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The Geometry of Random Fields
An important treatment of the geometric properties of sets generated by random fields, including a comprehensive treatment of the mathematical basics of random fields in general. It is a standard reference for all researchers with an interest in random fields, whether they be theoreticians or come from applied areas.
Random Fields and Their Geometry
This self-contained monograph contains a number of topics that focus on the many developments in the area of mathematical probability/statistics known as random fields. Robert Adler has been one of the major contributors to this subject. In an earlier work (1981) he dealt with a wide variety of geometrical problems that are unique to stochastic processes in dimensions higher than one, fashioning an interesting blend of geometry and probability. Some old classical topics (non-geometric in nature) are presented in the first few chapters, but the material has been recast in the post-1980 setting of entropy. This is followed by a treatment of random geometry which takes into account the recent w...
Random Fields and Geometry
This monograph is devoted to a completely new approach to geometric problems arising in the study of random fields. The groundbreaking material in Part III, for which the background is carefully prepared in Parts I and II, is of both theoretical and practical importance, and striking in the way in which problems arising in geometry and probability are beautifully intertwined. "Random Fields and Geometry" will be useful for probabilists and statisticians, and for theoretical and applied mathematicians who wish to learn about new relationships between geometry and probability. It will be helpful for graduate students in a classroom setting, or for self-study. Finally, this text will serve as a basic reference for all those interested in the companion volume of the applications of the theory.
Topological Complexity of Smooth Random Functions
These notes, based on lectures delivered in Saint Flour, provide an easy introduction to the authors’ 2007 Springer monograph “Random Fields and Geometry.” While not as exhaustive as the full monograph, they are also less exhausting, while still covering the basic material, typically at a more intuitive and less technical level. They also cover some more recent material relating to random algebraic topology and statistical applications. The notes include an introduction to the general theory of Gaussian random fields, treating classical topics such as continuity and boundedness. This is followed by a quick review of geometry, both integral and Riemannian, with an emphasis on tube formulae, to provide the reader with the material needed to understand and use the Gaussian kinematic formula, the main result of the notes. This is followed by chapters on topological inference and random algebraic topology, both of which provide applications of the main results.
The Dream of a Democratic Culture
This book presents a moderately revisionist history of the great books idea anchored in the following movements and struggles: fighting anti-intellectualism, advocating for the liberal arts, distributing cultural capital, and promoting a public philosophy, anchored in mid-century liberalism, that fostered a shared civic culture.
Aristotle for Everybody
Adler instructs the world in the "uncommon common sense" of Aristotelian logic, presenting Aristotle's understandings in a current, delightfully lucid way. Aristotle (384 - 322 B.C.) taught logic to Alexander the Great and, by virtue of his philosophical works, to every philosopher since, from Marcus Aurelius, to Thomas Aquinas, to Mortimer J. Adler. Now Adler instructs the world in the "uncommon common sense" of Aristotelian logic, presenting Aristotle's understandings in a current, delightfully lucid way. He brings Aristotle's work to an everyday level. By encouraging readers to think philosophically, Adler offers us a unique path to personal insights and understanding of intangibles, such as the difference between wants and needs, the proper way to pursue happiness, and the right plan for a good life.
Dialectic
First published in 2000. Routledge is an imprint of Taylor & Francis, an informa company.
