Special Issue on Effective Methods in Algebraic Geometry (MEGA 2005)
Author: Alicia Dickenstein
Publisher:
Published: 2007
Total Pages: 264
ISBN-13:
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Interactions of Classical and Numerical Algebraic Geometry
Author: Daniel James Bates
Publisher: American Mathematical Soc.
Published: 2009-09-16
Total Pages: 379
ISBN-13: 0821847465
DOWNLOAD EBOOKThis volume contains the proceedings of the conference on Interactions of Classical and Numerical Algebraic Geometry, held May 22-24, 2008, at the University of Notre Dame, in honor of the achievements of Professor Andrew J. Sommese. While classical algebraic geometry has been studied for hundreds of years, numerical algebraic geometry has only recently been developed. Due in large part to the work of Andrew Sommese and his collaborators, the intersection of these two fields is now ripe for rapid advancement. The primary goal of both the conference and this volume is to foster the interaction between researchers interested in classical algebraic geometry and those interested in numerical methods. The topics in this book include (but are not limited to) various new results in complex algebraic geometry, a primer on Seshadri constants, analyses and presentations of existing and novel numerical homotopy methods for solving polynomial systems, a numerical method for computing the dimensions of the cohomology of twists of ideal sheaves, and the application of algebraic methods in kinematics and phylogenetics.
Approximate Commutative Algebra
Author: Lorenzo Robbiano
Publisher: Springer Science & Business Media
Published: 2009-09-18
Total Pages: 237
ISBN-13: 3211993142
DOWNLOAD EBOOKApproximate 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.
Effective Methods in Algebraic Geometry
Author: Teo Mora
Publisher: Springer Science & Business Media
Published: 1991
Total Pages: 524
ISBN-13: 9780817635466
DOWNLOAD EBOOKOn Lack of Effectiveness in Semi-algebraic Geometry.- A simple constructive proof of Canonical Resolution of Singularities.- Local Membership Problems for Polynomial Ideals.- Un Algorithme pour le Calcul des Résultants.- On algorithms for real algebraic plane curves.- Duality methods for the membership problem.- Exemples d'ensembles de Points en Position Uniforme.- Efficient Algorithms and Bounds for Wu-Ritt Characteristic Sets.- Noetherian Properties and Growth of some Associative Algebras.- Codes and Elliptic Curves.- Algorithmes - disons rapides - pour la décomposition d'une variété algébrique en composantes irréductibles et équidimensionnelles.- Complexity of Solving Systems of Linear Equations over the Rings of Differential Operators.- Membership problem, Representation problem and the Computation of the Radical for one-dimensional Ideals.- On the Complexity of Zero-dimensional Algebraic Systems.- A Single Exponential Bound on the Complexity of Computing Gröbner Bases of Zero Dimensional Ideals.- Algorithms for a Multiple Algebraic Extension.- Elementary constructive theory of ordered fields.- Effective real Nullstellensatz and variants.- Algorithms for the Solution of Systems of Linear Equations in Commutative Rings.- Une conjecture sur les anneaux de Chow A(G, ?) renforcée par un calcul formel.- Construction de courbes de genre 2 à partir de leurs modules.- Computing Syzygies à la Gau?-Jordan.- The non-scalar Model of Complexity in Computational Geometry.- Géométrie et Interpretations Génériques, un Algorithme.- Canonical Bases: Relations with Standard Bases, Finiteness Conditions and Application to Tame Automorphisms.- The tangent cone algorithm and some applications to local algebraic geometry.- Effective Methods for Systems of Algebraic Partial Differential Equations.- Finding roots of equations involving functions defined by first order algebraic differential equations.- Some Effective Methods in the Openness of Loci for Cohen-Macaulay and Gorenstein Properties.- Sign determination on zero dimensional sets.- A Classification of Finite-dimensional Monomial Algebras.- An algorithm related to compactifications of adjoint groups.- Deciding Consistency of Systems of Polynomial in Exponent Inequalities in Subexponential Time.
Solving Polynomial Equations
Author: Alicia Dickenstein
Publisher: Springer Science & Business Media
Published: 2005-04-27
Total Pages: 433
ISBN-13: 3540243267
DOWNLOAD EBOOKThis book provides a general introduction to modern mathematical aspects in computing with multivariate polynomials and in solving algebraic systems. It presents the state of the art in several symbolic, numeric, and symbolic-numeric techniques, including effective and algorithmic methods in algebraic geometry and computational algebra, complexity issues, and applications ranging from statistics and geometric modelling to robotics and vision. Graduate students, as well as researchers in related areas, will find an excellent introduction to currently interesting topics. These cover Groebner and border bases, multivariate resultants, residues, primary decomposition, multivariate polynomial factorization, homotopy continuation, complexity issues, and their applications.
Progress in Cryptology - AFRICACRYPT 2010
Author: Daniel J. Bernstein
Publisher: Springer
Published: 2010-04-29
Total Pages: 448
ISBN-13: 3642126782
DOWNLOAD EBOOKThis book constitutes the proceedings of the Third International Conference on Cryptology in Africa, AFRICACRYPT 2010, held in Stellenbosch, South Africa, on May 3-6, 2010. The 25 papers presented together with three invited talks were carefully reviewed and selected from 82 submissions. The topics covered are signatures, attacks, protocols, networks, elliptic curves, side-channel attacks and fault attacks, public-key encryption, keys and PUFs, and ciphers and hash functions.
Computing Handbook, Third Edition
Author: Teofilo Gonzalez
Publisher: CRC Press
Published: 2014-05-07
Total Pages: 2330
ISBN-13: 1439898529
DOWNLOAD EBOOKComputing Handbook, Third Edition: Computer Science and Software Engineering mirrors the modern taxonomy of computer science and software engineering as described by the Association for Computing Machinery (ACM) and the IEEE Computer Society (IEEE-CS). Written by established leading experts and influential young researchers, the first volume of this popular handbook examines the elements involved in designing and implementing software, new areas in which computers are being used, and ways to solve computing problems. The book also explores our current understanding of software engineering and its effect on the practice of software development and the education of software professionals. Like the second volume, this first volume describes what occurs in research laboratories, educational institutions, and public and private organizations to advance the effective development and use of computers and computing in today’s world. Research-level survey articles provide deep insights into the computing discipline, enabling readers to understand the principles and practices that drive computing education, research, and development in the twenty-first century.
Computational Algebraic and Analytic Geometry
Author: Mika Seppälä
Publisher: American Mathematical Soc.
Published: 2012
Total Pages: 242
ISBN-13: 0821868691
DOWNLOAD EBOOKThis volume contains the proceedings of three AMS Special Sessions on Computational Algebraic and Analytic Geometry for Low-Dimensional Varieties held January 8, 2007, in New Orleans, LA; January 6, 2009, in Washington, DC; and January 6, 2011, in New Orleans, LA. Algebraic, analytic, and geometric methods are used to study algebraic curves and Riemann surfaces from a variety of points of view. The object of the study is the same. The methods are different. The fact that a multitude of methods, stemming from very different mathematical cultures, can be used to study the same objects makes this area both fascinating and challenging.
Mathematics for Machine Learning
Author: Marc Peter Deisenroth
Publisher: Cambridge University Press
Published: 2020-04-23
Total Pages: 392
ISBN-13: 1108569323
DOWNLOAD EBOOKThe fundamental mathematical tools needed to understand machine learning include linear algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability and statistics. These topics are traditionally taught in disparate courses, making it hard for data science or computer science students, or professionals, to efficiently learn the mathematics. This self-contained textbook bridges the gap between mathematical and machine learning texts, introducing the mathematical concepts with a minimum of prerequisites. It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models and support vector machines. For students and others with a mathematical background, these derivations provide a starting point to machine learning texts. For those learning the mathematics for the first time, the methods help build intuition and practical experience with applying mathematical concepts. Every chapter includes worked examples and exercises to test understanding. Programming tutorials are offered on the book's web site.
Computing Handbook
Author: Allen Tucker
Publisher: CRC Press
Published: 2022-05-29
Total Pages: 3851
ISBN-13: 1439898456
DOWNLOAD EBOOKThis two volume set of the Computing Handbook, Third Edition (previously theComputer Science Handbook) provides up-to-date information on a wide range of topics in computer science, information systems (IS), information technology (IT), and software engineering. The third edition of this popular handbook addresses not only the dramatic growth of computing as a discipline but also the relatively new delineation of computing as a family of separate disciplines as described by the Association for Computing Machinery (ACM), the IEEE Computer Society (IEEE-CS), and the Association for Information Systems (AIS). Both volumes in the set describe what occurs in research laboratories, educational institutions, and public and private organizations to advance the effective development and use of computers and computing in today's world. Research-level survey articles provide deep insights into the computing discipline, enabling readers to understand the principles and practices that drive computing education, research, and development in the twenty-first century. Chapters are organized with minimal interdependence so that they can be read in any order and each volume contains a table of contents and subject index, offering easy access to specific topics. The first volume of this popular handbook mirrors the modern taxonomy of computer science and software engineering as described by the Association for Computing Machinery (ACM) and the IEEE Computer Society (IEEE-CS). Written by established leading experts and influential young researchers, it examines the elements involved in designing and implementing software, new areas in which computers are being used, and ways to solve computing problems. The book also explores our current understanding of software engineering and its effect on the practice of software development and the education of software professionals. The second volume of this popular handbook demonstrates the richness and breadth of the IS and IT disciplines. The book explores their close links to the practice of using, managing, and developing IT-based solutions to advance the goals of modern organizational environments. Established leading experts and influential young researchers present introductions to the current status and future directions of research and give in-depth perspectives on the contributions of academic research to the practice of IS and IT development, use, and management.
