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Diffusions and Elliptic Operators
A discussion of the interplay of diffusion processes and partial differential equations with an emphasis on probabilistic methods. It begins with stochastic differential equations, the probabilistic machinery needed to study PDE, and moves on to probabilistic representations of solutions for PDE, regularity of solutions and one dimensional diffusions. The author discusses in depth two main types of second order linear differential operators: non-divergence operators and divergence operators, including topics such as the Harnack inequality of Krylov-Safonov for non-divergence operators and heat kernel estimates for divergence form operators, as well as Martingale problems and the Malliavin calculus. While serving as a textbook for a graduate course on diffusion theory with applications to PDE, this will also be a valuable reference to researchers in probability who are interested in PDE, as well as for analysts interested in probabilistic methods.
Real Analysis for Graduate Students
This book is a course on real analysis (measure and integration theory plus additional topics) designed for beginning graduate students. Its focus is on helping the student pass a preliminary or qualifying examination for the Ph.D. degree.
Probabilistic Techniques in Analysis
In recent years, there has been an upsurge of interest in using techniques drawn from probability to tackle problems in analysis. These applications arise in subjects such as potential theory, harmonic analysis, singular integrals, and the study of analytic functions. This book presents a modern survey of these methods at the level of a beginning Ph.D. student. Highlights of this book include the construction of the Martin boundary, probabilistic proofs of the boundary Harnack principle, Dahlberg's theorem, a probabilistic proof of Riesz' theorem on the Hilbert transform, and Makarov's theorems on the support of harmonic measure. The author assumes that a reader has some background in basic real analysis, but the book includes proofs of all the results from probability theory and advanced analysis required. Each chapter concludes with exercises ranging from the routine to the difficult. In addition, there are included discussions of open problems and further avenues of research.
Stochastic Processes
This comprehensive guide to stochastic processes gives a complete overview of the theory and addresses the most important applications. Pitched at a level accessible to beginning graduate students and researchers from applied disciplines, it is both a course book and a rich resource for individual readers. Subjects covered include Brownian motion, stochastic calculus, stochastic differential equations, Markov processes, weak convergence of processes and semigroup theory. Applications include the Black-Scholes formula for the pricing of derivatives in financial mathematics, the Kalman-Bucy filter used in the US space program and also theoretical applications to partial differential equations and analysis. Short, readable chapters aim for clarity rather than full generality. More than 350 exercises are included to help readers put their new-found knowledge to the test and to prepare them for tackling the research literature.
Teaching and Learning STEM
The widely used STEM education book, updated Teaching and Learning STEM: A Practical Guide covers teaching and learning issues unique to teaching in the science, technology, engineering, and math (STEM) disciplines. Secondary and postsecondary instructors in STEM areas need to master specific skills, such as teaching problem-solving, which are not regularly addressed in other teaching and learning books. This book fills the gap, addressing, topics like learning objectives, course design, choosing a text, effective instruction, active learning, teaching with technology, and assessment—all from a STEM perspective. You’ll also gain the knowledge to implement learner-centered instruction, wh...
Transformational Leadership
Transformational Leadership, Second Edition is intended for both the scholars and serious students of leadership. It is a comprehensive review of theorizing and empirical research that can serve as a reference and starting point for additional research on the theory. It can be used as a supplementary textbook in an intense course on leadership--or as a primary text in a course or seminar focusing on transformational leadership. New in the Second Edition: *New, updated examples of leadership have been included to help illustrate the concepts, as well as show the broad range of transformational leadership in a variety of settings. *New chapters have been added focusing specifically on the measurement of transformational leadership and transformational leadership and effectiveness. *The discussion of both predicators and effects of transformational leadership is greatly expanded. *Much more emphasis is given to authentic vs. inauthentic transformational leadership. *Suggestions are made for guiding the future of research and applications of transformational leadership. *A greatly expanded reference list is included.
Positive Harmonic Functions and Diffusion
In this book, Professor Pinsky gives a self-contained account of the theory of positive harmonic functions for second order elliptic operators, using an integrated probabilistic and analytic approach. The book begins with a treatment of the construction and basic properties of diffusion processes. This theory then serves as a vehicle for studying positive harmonic funtions. Starting with a rigorous treatment of the spectral theory of elliptic operators with nice coefficients on smooth, bounded domains, the author then develops the theory of the generalized principal eigenvalue, and the related criticality theory for elliptic operators on arbitrary domains. Martin boundary theory is considere...
The Bass Book
The first full-color, comprehensive history, tracing the entire development of one of the 20th century's most important musical instruments. Based on firsthand interviews with primary inventors and makers of past and present bass guitars, this new book examines the birth of the instrument, its popularization during the 1960s and 1970s, and modern variations of the instrument.
Securing Baritone, Bass-Baritone, and Bass Voices
The first thorough and comprehensive treatment of low male voices, this book draws on techniques and practical advice from Miller's years of professional experience as a performer and pedagogue. Focussing on securing the technical stability of the male voice, the book offers practical advice to students, their teachers, and professional performers, through numerous practical exercises and repertoire suggestions appropriate to various stages of development. Miller synthesizes historic vocal pedagogy with the latest research on the singing voice, always emphasizing the special nature of the male voice and the proper physiological functioning for vocal proficiency.
Seven Summits
Tour the globe and witness spectacular feats of human determination, endurance, and strength. Travel with dedicated mountaineers as they climb the "Seven Summits"—the highest peak of each of the seven continents. Stunning full-color photographs capture the breathtaking scenery and courageous athleticism of the climbers. Essays and diaries of mountaineers, along with striking photos, capture these harrowing adventures and take readers to each of the Seven Summits: McKinley (North America), Aconcagua (South America), Vinson (Antarctica), Kilmanjaro (Africa), Elbrus (Europe), Kosciuszko (Australia), and Everest (Asia).
