Computational Commutative Algebra 2 (Paperback)

Martin Kreuzer

ISBN 10: 3642064914 / ISBN 13: 9783642064913

Editore: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, Berlin, 2010

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Paperback. "The second volume of the authors' 'Computational commutative algebra'!covers on its 586 pages a wealth of interesting material with several unexpected applications. ! an encyclopedia on computational commutative algebra, a source for lectures on the subject as well as an inspiration for seminars. The text is recommended for all those who want to learn and enjoy an algebraic tool that becomes more and more relevant to different fields of applications." --ZENTRALBLATT MATH Hofstadters Law: It always takes longer than you think it will take, even if you take into account Hofstadters Law. Thus we have a con?rmed invariant which governs our writing: our velocity is one centimeter per year, after all e?ects due to Hofstadters Law have been taken into account. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Codice articolo 9783642064913

Dati bibliografici

• Titolo: Computational Commutative Algebra 2 (Paperback)
• Editore: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, Berlin
• Data di pubblicazione: 2010
• Lingua: Inglese
• ISBN 10: 3642064914
• ISBN 13: 9783642064913
• Rilegatura: Paperback
• Edizione: prima edizione
• Condizione: new

Descrizione articolo

Riassunto

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.

Dalla quarta di copertina

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!