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Department of Mathematics, Applied Mathematics, and Statistics Faculty Publications
Alice and Bob Meet Banach: The Interface of Asymptotic Geometric Analysis and Quantum Information Theory by Guillaume Aubrun; Stanislaw J. Szarek
The endeavor to construct a quantum computer stands as a pivotal scientific and technological pursuit of our era. Quantum Information Theory (QIT) lays the mathematical groundwork for this venture. Recent years have revealed a profound connection between QIT and Geometric Functional Analysis, particularly Asymptotic Geometric Analysis (AGA). AGA focuses on the quantitative aspects of convex shapes and their symmetries in high dimensions, which aligns closely with quantum theory where even small particle systems can span vast dimensional spaces.
ISBN: 9781470434687
Publication Date: 2017
Geometry and Martingales in Banach Spaces by Wojbor A. Woyczynski
Geometry and Martingales in Banach Spaces provides a compact exposition of the results explaining the interrelations between the metric geometry of Banach spaces, the theory of martingales, and general random vectors with values in those Banach spaces.
ISBN: 9781138616370
Publication Date: 2018
Large Deviations for Additive Functionals of Markov Chains by Alejandro D. de; Peter Ney
For a Markov chain X with general state space S and, the large deviation principle for n 1 =1 f(X) is proved under a condition on the chain which is weaker than uniform recurrence but stronger than geometric recurrence and an integrability condition on f, for a broad class of initial distributions.
ISBN: 9780821890899
Publication Date: 2014
Linear Algebra by Elizabeth S. Meckes; Mark W. Meckes
Offers a unified treatment of matrix-oriented and theoretical approaches to the course, which will be useful for classes with a mix of mathematics, physics, engineering, and computer science students. Major topics include singular value decomposition, the spectral theorem, linear systems of equations, vector spaces, linear maps, matrices, eigenvalues and eigenvectors, linear independence, bases, coordinates, dimension, matrix factorizations, inner products, norms, and determinants.
ISBN: 9781107177901
Publication Date: 2018
Math on File: Algebra by James Alexander
An invaluable resource to supplement classroom instruction in a core area of the mathematics curriculum. The volume provides approximately 50 engaging problem sets, ranging from simple to challenging, that are appropriate for group work in-class or individual out-of-class assignments.
ISBN: 0816046328
Publication Date: 2002
Math on File: Calculus by J. Alexander
An essential classroom resource designed to supplement the study of calculus a core area of the advanced mathematics curriculum.
ISBN: 0816048576
Publication Date: 2004
Math on File: Geometry by J. Alexander
A classroom resource designed to supplement the study of geometry - a core area of the high school mathematics curriculum. The problem sets cover core, remedial, and enriched material so that all levels of students can find appropriately challenging and rewarding topics to work with as they gain functional, mathematical literacy.
ISBN: 0816048568
Publication Date: 2003
Toposes, Triples, and Theories by M. Barr; C. H. Wells
This book introduces three key concepts and their connections. A topos is a type of generalized set theory, while the concept of triple initially emerged as "standard constructions" in Godement's book on sheaf theory for computing sheaf cohomology. Later, Peter Huber discovered that triples contain much of the information of adjoint pairs. Linton also discovered that triples offer an equivalent approach to Lawvere's theory of equational theories, or rather, the infinite generalizations of that theory.
ISBN: 0387961151
Publication Date: 1984
Alice and Bob Meet Banach: The Interface of Asymptotic Geometric Analysis and Quantum Information Theory by
The endeavor to construct a quantum computer stands as a pivotal scientific and technological pursuit of our era. Quantum Information Theory (QIT) lays the mathematical groundwork for this venture. Recent years have revealed a profound connection between QIT and Geometric Functional Analysis, particularly Asymptotic Geometric Analysis (AGA). AGA focuses on the quantitative aspects of convex shapes and their symmetries in high dimensions, which aligns closely with quantum theory where even small particle systems can span vast dimensional spaces.
Burgers- KPZ Turbulence: Göttingen Lectures by
These lecture notes are woven around Burgers' turbulence/KPZ model of interface growth, a study of the nonlinear parabolic equation with random initial data.
Category Theory for Computing Science by
A wide coverage of topics in category theory and computer science is developed in this text, including introductory treatments of cartesian closed categories, sketches and elementary categorical model theory, and triples.
Computational Mathematical Modeling by
The book concentrates on two modeling paradigms. The macroscopic, in which phenomena are described in terms of time evolution via ordinary differential equations, and the microscopic, which requires knowledge of random events and probability.
Distributions in the Physical and Engineering Sciences by
This book gives the reader, specialist and non-specialist, useable and modern mathematical tools in their research and analysis. It shows how the theory of distributions, also called the theory of generalized functions, can be used by graduate students and researchers in applied mathematics, physical sciences, and engineering.
Dynamics of Topologically Generic Homeomorphisms by
This work aims to elucidate the complex dynamics of generic homeomorphisms on compact metric spaces.
A First Course in Statistics for Signal Analysis by
This self-contained and user-friendly textbook is designed for a first, one-semester course in statistical signal analysis for students in engineering and the physical sciences.
Geometry and Martingales in Banach Spaces by
Geometry and Martingales in Banach Spaces provides a compact exposition of the results explaining the interrelations between the metric geometry of Banach spaces, the theory of martingales, and general random vectors with values in those Banach spaces.
Introduction to Bayesian Scientific Computing by
The book's highly accessible approach makes it particularly ideal if you want to become acquainted with the Bayesian approach to computational science, but do not need to be fully immersed in detailed statistical analysis.
Introductory Statistics and Random Phenomena: Uncertainty, Complexity, And Chaotic Behavior in Engineering and Science by
The present book is based on a course developed as part of the large NSF-funded Gateway Coalition Initiative in Engineering Education. The Coalition aimed to restructure the engineering curriculum by incorporating recent technological innovations.
Large Deviations for Additive Functionals of Markov Chains by
For a Markov chain X with general state space S and, the large deviation principle for n 1 =1 f(X) is proved under a condition on the chain which is weaker than uniform recurrence but stronger than geometric recurrence and an integrability condition on f, for a broad class of initial distributions.
The Life of Stefan Banach by
This book is a biographical account of mathematician Stefan Banach, written by a Polish reporter. It sheds light on his life, personality, and work, based on original archival sources, interviews, and conversations with mathematicians. The book also includes a chapter on the famous Scottish cafe, which has a mythical dimension in mathematical lore.
Linear Algebra by
Offers a unified treatment of matrix-oriented and theoretical approaches to the course, which will be useful for classes with a mix of mathematics, physics, engineering, and computer science students. Major topics include singular value decomposition, the spectral theorem, linear systems of equations, vector spaces, linear maps, matrices, eigenvalues and eigenvectors, linear independence, bases, coordinates, dimension, matrix factorizations, inner products, norms, and determinants.
Math on File: Algebra by
An invaluable resource to supplement classroom instruction in a core area of the mathematics curriculum. The volume provides approximately 50 engaging problem sets, ranging from simple to challenging, that are appropriate for group work in-class or individual out-of-class assignments.
Math on File: Calculus by
An essential classroom resource designed to supplement the study of calculus a core area of the advanced mathematics curriculum.
Math on File: Geometry by
A classroom resource designed to supplement the study of geometry - a core area of the high school mathematics curriculum. The problem sets cover core, remedial, and enriched material so that all levels of students can find appropriately challenging and rewarding topics to work with as they gain functional, mathematical literacy.
Nonlinear Stochastic PDE's by
The selection of topics reflected the personal interests of the organizers with two areas of emphasis: the hydrodynamic limit problems and Burgers' turbulence and related models. The talks and the papers reflect research directions currently pursued in these areas.
Probability Theory and Harmonic Analysis by
Papers from the Mini-Conference on Probability and Harmonic Analysis held in Cleveland, Ohio, May 10-12, 1983.
The Random Matrix Theory of the Classical Compact Groups by
This is the first book to provide a comprehensive overview of foundational results and recent progress in random matrices from the classical compact groups, drawing on the subject's deep connections to geometry, analysis, algebra, physics, and statistics.
Random Series and Stochastic Integrals: Single and Multiple by
This book studies the foundations of the theory of linear and nonlinear forms in single and multiple random variables including the single and multiple random series and stochastic integrals, both Gaussian and non-Gaussian.
Stochastic Models in Geosystems by
The common underlying theme was stochastic modeling of geophysical phenomena and papers appearing in this volume reflect several research directions that are currently pursued in these areas.
Stochastic Ordinary and Stochastic Partial Differential Equations by
The present volume analyzes mathematical models of time-dependent physical p-nomena on three levels microscopic, mesoscopic, and macroscopic.
Symmetries and Laplacians by
Designed as an introduction to harmonic analysis and group representations, this book covers a wide range of topics.
