Mathematics: Frontiers and Perspectives
Mathematics: Frontiers and Perspectives

Author: Vladimir Igorevich Arnolʹd

Publisher: American Mathematical Soc.

Published: 2000

Total Pages: 476

ISBN-13: 9780821826973

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A celebration of the state of mathematics at the end of the millennium. Produced under the auspices of the International Mathematical Union (IMU), the book was born as part of the activities of World Mathematical Year 2000. It consists of 28 articles written by influential mathematicians.

A Member of the Third House
A Member of the Third House

Author: Hamlin Garland

Publisher: Somerset Publishers Incorporated

Published: 1892

Total Pages: 266

ISBN-13:

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Garland's third book, a novel with a muckraking, populist theme typical of his earlier works: a state legislature is corrupted by railroad magnates.

Fully Nonlinear Elliptic Equations
Fully Nonlinear Elliptic Equations

Author: Luis A. Caffarelli

Publisher: American Mathematical Soc.

Published: 1995

Total Pages: 114

ISBN-13: 0821804375

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The goal of the book is to extend classical regularity theorems for solutions of linear elliptic partial differential equations to the context of fully nonlinear elliptic equations. This class of equations often arises in control theory, optimization, and other applications. The authors give a detailed presentation of all the necessary techniques. Instead of treating these techniques in their greatest generality, they outline the key ideas and prove the results needed for developing the subsequent theory. Topics discussed in the book include the theory of viscosity solutions for nonlinear equations, the Alexandroff estimate and Krylov-Safonov Harnack-type inequality for viscosity solutions, uniqueness theory for viscosity solutions, Evans and Krylov regularity theory for convex fully nonlinear equations, and regularity theory for fully nonlinear equations with variable coefficients.

The Genesis of the Langlands Program
The Genesis of the Langlands Program

Author: Julia Mueller

Publisher: Cambridge University Press

Published: 2021-08-05

Total Pages: 451

ISBN-13: 1108710948

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A step-by-step guide to Langlands' early work leading up the Langlands Program for mathematicians and advanced students.

The Arnoldfest
The Arnoldfest

Author: Vladimir Igorevich Arnolʹd

Publisher: American Mathematical Soc.

Published: 1999

Total Pages: 575

ISBN-13: 0821809458

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This volume presents articles originating from invited talks at an exciting international conference held at The Fields Institute in Toronto celebrating the sixtieth birthday of the renowned mathematician, Vladimir Arnold. Experts from the world over--including several from "Arnold's school"--gave illuminating talks and lively poster sessions. The presentations focused on Arnold's main areas of interest: singularity theory, the theory of curves, symmetry groups, dynamical systems, mechanics, and related areas of mathematics. The book begins with notes of three lectures by V. Arnold given in the framework of the Institute's Distinguished Lecturer program. The topics of the lectures are: (1) From Hilbert's Superposition Problem to Dynamical Systems (2) Symplectization, Complexification, and Mathematical Trinities (3) Topological Problems in Wave Propagation Theory and Topological Economy Principle in Algebraic Geometry. Arnold's three articles include insightful comments on Russian and Western mathematics and science. Complementing the first is Jurgen Moser's "Recollections", concerning some of the history of KAM theory.

Thermodynamic Formalism and Holomorphic Dynamical Systems
Thermodynamic Formalism and Holomorphic Dynamical Systems

Author: Michel Zinsmeister

Publisher: American Mathematical Soc.

Published: 2000

Total Pages: 100

ISBN-13: 9780821819487

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The purpose of thermodynamics and statistical physics is to understand the equilibrium of a gas or the different states of matter. To understand the strange fractal sets appearing when one iterates a quadratic polynomial is one of the goals of the theory of holomorphic dynamical systems. These two theories are strongly linked: The laws of thermodynamics happen to be an extremely powerful tool for understanding the objects of holomorphic dynamical systems. A "thermodynamic formalism" has been developed, bringing together notions that are a priori unrelated. While the deep reasons of this parallelism remain unknown, the goal of this book is to describe this formalism both from the physical and mathematical point of view in order to understand how it works and how useful it can be. This translation is a slightly revised version of the original French edition. The main changes are in Chapters 5 and 6 and consist of clarification of some proofs and a new presentation of the basics in iteration of polynomials.

Algorithmic Problems in Groups and Semigroups
Algorithmic Problems in Groups and Semigroups

Author: Jean-Camille Birget

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 312

ISBN-13: 1461213886

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This volume contains papers which are based primarily on talks given at an inter national conference on Algorithmic Problems in Groups and Semigroups held at the University of Nebraska-Lincoln from May ll-May 16, 1998. The conference coincided with the Centennial Celebration of the Department of Mathematics and Statistics at the University of Nebraska-Lincoln on the occasion of the one hun dredth anniversary of the granting of the first Ph.D. by the department. Funding was provided by the US National Science Foundation, the Department of Math ematics and Statistics, and the College of Arts and Sciences at the University of Nebraska-Lincoln, through the College's focus program in Discrete, Experimental and Applied Mathematics. The purpose of the conference was to bring together researchers with interests in algorithmic problems in group theory, semigroup theory and computer science. A particularly useful feature of this conference was that it provided a framework for exchange of ideas between the research communities in semigroup theory and group theory, and several of the papers collected here reflect this interac tion of ideas. The papers collected in this volume represent a cross section of some of the results and ideas that were discussed in the conference. They reflect a synthesis of overlapping ideas and techniques stimulated by problems concerning finite monoids, finitely presented mono ids, finitely presented groups and free groups.