An Excursion Through Discrete Differential Geometry
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An Excursion Through Discrete Differential Geometry
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Author : American Mathematical Society. Short Course, Discrete Differential Geometry
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-09-02
An Excursion Through Discrete Differential Geometry written by American Mathematical Society. Short Course, Discrete Differential Geometry and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-02 with Education categories.
Discrete Differential Geometry (DDG) is an emerging discipline at the boundary between mathematics and computer science. It aims to translate concepts from classical differential geometry into a language that is purely finite and discrete, and can hence be used by algorithms to reason about geometric data. In contrast to standard numerical approximation, the central philosophy of DDG is to faithfully and exactly preserve key invariants of geometric objects at the discrete level. This process of translation from smooth to discrete helps to both illuminate the fundamental meaning behind geometric ideas and provide useful algorithmic guarantees. This volume is based on lectures delivered at the 2018 AMS Short Course ``Discrete Differential Geometry,'' held January 8-9, 2018, in San Diego, California. The papers in this volume illustrate the principles of DDG via several recent topics: discrete nets, discrete differential operators, discrete mappings, discrete conformal geometry, and discrete optimal transport.
Mathematical And Computational Methods For Complex Social Systems
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Author : Heather Z. Brooks
language : en
Publisher: American Mathematical Society
Release Date : 2025-04-17
Mathematical And Computational Methods For Complex Social Systems written by Heather Z. Brooks and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-17 with Mathematics categories.
The spread of memes and misinformation on social media, political redistricting, gentrification in urban communities, pedestrian movement in crowds, and the dynamics of voters are among the many social phenomena that researchers investigate in the field of complex systems. In the study of complex social systems, there is often also societal relevance to improving our understanding of how individuals interact with each other and their environment, giving rise to collective group dynamics. The mathematical and computational study of complex social systems relies on and motivates the development of methods in many topics, including mathematical modeling, data analysis, network science, and topology and geometry. This volume is a collection of diverse articles about complex social systems. This collection includes both (1) survey and tutorial articles that introduce complex social systems and methods to study them and (2) manuscripts with original research that highlight a variety of mathematical areas and applications. This book introduces the study of complex social systems to a broad mathematical audience. It will particularly appeal to people who are interested in applied mathematics.
3d Printing In Mathematics
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Author : Maria Trnkova
language : en
Publisher: American Mathematical Society
Release Date : 2023-11-07
3d Printing In Mathematics written by Maria Trnkova and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-07 with Mathematics categories.
This volume is based on lectures delivered at the 2022 AMS Short Course “3D Printing: Challenges and Applications” held virtually from January 3–4, 2022. Access to 3D printing facilities is quickly becoming ubiquitous across college campuses. However, while equipment training is readily available, the process of taking a mathematical idea and making it into a printable model presents a big hurdle for most mathematicians. Additionally, there are still many open questions around what objects are possible to print, how to design algorithms for doing so, and what kinds of geometries have desired kinematic properties. This volume is focused on the process and applications of 3D printing for mathematical education, research, and visualization, alongside a discussion of the challenges and open mathematical problems that arise in the design and algorithmic aspects of 3D printing. The articles in this volume are focused on two main topics. The first is to make a bridge between mathematical ideas and 3D visualization. The second is to describe methods and techniques for including 3D printing in mathematical education at different levels— from pedagogy to research and from demonstrations to individual projects. We hope to establish the groundwork for engaged academic discourse on the intersections between mathematics, 3D printing and education.
Mean Field Games
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Author : François Delarue
language : en
Publisher: American Mathematical Society
Release Date : 2021-12-14
Mean Field Games written by François Delarue and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-14 with Mathematics categories.
This volume is based on lectures delivered at the 2020 AMS Short Course “Mean Field Games: Agent Based Models to Nash Equilibria,” held January 13–14, 2020, in Denver, Colorado. Mean field game theory offers a robust methodology for studying large systems of interacting rational agents. It has been extraordinarily successful and has continued to develop since its inception. The six chapters that make up this volume provide an overview of the subject, from the foundations of the theory to applications in economics and finance, including computational aspects. The reader will find a pedagogical introduction to the main ingredients, from the forward-backward mean field game system to the master equation. Also included are two detailed chapters on the connection between finite games and mean field games, with a pedestrian description of the different methods available to solve the convergence problem. The volume concludes with two contributions on applications of mean field games and on existing numerical methods, with an opening to machine learning techniques.
Communications In Analysis And Geometry
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Author :
language : en
Publisher:
Release Date : 2008
Communications In Analysis And Geometry written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Geometry categories.
Methods And Applications Of Analysis
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Author :
language : en
Publisher:
Release Date : 2007
Methods And Applications Of Analysis written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematical analysis categories.
The Asian Journal Of Mathematics
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Author :
language : en
Publisher:
Release Date : 2008
The Asian Journal Of Mathematics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
Advances In Theoretical And Mathematical Physics
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Author :
language : en
Publisher:
Release Date : 2009
Advances In Theoretical And Mathematical Physics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematical physics categories.
Pure And Applied Mathematics Quarterly
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Author :
language : en
Publisher:
Release Date : 2009
Pure And Applied Mathematics Quarterly written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
Discrete Differential Geometry
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Author : Alexander I. Bobenko
language : en
Publisher: American Mathematical Society
Release Date : 2023-09-14
Discrete Differential Geometry written by Alexander I. Bobenko and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-14 with Mathematics categories.
An emerging field of discrete differential geometry aims at the development of discrete equivalents of notions and methods of classical differential geometry. The latter appears as a limit of a refinement of the discretization. Current interest in discrete differential geometry derives not only from its importance in pure mathematics but also from its applications in computer graphics, theoretical physics, architecture, and numerics. Rather unexpectedly, the very basic structures of discrete differential geometry turn out to be related to the theory of integrable systems. One of the main goals of this book is to reveal this integrable structure of discrete differential geometry. For a given smooth geometry one can suggest many different discretizations. Which one is the best? This book answers this question by providing fundamental discretization principles and applying them to numerous concrete problems. It turns out that intelligent theoretical discretizations are distinguished also by their good performance in applications. The intended audience of this book is threefold. It is a textbook on discrete differential geometry and integrable systems suitable for a one semester graduate course. On the other hand, it is addressed to specialists in geometry and mathematical physics. It reflects the recent progress in discrete differential geometry and contains many original results. The third group of readers at which this book is targeted is formed by specialists in geometry processing, computer graphics, architectural design, numerical simulations, and animation. They may find here answers to the question “How do we discretize differential geometry?” arising in their specific field. Prerequisites for reading this book include standard undergraduate background (calculus and linear algebra). No knowledge of differential geometry is expected, although some familiarity with curves and surfaces can be helpful.