The Random Matrix Theory of the Classical Compact Groups
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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.
Geometry and Martingales in Banach Spaces
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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.
Linear Algebra
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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.
Alice and Bob Meet Banach: The Interface of Asymptotic Geometric Analysis and Quantum Information Theory
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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.
Large Deviations for Additive Functionals of Markov Chains
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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.
Computational Mathematical Modeling
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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
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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.
A First Course in Statistics for Signal Analysis
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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.
Introduction to Bayesian Scientific Computing
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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.
Stochastic Ordinary and Stochastic Partial Differential Equations
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The present volume analyzes mathematical models of time-dependent physical p-nomena on three levels microscopic, mesoscopic, and macroscopic.
Math on File: Calculus
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An essential classroom resource designed to supplement the study of calculus a core area of the advanced mathematics curriculum.
Math on File: Geometry
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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.
Dynamics of Topologically Generic Homeomorphisms
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This work aims to elucidate the complex dynamics of generic homeomorphisms on compact metric spaces.
Math on File: Algebra
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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.
Burgers- KPZ Turbulence: Göttingen Lectures
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These lecture notes are woven around Burgers' turbulence/KPZ model of interface growth, a study of the nonlinear parabolic equation with random initial data.
Introductory Statistics and Random Phenomena: Uncertainty, Complexity, And Chaotic Behavior in Engineering and Science
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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.
The Life of Stefan Banach
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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.
Stochastic Models in Geosystems
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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.
Nonlinear Stochastic PDE's
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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.
Category Theory for Computing Science
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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.
Random Series and Stochastic Integrals: Single and Multiple
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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.
Symmetries and Laplacians
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Designed as an introduction to harmonic analysis and group representations, this book covers a wide range of topics.
Probability Theory and Harmonic Analysis
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Papers from the Mini-Conference on Probability and Harmonic Analysis held in Cleveland, Ohio, May 10-12, 1983.
Toposes, Triples, and Theories
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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.
