Computational Commutative Algebra 2 - Softcover

Kreuzer, Martin; Robbiano, Lorenzo

Softcover

ISBN 10: 3642064914 ISBN 13: 9783642064913

Verlag: Springer, 2010

Inhaltsangabe

Hofstadter’s Law: It always takes longer than you think it will take, even if you take into account Hofstadter’s Law. (Douglas R. Hofstadter) Dear Reader, why did we begin the foreword of this second volume with the same quote as the ?rst? There we wrote that it took three years of intense work just to ?ll three centimeters of your bookshelf. The completion of this volume took four years and it is about four centimeters thick. Thus we have a con?rmed invariant which governs our writing: our velocity is one centimeter per year, after all e?ects due to Hofstadter’s Law have been taken into account. When westartedthisprojectinthelastmillennium,weplannedabookforlearning, teaching, reading and, most of all, enjoying the topic at hand. Surely there is no law which says that a mathematical book has to be dull, boring, dry, or tedious. But how do you make it enjoyable? Our approach has been to ?ll it with amusing quotes, varied jokes, funny word games, ?owery metaphors and occasional literarye?orts. There are two possible drawbacks of this method. Firstly, not everyone has the same sense of humour and not every metaphor works as intended. For instance, it is easy to joke about certain politicians, but what happens if they read this book? And when we wrote of a small boat sailing slowly into the Brazilian sunset, it was pointed out to us that this entails a geographical problem. Secondly, it is very di?cult to write humorously in a foreign language.

Über diesen Titel

Über die Autorin bzw. den Autor

Martin Kreuzer holds the Chair of Symbolic Computation at the University of Passau, Germany. Starting out in Commutative Algebra and Algebraic Geometry, his research interests have developed further into Computer Algebra and its applications, including industrial applications and algebraic cryptography. He is the author or co-author of five monographs on computational algebra, cryptography and logic.

In his spare time, he plays correspondence chess, for which he is an international grandmaster and a severalfold world team champion.

Lorenzo Robbiano is a retired professor at the University of Genova, Italy. He is the co-author (with Martin Kreuzer) of the two books "Computational Commutative Algebra 1" and "Computational Commutative Algebra 2". Since 1987 he has been the team leader of the project CoCoA. His research interests have evolved from Algebraic Geometry to Commutative Algebra, and in the last years to Computer Algebra.

Von der hinteren Coverseite

Computational Commutative Algebra 2 is the natural continuation of Computational Commutative Algebra 1 with some twists, starting with the differently coloured cover graphics.

The first volume had 3 chapters, 20 sections, 44 tutorials, and some amusing quotes. Since bigger is better, this book contains 3 chapters filling almost twice as many pages, 23 sections (some as big as a whole chapter), and 55 tutorials (some as big as a whole section).

The number of jokes and quotes has increased exponentially due to the little-known fact that a good mathematical joke is better than a dozen mediocre papers.

The main part of this book is a breathtaking passeggiata through the computational domains of graded rings and modules and their Hilbert functions. Besides Gröbner bases, we encounter Hilbert bases, border bases, SAGBI bases, and even SuperG bases.

The tutorials traverse areas ranging from algebraic geometry and combinatorics to photogrammetry, magic squares, coding theory, statistics, and automatic theorem proving. Whereas in the first volume gardening and chess playing were not treated, in this volume they are.

This is a book for learning, teaching, reading, and most of all, enjoying the topic at hand. The theories it describes can be applied to anything from children's toys to oil production. If you buy it, probably one spot on your desk will be lost forever!

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 2010
• Sprache: Englisch
• ISBN 10: 3642064914
• ISBN 13: 9783642064913
• Einband: Taschenbuch
• Anzahl der Seiten: 596
• Kontakt zum Hersteller: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3,69115 Heidelberg, Germany; Heidelberg; Deutschland