Lorenzo Robbiano - Böcker

Approximate Commutative Algebra is an emerging field of research which endeavours to bridge the gap between traditional exact Computational Commutative Algebra and approximate numerical computation. The last 50 years have seen enormous progress in the realm of exact Computational Commutative Algebra, and given the importance of polynomials in scientific modelling, it is very natural to want to extend these ideas to handle approximate, empirical data deriving from physical measurements of phenomena in the real world. In this volume nine contributions from established researchers describe various approaches to tackling a variety of problems arising in Approximate Commutative Algebra.

This book combines, in a novel and general way, an extensive development of the theory of families of commuting matrices with applications to zero-dimensional commutative rings, primary decompositions and polynomial system solving. It integrates the Linear Algebra of the Third Millennium, developed exclusively here, with classical algorithmic and algebraic techniques. Even the experienced reader will be pleasantly surprised to discover new and unexpected aspects in a variety of subjects including eigenvalues and eigenspaces of linear maps, joint eigenspaces of commuting families of endomorphisms, multiplication maps of zero-dimensional affine algebras, computation of primary decompositions and maximal ideals, and solution of polynomial systems. This book completes a trilogy initiated by the uncharacteristically witty books Computational Commutative Algebra 1 and 2 by the same authors. The material treated here is not available in book form, and much of it is notavailable at all. The authors continue to present it in their lively and humorous style, interspersing core content with funny quotations and tongue-in-cheek explanations.

This book combines, in a novel and general way, an extensive development of the theory of families of commuting matrices with applications to zero-dimensional commutative rings, primary decompositions and polynomial system solving. It integrates the Linear Algebra of the Third Millennium, developed exclusively here, with classical algorithmic and algebraic techniques. Even the experienced reader will be pleasantly surprised to discover new and unexpected aspects in a variety of subjects including eigenvalues and eigenspaces of linear maps, joint eigenspaces of commuting families of endomorphisms, multiplication maps of zero-dimensional affine algebras, computation of primary decompositions and maximal ideals, and solution of polynomial systems. This book completes a trilogy initiated by the uncharacteristically witty books Computational Commutative Algebra 1 and 2 by the same authors. The material treated here is not available in book form, and much of it is notavailable at all. The authors continue to present it in their lively and humorous style, interspersing core content with funny quotations and tongue-in-cheek explanations.

"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

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.

"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

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, what you are holding in your hands now is for youabook. But for us, for our families and friends, it has been known as the book over the last three years. Three years of intense work just to ?ll three centimeters of your bookshelf! This amounts to about one centimeter per year, or roughly two-?fths of an inch per year if you are non-metric. Clearly we had ample opportunity to experience the full force of Hofstadter’s Law. Writing a book about Computational Commutative Algebra is not - like computing a Gr¨ obner basis: you need unshakeable faith to believe that the project will ever end; likewise, you must trust in the Noetherianity of polynomial rings to believe that Buchberger’s Algorithm will ever terminate. Naturally, we hope that the ?nal result proves our e?orts worthwhile. This is a book for learning, teaching, reading, and, most of all, enjoying the topic at hand.

Da dove viene questo strano titolo Algebra lineare per tutti? Tutti in che senso? E` luogo comune il fatto che la matematica non sia materia per tutti ed è vero che uno degli ostacoli alla sua diffusione sono spesso i matematici stessi (per fortuna non tutti). Alcuni di essi tendono a sviluppare un linguaggio astruso, difficile, o addirittura talvolta incomprensibile persino per gli esperti di settori limitrofi. E se provassimo a chiedere ad un matematico di professione di estraniarsi per un poco dal suo linguaggio abitudinario e parlare e scrivere in modo più lineare? E se gli chiedessimo addirittura di essere vivace? E perché non esagerare e chiedergli di essere a tratti persino divertente? Lo scopo di questo libro è quello di fornire i primi strumenti matematici relativi ad un capitolo della scienza che si chiama Algebra Lineare. Il testo è stato scritto da un matematico che ha cercato di uscire dal suo personaggio per venire incontro ad un pubblico ampio. La sfida è quella di rendere accessibili a tutti i primi rudimenti di un sapere fondamentale per la scienza e la tecnologia.

This book provides students with the rudiments of Linear Algebra, a fundamental subject for students in all areas of science and technology. The book would also be good for statistics students studying linear algebra.It is the translation of a successful textbook currently being used in Italy. The author is a mathematician sensitive to the needs of a general audience. In addition to introducing fundamental ideas in Linear Algebra through a wide variety of interesting examples, the book also discusses topics not usually covered in an elementary text (e.g. the "cost" of operations, generalized inverses, approximate solutions).  The challenge is to show why the "everyone" in the title can find Linear Algebra useful and easy to learn.The translation has been prepared by a native English speaking mathematician, Professor Anthony V. Geramita.