Topics in Algebraic Geometry and Geometric Modeling

Topics in Algebraic Geometry and Geometric Modeling
Author: Ron Goldman
Publisher: American Mathematical Soc.
Total Pages: 378
Release: 2003
Genre: Mathematics
ISBN: 0821834207

Algebraic geometry and geometric modeling both deal with curves and surfaces generated by polynomial equations. Algebraic geometry investigates the theoretical properties of polynomial curves and surfaces; geometric modeling uses polynomial, piecewise polynomial, and rational curves and surfaces to build computer models of mechanical components and assemblies for industrial design and manufacture. The NSF sponsored the four-day ''Vilnius Workshop on Algebraic Geometry and Geometric Modeling'', which brought together some of the top experts in the two research communities to examine a wide range of topics of interest to both fields. This volume is an outgrowth of that workshop. Included are surveys, tutorials, and research papers. In addition, the editors have included a translation of Minding's 1841 paper, ''On the determination of the degree of an equations obtained by elimination'', which foreshadows the modern application of mixed volumes in algebraic geometry. The volume is suitable for mathematicians, computer scientists, and engineers interested in applications of algebraic geometry to geometric modeling.

Solving Systems of Polynomial Equations

Solving Systems of Polynomial Equations
Author: Bernd Sturmfels
Publisher: American Mathematical Soc.
Total Pages: 162
Release: 2002
Genre: Mathematics
ISBN: 0821832514

Bridging a number of mathematical disciplines, and exposing many facets of systems of polynomial equations, Bernd Sturmfels's study covers a wide spectrum of mathematical techniques and algorithms, both symbolic and numerical.

Algorithmic Game Theory

Algorithmic Game Theory
Author: Panagiotis Kanellopoulos
Publisher: Springer Nature
Total Pages: 596
Release: 2022-09-13
Genre: Computers
ISBN: 3031157141

This book constitutes the proceedings of the 15th International Symposium on Algorithmic Game Theory, SAGT 2022, which took place in Colchester, UK, in September 2022. The 31 full papers included in this book were carefully reviewed and selected from 83 submissions. They were organized in topical sections as follows: Auctions, markets and mechanism design; computational aspects in games; congestion and network creation games; data sharing and learning; social choice and stable matchings.

Hilbert's Tenth Problem: Relations with Arithmetic and Algebraic Geometry

Hilbert's Tenth Problem: Relations with Arithmetic and Algebraic Geometry
Author: Jan Denef
Publisher: American Mathematical Soc.
Total Pages: 384
Release: 2000
Genre: Mathematics
ISBN: 0821826220

This book is the result of a meeting that took place at the University of Ghent (Belgium) on the relations between Hilbert's tenth problem, arithmetic, and algebraic geometry. Included are written articles detailing the lectures that were given as well as contributed papers on current topics of interest. The following areas are addressed: an historical overview of Hilbert's tenth problem, Hilbert's tenth problem for various rings and fields, model theory and local-global principles, including relations between model theory and algebraic groups and analytic geometry, conjectures in arithmetic geometry and the structure of diophantine sets, for example with Mazur's conjecture, Lang's conjecture, and Bücchi's problem, and results on the complexity of diophantine geometry, highlighting the relation to the theory of computation. The volume allows the reader to learn and compare different approaches (arithmetical, geometrical, topological, model-theoretical, and computational) to the general structural analysis of the set of solutions of polynomial equations. It would make a nice contribution to graduate and advanced graduate courses on logic, algebraic geometry, and number theory

The Importance of Being Understood

The Importance of Being Understood
Author: Adam Morton
Publisher: Routledge
Total Pages: 240
Release: 2005-06-29
Genre: Philosophy
ISBN: 1134484305

The Importance of Being Understood is an innovative and thought-provoking exploration of the links between the way we think about each other's mental states and the fundamentally cooperative nature of everyday life. Adam Morton begins with a consideration of 'folk psychology', the tendency to attribute emotions, desires, beliefs and thoughts to human minds. He takes the view that it is precisely this tendency that enables us to understand, predict and explain the actions of others, which in turn helps us to decide on our own course of action. This relection suggests, claims Morton, that certain types of cooperative activity are dependent on everyday psychological understanding conversely, that we act in such a way as to make our actions easily intelligible to others so that we can benefit from being understood. This idea of 'beneficial circularities' is at the core of Morton's investigation of the interdependencies between folk psychology and social behaviour: we understand each other because we have learned to make ourselves intelligible. Using examples of cooperative activities such as car driving and playing tennis, Adam Morton analyses the concepts of belief and simulation, the idea of explanation by motive, and the causal force of psychological explanation. In addition to argument and analysis, Morton also includes more speculative explorations of topics such as moral progress and presents a new point of view on how and why cultures differ. The Importance of Being Understood forges new links between ethics and the philosophy of mind and will be of interest to anyone in either field, as well as developmental psychologists.

Stability and Perfection of Nash Equilibria

Stability and Perfection of Nash Equilibria
Author: Eric van Damme
Publisher: Springer Science & Business Media
Total Pages: 354
Release: 2012-12-06
Genre: Mathematics
ISBN: 3642582427

I have been pleased with the favourable reception of the first edition of this book and I am grateful to have the opportunity to prepare this second edition. In this revised and enlarged edition I corrected some misprints and errors that occurred in the first edition (fortunately I didn't find too many) and I added a large number of notes that give the reader an impression of what kind of results have been obtained since the first edition was printed and that give an indication of the direction the subject is taking. Many of the notes discuss (or refer to papers discussing) applications of the refinements that are considered. Of course, it is the quantity and the quality of the insights and the applications that lend the refinements their validity. Although the guide to the applications is far from complete, the notes certainly allow the reader to form a good judgement of which refinements have really yielded new insights. Hence, as in the first edition, I will refrain from speculating on which refinements of Nash equilibria will survive in the long run. To defend this position let me also cite Binmore [1990] who compares writing about refinements to the Herculean task of defeating the nine-headed Hydra which grew too heads for each that was struck off. It is a pleasure to have the opportunity to thank my secretary, Marjoleine de Wit, who skilfully and, as always, cheerfully typed the manuscript and did the proofreading.