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Author: Jean-Benoît Bost Publisher: Birkhäuser ISBN: 3319496387 Category : Mathematics Languages : fr Pages : 361
Book Description
This volume presents original research articles and extended surveys related to the mathematical interest and work of Jean-Michel Bismut. His outstanding contributions to probability theory and global analysis on manifolds have had a profound impact on several branches of mathematics in the areas of control theory, mathematical physics and arithmetic geometry. Contributions by: K. Behrend N. Bergeron S. K. Donaldson J. Dubédat B. Duplantier G. Faltings E. Getzler G. Kings R. Mazzeo J. Millson C. Moeglin W. Müller R. Rhodes D. Rössler S. Sheffield A. Teleman G. Tian K-I. Yoshikawa H. Weiss W. Werner The collection is a valuable resource for graduate students and researchers in these fields.
Author: Jean-Benoît Bost Publisher: Birkhäuser ISBN: 3319496387 Category : Mathematics Languages : fr Pages : 361
Book Description
This volume presents original research articles and extended surveys related to the mathematical interest and work of Jean-Michel Bismut. His outstanding contributions to probability theory and global analysis on manifolds have had a profound impact on several branches of mathematics in the areas of control theory, mathematical physics and arithmetic geometry. Contributions by: K. Behrend N. Bergeron S. K. Donaldson J. Dubédat B. Duplantier G. Faltings E. Getzler G. Kings R. Mazzeo J. Millson C. Moeglin W. Müller R. Rhodes D. Rössler S. Sheffield A. Teleman G. Tian K-I. Yoshikawa H. Weiss W. Werner The collection is a valuable resource for graduate students and researchers in these fields.
Author: M.K. Murray Publisher: Routledge ISBN: 1351455117 Category : Mathematics Languages : en Pages : 164
Book Description
Several years ago our statistical friends and relations introduced us to the work of Amari and Barndorff-Nielsen on applications of differential geometry to statistics. This book has arisen because we believe that there is a deep relationship between statistics and differential geometry and moreoever that this relationship uses parts of differential geometry, particularly its 'higher-order' aspects not readily accessible to a statistical audience from the existing literature. It is, in part, a long reply to the frequent requests we have had for references on differential geometry! While we have not gone beyond the path-breaking work of Amari and Barndorff- Nielsen in the realm of applications, our book gives some new explanations of their ideas from a first principles point of view as far as geometry is concerned. In particular it seeks to explain why geometry should enter into parametric statistics, and how the theory of asymptotic expansions involves a form of higher-order differential geometry. The first chapter of the book explores exponential families as flat geometries. Indeed the whole notion of using log-likelihoods amounts to exploiting a particular form of flat space known as an affine geometry, in which straight lines and planes make sense, but lengths and angles are absent. We use these geometric ideas to introduce the notion of the second fundamental form of a family whose vanishing characterises precisely the exponential families.
Author: Ovidiu Calin Publisher: Springer ISBN: 3319077791 Category : Mathematics Languages : en Pages : 389
Book Description
This book covers topics of Informational Geometry, a field which deals with the differential geometric study of the manifold probability density functions. This is a field that is increasingly attracting the interest of researchers from many different areas of science, including mathematics, statistics, geometry, computer science, signal processing, physics and neuroscience. It is the authors’ hope that the present book will be a valuable reference for researchers and graduate students in one of the aforementioned fields. This textbook is a unified presentation of differential geometry and probability theory, and constitutes a text for a course directed at graduate or advanced undergraduate students interested in applications of differential geometry in probability and statistics. The book contains over 100 proposed exercises meant to help students deepen their understanding, and it is accompanied by software that is able to provide numerical computations of several information geometric objects. The reader will understand a flourishing field of mathematics in which very few books have been written so far.
Author: Melissa Agnew Publisher: ISBN: 9781933445212 Category : Languages : en Pages :
Book Description
Based on the popularity of the original Engaging Math book, Kagan how offers this rich array of ready-go-do activities for the geometry and data analysis & probability strands. You'll find interactive Kagan Structures for pair work, teamwork, and whole-class engagement. Geometry activities cover; shapes and their attributes, edges, faces, vertices, symmetry, congruent, similar, transformations, angels, points, lines, segments, rays, parallel, perpendicular, and intersecting. Data Analysis & Probability activities cover: picture graphs,line graphs, bar graphs, line plots, charts, pie graphs, directional maps and grids, coordinate grids, mean, median, mode, data and probability. Engaging Math just got easier.
Author: Pierre Henry-Labordere Publisher: CRC Press ISBN: 1420087002 Category : Business & Economics Languages : en Pages : 403
Book Description
Analysis, Geometry, and Modeling in Finance: Advanced Methods in Option Pricing is the first book that applies advanced analytical and geometrical methods used in physics and mathematics to the financial field. It even obtains new results when only approximate and partial solutions were previously available.Through the problem of option pricing, th
Author: Eric Carlen Publisher: Springer ISBN: 1493970054 Category : Mathematics Languages : en Pages : 626
Book Description
This volume presents some of the research topics discussed at the 2014-2015 Annual Thematic Program Discrete Structures: Analysis and Applications at the Institute of Mathematics and its Applications during the Spring 2015 where geometric analysis, convex geometry and concentration phenomena were the focus. Leading experts have written surveys of research problems, making state of the art results more conveniently and widely available. The volume is organized into two parts. Part I contains those contributions that focus primarily on problems motivated by probability theory, while Part II contains those contributions that focus primarily on problems motivated by convex geometry and geometric analysis. This book will be of use to those who research convex geometry, geometric analysis and probability directly or apply such methods in other fields.
Author: Jean-Benoît Bost
Author: Jean-Benoît Bost
Author: Jean-Benoît Bost
Author: M.K. Murray
Author: Ovidiu Calin
Author: Melissa Agnew
Author: R. Chuaqui
Author: Christopher J. Bishop
Author: Pierre Henry-Labordere
Author: Luis A. Santaló
Author: Eric Carlen