Noether normalization, spectra of rings, discrete valuation rings, and more. But this book makes them very clear. It is more geometrical, and has more motivation, than Atiyah and MacDonald INTRODUCTION TO COMMUTATIVE ALGEBRA. It is briefer and more surveyable than Eisenbud COMMUTATIVE ALGEBRA. If you go on in the subject you ...

Combinatorial Commutative Algebra (Graduate Texts in Mathematics)

1 review
Ezra Miller, Bernd Sturmfels

Springer, 2005

Coherent and Useful
This book does a good job at introducing some of the most interesting combinatorial problems in monomial resolutions. Although their chapter on toric varieties is somewhat weak, most of the other chapters (square-free monomial ideals, Borel-fixed ideals, staircases associated to monomial ideals in three variables, etc.) are very well written with challenging and revealing exercises at the end.

Commutative Algebra: with a View Toward Algebraic Geometry (Graduate Texts in Mathematics)

7 reviews
David Eisenbud

Springer, 1999

Superb
If one is interested in taking on a thorough study of algebraic geometry, this book is a perfect starting point. The writing is excellent, and the student will find many exercises that illustrate and extend the results in each chapter. Readers are expected to have an undergraduate background in algebra, and maybe some analysis and elementary notions from differential geometry. Space does not ...

Introduction To Commutative Algebra (on Demand)

6 reviews
Michael Atiyah

Westview Press, 1994

A gem of mathematical writing
This is how mathematics texts SHOULD be written. As in technical writing, the smaller text is the better written text. Everything is clean and direct, with clairity obviously a prime consideration. One never gets mired down. The proofs are always as close to a "THE BOOK" proof as possible, with illuminating examples, and plenty of excercises, many with outlines for solution, which makes the ...

A Singular Introduction to Commutative Algebra
Gert-Martin Greuel, Gerhard Pfister

Springer, 2007

From the reviews of the first edition: "It is certainly no exaggeration to say that ? A Singular Introduction to Commutative Algebra aims to lead a further stage in the computational revolution in commutative algebra ? . Among the great strengths and most distinctive features ? is a new, completely unified treatment of the global and local theories. ? making it one of the most flexible and most efficient systems of its type....another ...

Algebraic Statistics: Computational Commutative Algebra in Statistics (Monographs on Statistics and Applied ...
Giovanni Pistone, Eva Riccomagno, ...

Chapman & Hall/CRC, 2000

Written by pioneers in this exciting new field, Algebraic Statistics introduces the application of polynomial algebra to experimental design, discrete probability, and statistics. It begins with an introduction to Gröbner bases and a thorough description of their applications to experimental design. A special chapter covers the binary case with new application to coherent systems in reliability and two level factorial designs. The work paves ...

Combinatorics and Commutative Algebra (Progress in Mathematics)

2 reviews
Richard P. Stanley

Birkhäuser Boston, 2004

great book
Great book - just be ready to get hold of some other books to fill in the details. If you're not entirely comfortable with the stuff in chapter 0 concerning modules (projectivity, injectivity), tor and ext, and homology from topology, maybe find a quick introduction to these elsewhere - while its certainly possible to learn about these things from chapter 0 of this book, it's not exactly the ...

Commutative Algebra (Graduate Texts in Mathematics)
David Eisenbud

Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 1995

Topics in Commutative Ring Theory

1 review
John J. Watkins

Princeton University Press, 2007

Well-written and a lot of fun (for a math book!)
I wanted to wait until I finished the book, but since there are no reviews... This is a treasure of a book. The book itself is very well made, well-bound, and uses good quality paper. The print is very clear and easy to read, (no clutter). The basic format is a few pages explaining a topic on Rings, some proofs and examples as you go along, and then problems for each chapter. The explanations ...

Commutative Algebras of Toeplitz Operators on the Bergman Space (Operator Theory: Advances and Applications)
Nikolai Vasilevski

Birkhäuser Basel, 2008

This book is devoted to the spectral theory of commutative C*-algebras of Toeplitz operators on the Bergman space and its applications. For each such commutative algebra there is a unitary operator which reduces Toeplitz operators from this algebra to certain multiplication operators, thus providing their spectral type representations. This yields a powerful research tool giving direct access to the majority of the important properties of the ...

Six Lectures on Commutative Algebra (Progress in Mathematics, Vol 166)
J. Elias

Birkhauser, 1998

Interest in commutative algebra has surged over the past decades. In order to survey and highlight recent developments in this rapidly expanding field, the Centre de Recerca Matematica in Bellaterra organized the Summer School on Commutative Algebra 1996 which was held from July 16 to 26, 1996. Lecture series were presented by six high-level specialists, L. Avramov (Purdue), M.K. Green (UCLA), C. Huneke (Purdue), P. Schenzel (Halle), G. Valla ...

Computational Methods in Commutative Algebra and Algebraic Geometry
Wolmer V. Vasconcelos

Springer, 2004

From the reviews: "... Many parts of the book can be read by anyone with a basic abstract algebra course... it was one of the author's intentions to equip students who are interested in computational problems with the necessary algebraic background in pure mathematics and to encourage them to do further research in commutative algebra and algebraic geometry. But researchers will also benefit from this exposition. They will find an up-to-date ...

Commutative Semigroups (Advances in Mathematics)
P.A. Grillet

Springer, 2001

This is the first book about commutative semigroups in general. Emphasis is on structure but the other parts of the theory are at least surveyed and a full set of about 850 references is included. The book is intended for mathematicians who do research on semigroups or who encounter commutative semigroups in their research.

Commutative Semigroup Rings (Chicago Lectures in Mathematics)

1 review
Robert Gilmer

University Of Chicago Press, 1984

power series
generalized power serie

Commutative Algebra: Chapters 1-7
Nicolas Bourbaki

Springer, 2004

This is the softcover reprint of the English translation of 1972 (available from Springer since 1989) of the first 7 chapters of Bourbaki's 'Algèbre commutative'. It provides a very complete treatment of commutative algebra, enabling the reader to go further and study algebraic or arithmetic geometry. The first 3 chapters treat in succession the concepts of flatness, localization and completions (in the general setting of graduations and ...

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