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To increase faculty participation and to recognize the strategic educational position held by undergraduate research, scholarship, and creative activities (URSCA) in many institutions, faculty mentorship of undergraduate students needs to be valued as a standard component of workload and formally included in activity reports and evaluations, including those that lead to reappointment, tenure, and promotion. This white paper presents the need for recognition of faculty mentorship of URSCA, recommends best practices for institutions to adopt, offers a selection of case studies where some of these practices are already established, and summarizes the challenges ahead.
An Introduction to Stochastic Modeling provides information pertinent to the standard concepts and methods of stochastic modeling. This book presents the rich diversity of applications of stochastic processes in the sciences. Organized into nine chapters, this book begins with an overview of diverse types of stochastic models, which predicts a set of possible outcomes weighed by their likelihoods or probabilities. This text then provides exercises in the applications of simple stochastic analysis to appropriate problems. Other chapters consider the study of general functions of independent, identically distributed, nonnegative random variables representing the successive intervals between renewals. This book discusses as well the numerous examples of Markov branching processes that arise naturally in various scientific disciplines. The final chapter deals with queueing models, which aid the design process by predicting system performance. This book is a valuable resource for students of engineering and management science. Engineers will also find this book useful.
The book is an introduction to quantum field theory applied to condensed matter physics. The topics cover modern applications in electron systems and electronic properties of mesoscopic systems and nanosystems. The textbook is developed for a graduate or advanced undergraduate course with exercises which aim at giving students the ability to confront real problems.
This book presents in detail a pair of models of the economics of climate change. The models, called RICE-99 (for the Regional Dynamic Integrated model of Climate and the Economy) and DICE-99 (for the Dynamic Integrated Model of Climate and the Economy) build on the authors' earlier work, particularly their RICE and DICE models of the early 1990s. Humanity is risking the health of the natural environment through a myriad of interventions, including the atmospheric emission of trace gases such as carbon dioxide, the use of ozone-depleting chemicals, the engineering of massive land-use changes, and the destruction of the habitats of many species. It is imperative that we learn to protect our common geophysical and biological resources. Although scientists have studied greenhouse warming for decades, it is only recently that society has begun to consider the economic, political, and institutional aspects of environmental intervention. To do so raises formidable challenges of data modeling, uncertainty, international coordination, and institutional design. Attempts to deal with complex scientific and economic issues have increasingly involved the use of models to help analysts and decision makers understand likely future outcomes as well as the implications of alternative policies. This book presents in detail a pair of models of the economics of climate change. The models, called RICE-99 (for the Regional Dynamic Integrated model of Climate and the Economy) and DICE-99 (for the Dynamic Integrated Model of Climate and the Economy) build on the authors' earlier work, particularly their RICE and DICE models of the early 1990s. They can help policy makers design better economic and environmental policies.
Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.
This book provides an introduction to the mathematical and algorithmic foundations of data science, including machine learning, high-dimensional geometry, and analysis of large networks. Topics include the counterintuitive nature of data in high dimensions, important linear algebraic techniques such as singular value decomposition, the theory of random walks and Markov chains, the fundamentals of and important algorithms for machine learning, algorithms and analysis for clustering, probabilistic models for large networks, representation learning including topic modelling and non-negative matrix factorization, wavelets and compressed sensing. Important probabilistic techniques are developed including the law of large numbers, tail inequalities, analysis of random projections, generalization guarantees in machine learning, and moment methods for analysis of phase transitions in large random graphs. Additionally, important structural and complexity measures are discussed such as matrix norms and VC-dimension. This book is suitable for both undergraduate and graduate courses in the design and analysis of algorithms for data.