Overview

The main TOPIC of this book is that of Groebner bases and their applications. The main PURPOSE of this book is that of bridging the current gap in the literature between theory and real computation. The book can be used by teachers and students alike as a comprehensive guide to both the theory and the practice of Computational Commutative Algebra. It has been made as self-contained as possible, and thus is ideally suited as a textbook for graduate or advanced undergraduate courses. Numerous applications are described, covering fields as disparate as algebraic geometry and financial markets. To aid a deeper understanding of these applications there are 44 tutorials aimed at illustrating how the theory can be used in these cases. The computational aspects of the tutorials can be carried out with the computer algebra system CoCoA, an introduction to which appears in an appendix. Besides the tutorials there are plenty of exercises, some of a theoretical nature and others more practical.

Full Product Details

Author:   Martin Kreuzer ,  Lorenzo Robbiano
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   1st ed. 2000. Corr. 2nd printing 2008
Dimensions:   Width: 15.50cm , Height: 1.90cm , Length: 23.50cm
Weight:   0.683kg
ISBN:  

9783540677338

ISBN 10:   354067733
Pages:   322
Publication Date:   27 September 2000
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

Foreword.- Introduction.- 1. Foundations.- 2. Gröbner Bases.- 3. First Applications.- A. How to Get Started with CoCoA.- B. How to Program CoCoA.- C. A Potpourri of CoCoA Programs.- D. Hints for Selected Exercises.- Notation.- Bibliography.- Index.

Reviews

From the reviews: <p>.,. This is one of the most refreshing mathematical books I have ever held in my hands. The authors do not believe in teaching by spreading out the material, but they introduce it via questions and discussions, they explore it in an intuitive fashion, exercise it through well-chosen examples, and start the reader on his own expeditions through numerous tutorials, i.e., guided projects. This is academic teaching at its best: if I had not seen it, I should not have believed that it can be done so well. ... In conclusion, this book gives students a stimulating introduction to commutative algebra very much geared to their need, and it provides numerous useful ideas to those who teach the subject. (H.Stetter, IMN - Internationale Mathematische Nachrichten 2003, Vol. 57, Issue 193) <p> This account of polynomial rings, GrAbner bases and applications such as computations of syzygies is written from the point of view of a computer user; as a result, it often provides new insights. The exercises and tutorials (how to work with CoCoA) add to the usefulness of the volume. (Mathematika 48, 2001) <p> Das Buch ist in einem aufmunternd lockeren Stil geschrieben und fA1/4r Studierende gut zum Selbststudium geeignet. Der prAsentierte Stoff wird durch viele Beispiele und Aoebungsaufgaben (teilweise mit Anleitungen im Anhang) ergAnzt. Weiter sind in jedem Abschnitt sorgfAltig ausgearbeitete Tutorials angefA1/4gt, die zur Benutzung von Computeralgebrasystemen, insbesondere CoCoA, anregen sollen. (Computeralgebra-Rundbrief, Nr. 28, MArz 2001) <p> Four years ago the authors published the first volume of a projected seris about computational commutative algebra which took threeyears of intense work just to fill three centimeters of your bookshelf. Now they have gifted us with the second volume, and they say that the completion of this volume took four years and it is about four centimeters thick. Thus we have a confirmed invariant which governs our writing: our velocity is one centimeter per year. These quotations from the foreword of the book give a clue of how amusing it is, and also how mathematically solid it is. <p>In this second volume the authors continue with the same style as the first, an almost humorous one. [...] <p>It was a pleasure to review this nice book but, as always, the equilibrium of the world depends on good and bad things, and the bad thing is the authors' decision to not write a third volume. In their own words: Alas, we have to inform you that this is absolutely and definitely the second and last volume of the trilogy. Fortunately, these two volumes collect so large an amount of information and inspiration that we can say the authors actually fulfilled our expectations. <p>Paulo F. Machado, Mathematical Review Clippings 2006h <p> An excellent, non-standard, elementary and self-contained introduction to the theory of GrAbner bases and its applications a ] . Moreover, the style is very friendly and relaxing a ] . As it is now, this book can be used either to introduce the theory of GrAbner bases to students with a basic knowledge of algebra or to provide a first introduction to commutative algebra a ] . (Laureano GonzA(c)lez-Vega and TomAs Recio, ACM SIGSAM Bulletin, Vol. 38 (2), 2004)

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