Computational Commutative And Non Commutative Algebraic Geometry
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| Author | : Wolmer Vasconcelos |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 432 |
| Release | : 2004-05-18 |
| Genre | : Mathematics |
| ISBN | : 9783540213116 |
This ACM volume deals with tackling problems that can be represented by data structures which are essentially matrices with polynomial entries, mediated by the disciplines of commutative algebra and algebraic geometry. The discoveries stem from an interdisciplinary branch of research which has been growing steadily over the past decade. The author covers a wide range, from showing how to obtain deep heuristics in a computation of a ring, a module or a morphism, to developing means of solving nonlinear systems of equations - highlighting the use of advanced techniques to bring down the cost of computation. Although intended for advanced students and researchers with interests both in algebra and computation, many parts may be read by anyone with a basic abstract algebra course.
| Author | : David Eisenbud |
| Publisher | : Cambridge University Press |
| Total Pages | : 463 |
| Release | : 2015-11-19 |
| Genre | : Mathematics |
| ISBN | : 1107065623 |
This book surveys fundamental current topics in these two areas of research, emphasising the lively interaction between them. Volume 1 contains expository papers ideal for those entering the field.
| Author | : Martin Kreuzer |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 325 |
| Release | : 2008-07-15 |
| Genre | : Mathematics |
| ISBN | : 354067733X |
This introduction to polynomial rings, Gröbner bases and applications bridges the gap in the literature between theory and actual computation. It details numerous applications, covering fields as disparate as algebraic geometry and financial markets. To aid in a full understanding of these applications, more than 40 tutorials illustrate how the theory can be used. The book also includes many exercises, both theoretical and practical.
| Author | : David Eisenbud |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 784 |
| Release | : 2013-12-01 |
| Genre | : Mathematics |
| ISBN | : 1461253500 |
This is a comprehensive review of commutative algebra, from localization and primary decomposition through dimension theory, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. The book gives a concise treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. Many exercises included.
| Author | : Michael F. Atiyah |
| Publisher | : CRC Press |
| Total Pages | : 140 |
| Release | : 2018-03-09 |
| Genre | : Mathematics |
| ISBN | : 0429973268 |
First Published in 2018. This book grew out of a course of lectures given to third year undergraduates at Oxford University and it has the modest aim of producing a rapid introduction to the subject. It is designed to be read by students who have had a first elementary course in general algebra. On the other hand, it is not intended as a substitute for the more voluminous tracts such as Zariski-Samuel or Bourbaki. We have concentrated on certain central topics, and large areas, such as field theory, are not touched. In content we cover rather more ground than Northcott and our treatment is substantially different in that, following the modern trend, we put more emphasis on modules and localization.
| Author | : Gwyn Bellamy |
| Publisher | : Cambridge University Press |
| Total Pages | : 367 |
| Release | : 2016-06-20 |
| Genre | : Mathematics |
| ISBN | : 1107129540 |
This book provides a comprehensive introduction to the interactions between noncommutative algebra and classical algebraic geometry.
| Author | : Alain Connes |
| Publisher | : Springer |
| Total Pages | : 364 |
| Release | : 2003-12-15 |
| Genre | : Mathematics |
| ISBN | : 3540397027 |
Noncommutative Geometry is one of the most deep and vital research subjects of present-day Mathematics. Its development, mainly due to Alain Connes, is providing an increasing number of applications and deeper insights for instance in Foliations, K-Theory, Index Theory, Number Theory but also in Quantum Physics of elementary particles. The purpose of the Summer School in Martina Franca was to offer a fresh invitation to the subject and closely related topics; the contributions in this volume include the four main lectures, cover advanced developments and are delivered by prominent specialists.
| Author | : Thomas A. Garrity |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 363 |
| Release | : 2013-02-01 |
| Genre | : Mathematics |
| ISBN | : 0821893963 |
Algebraic Geometry has been at the center of much of mathematics for hundreds of years. It is not an easy field to break into, despite its humble beginnings in the study of circles, ellipses, hyperbolas, and parabolas. This text consists of a series of ex
| Author | : Gert-Martin Greuel |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 601 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3662049635 |
This book can be understood as a model for teaching commutative algebra, and takes into account modern developments such as algorithmic and computational aspects. As soon as a new concept is introduced, the authors show how the concept can be worked on using a computer. The computations are exemplified with the computer algebra system Singular, developed by the authors. Singular is a special system for polynomial computation with many features for global as well as for local commutative algebra and algebraic geometry. The book includes a CD containing Singular as well as the examples and procedures explained in the book.
| Author | : Svetlana Cojocaru |
| Publisher | : IOS Press |
| Total Pages | : 336 |
| Release | : 2005 |
| Genre | : Electronic books |
| ISBN | : 1586035053 |
