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| Author | : Lou Van den Dries |
| Publisher | : Cambridge University Press |
| Total Pages | : 196 |
| Release | : 1998-05-07 |
| Genre | : Mathematics |
| ISBN | : 0521598389 |
These notes give a self-contained treatment of the theory of o-minimal structures from a geometric and topological viewpoint, assuming only rudimentary algebra and analysis. This book should be of interest to model theorists, analytic geometers and topologists.
| Author | : L. P. D. van den Dries |
| Publisher | : |
| Total Pages | : 192 |
| Release | : 1998 |
| Genre | : Electronic books |
| ISBN | : 9781107367524 |
These notes give a self-contained treatment of the theory of o-minimal structures.
| Author | : Deirdre Haskell |
| Publisher | : Cambridge University Press |
| Total Pages | : 244 |
| Release | : 2000-07-03 |
| Genre | : Mathematics |
| ISBN | : 9780521780681 |
Model theory has made substantial contributions to semialgebraic, subanalytic, p-adic, rigid and diophantine geometry. These applications range from a proof of the rationality of certain Poincare series associated to varieties over p-adic fields, to a proof of the Mordell-Lang conjecture for function fields in positive characteristic. In some cases (such as the latter) it is the most abstract aspects of model theory which are relevant. This book, originally published in 2000, arising from a series of introductory lectures for graduate students, provides the necessary background to understanding both the model theory and the mathematics behind these applications. The book is unique in that the whole spectrum of contemporary model theory (stability, simplicity, o-minimality and variations) is covered and diverse areas of geometry (algebraic, diophantine, real analytic, p-adic, and rigid) are introduced and discussed, all by leading experts in their fields.
| Author | : G. O. Jones |
| Publisher | : Cambridge University Press |
| Total Pages | : 235 |
| Release | : 2015-08-13 |
| Genre | : Mathematics |
| ISBN | : 1107462495 |
This book brings the researcher up to date with recent applications of mathematical logic to number theory.
| Author | : Mário J. Edmundo |
| Publisher | : Cuvillier Verlag |
| Total Pages | : 223 |
| Release | : 2005 |
| Genre | : |
| ISBN | : 386537557X |
| Author | : Tamal Krishna Dey |
| Publisher | : Cambridge University Press |
| Total Pages | : 456 |
| Release | : 2022-03-10 |
| Genre | : Mathematics |
| ISBN | : 1009103199 |
Topological data analysis (TDA) has emerged recently as a viable tool for analyzing complex data, and the area has grown substantially both in its methodologies and applicability. Providing a computational and algorithmic foundation for techniques in TDA, this comprehensive, self-contained text introduces students and researchers in mathematics and computer science to the current state of the field. The book features a description of mathematical objects and constructs behind recent advances, the algorithms involved, computational considerations, as well as examples of topological structures or ideas that can be used in applications. It provides a thorough treatment of persistent homology together with various extensions – like zigzag persistence and multiparameter persistence – and their applications to different types of data, like point clouds, triangulations, or graph data. Other important topics covered include discrete Morse theory, the Mapper structure, optimal generating cycles, as well as recent advances in embedding TDA within machine learning frameworks.
| Author | : Chris Miller |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 247 |
| Release | : 2012-09-14 |
| Genre | : Mathematics |
| ISBN | : 1461440416 |
This volume was produced in conjunction with the Thematic Program in o-Minimal Structures and Real Analytic Geometry, held from January to June of 2009 at the Fields Institute. Five of the six contributions consist of notes from graduate courses associated with the program: Felipe Cano on a new proof of resolution of singularities for planar analytic vector fields; Chris Miller on o-minimality and Hardy fields; Jean-Philippe Rolin on the construction of o-minimal structures from quasianalytic classes; Fernando Sanz on non-oscillatory trajectories of vector fields; and Patrick Speissegger on pfaffian sets. The sixth contribution, by Antongiulio Fornasiero and Tamara Servi, is an adaptation to the nonstandard setting of A.J. Wilkie's construction of o-minimal structures from infinitely differentiable functions. Most of this material is either unavailable elsewhere or spread across many different sources such as research papers, conference proceedings and PhD theses. This book will be a useful tool for graduate students or researchers from related fields who want to learn about expansions of o-minimal structures by solutions, or images thereof, of definable systems of differential equations.
| Author | : Pierre Simon |
| Publisher | : Cambridge University Press |
| Total Pages | : 165 |
| Release | : 2015-07-16 |
| Genre | : Mathematics |
| ISBN | : 1107057752 |
The first book to introduce the rapidly developing subject of NIP theories, for students and researchers in model theory.
| Author | : David Marker |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 342 |
| Release | : 2006-04-06 |
| Genre | : Mathematics |
| ISBN | : 0387227342 |
Assumes only a familiarity with algebra at the beginning graduate level; Stresses applications to algebra; Illustrates several of the ways Model Theory can be a useful tool in analyzing classical mathematical structures
| Author | : Danny Calegari |
| Publisher | : Oxford University Press on Demand |
| Total Pages | : 378 |
| Release | : 2007-05-17 |
| Genre | : Mathematics |
| ISBN | : 0198570082 |
This unique reference, aimed at research topologists, gives an exposition of the 'pseudo-Anosov' theory of foliations of 3-manifolds. This theory generalizes Thurston's theory of surface automorphisms and reveals an intimate connection between dynamics, geometry and topology in 3 dimensions. Significant themes returned to throughout the text include the importance of geometry, especially the hyperbolic geometry of surfaces, the importance of monotonicity, especially in1-dimensional and co-dimensional dynamics, and combinatorial approximation, using finite combinatorical objects such as train-tracks, branched surfaces and hierarchies to carry more complicated continuous objects.
