Metric Algebraic Geometry
Metric Algebraic Geometry

Author: Paul Breiding

Publisher: Springer Nature

Published: 2024

Total Pages: 225

ISBN-13: 3031514629

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Zusammenfassung: Metric algebraic geometry combines concepts from algebraic geometry and differential geometry. Building on classical foundations, it offers practical tools for the 21st century. Many applied problems center around metric questions, such as optimization with respect to distances. After a short dive into 19th-century geometry of plane curves, we turn to problems expressed by polynomial equations over the real numbers. The solution sets are real algebraic varieties. Many of our metric problems arise in data science, optimization and statistics. These include minimizing Wasserstein distances in machine learning, maximum likelihood estimation, computing curvature, or minimizing the Euclidean distance to a variety. This book addresses a wide audience of researchers and students and can be used for a one-semester course at the graduate level. The key prerequisite is a solid foundation in undergraduate mathematics, especially in algebra and geometry. This is an open access book

Algebraic Geometry
Algebraic Geometry

Author: Solomon Lefschetz

Publisher: Courier Corporation

Published: 2012-09-05

Total Pages: 250

ISBN-13: 0486154726

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An introduction to algebraic geometry and a bridge between its analytical-topological and algebraical aspects, this text for advanced undergraduate students is particularly relevant to those more familiar with analysis than algebra. 1953 edition.

Computational Algebraic Geometry
Computational Algebraic Geometry

Author: Frederic Eyssette

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 334

ISBN-13: 1461227526

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The theory and practice of computation in algebraic geometry and related domains, from a mathematical point of view, has generated an increasing interest both for its rich theoretical possibilities and its usefulness in applications in science and engineering. In fact, it is one of the master keys for future significant improvement of the computer algebra systems (e.g., Reduce, Macsyma, Maple, Mathematica, Axiom, Macaulay, etc.) that have become such useful tools for many scientists in a variety of disciplines. The major themes covered in this volume, arising from papers p- sented at the conference MEGA-92 were: - Effective methods and complexity issues in commutative algebra, projective geometry, real geometry, and algebraic number theory - Algebra-geometric methods in algebraic computing and applica tions. MEGA-92 was the second of a new series of European conferences on the general theme of Effective Methods in Algebraic Geometry. It was held in Nice, France, on April 21-25, 1992 and built on the themes presented at MEGA-90 (Livomo, Italy, April 17-21, 1990). The next conference - MEGA-94 - will be held in Santander, Spain in the spring of 1994. The Organizing committee that initiatiod and supervises this bi enniel conference consists of A. Conte (Torino), J.H. Davenport (Bath), A. Galligo (Nice), D. Yu. Grigoriev (Petersburg), J. Heintz (Buenos Aires), W. Lassner (Leipzig), D. Lazard (paris), H.M. MOller (Hagen), T. Mora (Genova), M. Pohst (DUsseldort), T. Recio (Santander), J.J.

Introduction to Algebraic Geometry
Introduction to Algebraic Geometry

Author: Serge Lang

Publisher: Courier Dover Publications

Published: 2019-03-20

Total Pages: 273

ISBN-13: 0486834220

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Author Serge Lang defines algebraic geometry as the study of systems of algebraic equations in several variables and of the structure that one can give to the solutions of such equations. The study can be carried out in four ways: analytical, topological, algebraico-geometric, and arithmetic. This volume offers a rapid, concise, and self-contained introductory approach to the algebraic aspects of the third method, the algebraico-geometric. The treatment assumes only familiarity with elementary algebra up to the level of Galois theory. Starting with an opening chapter on the general theory of places, the author advances to examinations of algebraic varieties, the absolute theory of varieties, and products, projections, and correspondences. Subsequent chapters explore normal varieties, divisors and linear systems, differential forms, the theory of simple points, and algebraic groups, concluding with a focus on the Riemann-Roch theorem. All the theorems of a general nature related to the foundations of the theory of algebraic groups are featured.

Metric Algebraic Geometry
Metric Algebraic Geometry

Author: Paul Breiding

Publisher: Birkhäuser

Published: 2024-02-17

Total Pages: 0

ISBN-13: 9783031514616

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Metric algebraic geometry combines concepts from algebraic geometry and differential geometry. Building on classical foundations, it offers practical tools for the 21st century. Many applied problems center around metric questions, such as optimization with respect to distances. After a short dive into 19th-century geometry of plane curves, we turn to problems expressed by polynomial equations over the real numbers. The solution sets are real algebraic varieties. Many of our metric problems arise in data science, optimization and statistics. These include minimizing Wasserstein distances in machine learning, maximum likelihood estimation, computing curvature, or minimizing the Euclidean distance to a variety. This book addresses a wide audience of researchers and students and can be used for a one-semester course at the graduate level. The key prerequisite is a solid foundation in undergraduate mathematics, especially in algebra and geometry. This is an open access book.

Introduction to Algebraic Geometry
Introduction to Algebraic Geometry

Author: Steven Dale Cutkosky

Publisher: American Mathematical Soc.

Published: 2018-06-01

Total Pages: 498

ISBN-13: 1470435187

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This book presents a readable and accessible introductory course in algebraic geometry, with most of the fundamental classical results presented with complete proofs. An emphasis is placed on developing connections between geometric and algebraic aspects of the theory. Differences between the theory in characteristic and positive characteristic are emphasized. The basic tools of classical and modern algebraic geometry are introduced, including varieties, schemes, singularities, sheaves, sheaf cohomology, and intersection theory. Basic classical results on curves and surfaces are proved. More advanced topics such as ramification theory, Zariski's main theorem, and Bertini's theorems for general linear systems are presented, with proofs, in the final chapters. With more than 200 exercises, the book is an excellent resource for teaching and learning introductory algebraic geometry.

Methods of Algebraic Geometry
Methods of Algebraic Geometry

Author: William Vallance Douglas Hodge

Publisher: CUP Archive

Published: 1947

Total Pages: 412

ISBN-13:

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This classic work, in three volumes, provides a lucid and rigorous account of the foundations of modern algebraic geometry. The authors have confined themselves to fundamental concepts and geometrical methods, and do not give detailed developments of geometrical properties but geometrical meaning has been emphasized throughout.

3264 and All That
3264 and All That

Author: David Eisenbud

Publisher: Cambridge University Press

Published: 2016-04-14

Total Pages: 633

ISBN-13: 1107017084

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3264, the mathematical solution to a question concerning geometric figures.

Algebraic Geometry
Algebraic Geometry

Author: Elena Rubei

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2014-05-27

Total Pages: 240

ISBN-13: 3110316234

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Algebraic geometry is one of the most classic subjects of university research in mathematics. It has a very complicated language that makes life very difficult for beginners. This book is a little dictionary of algebraic geometry: for every of the most common words in algebraic geometry, it contains its definition, several references and the statements of the main theorems about that term (without their proofs). Also some terms of other subjects, close to algebraic geometry, have been included. It was born to help beginners that know some basic facts of algebraic geometry, but not every basic fact, to follow seminars and to read papers, by providing them with basic definitions and statements. The form of a dictionary makes it very easy and quick to consult.