Random Explorations

Author : Gregory F. Lawler
Publisher : American Mathematical Society
ISBN 13 : 1470467666
Total Pages : 215 pages
Book Rating : 4.61/5 ( download)

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Download or read book Random Explorations written by Gregory F. Lawler and published by American Mathematical Society. This book was released on 2022-12-06 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: The title “Random Explorations” has two meanings. First, a few topics of advanced probability are deeply explored. Second, there is a recurring theme of analyzing a random object by exploring a random path. This book is an outgrowth of lectures by the author in the University of Chicago Research Experiences for Undergraduate (REU) program in 2020. The idea of the course was to expose advanced undergraduates to ideas in probability research. The book begins with Markov chains with an emphasis on transient or killed chains that have finite Green's function. This function, and its inverse called the Laplacian, is discussed next to relate two objects that arise in statistical physics, the loop-erased random walk (LERW) and the uniform spanning tree (UST). A modern approach is used including loop measures and soups. Understanding these approaches as the system size goes to infinity requires a deep understanding of the simple random walk so that is studied next, followed by a look at the infinite LERW and UST. Another model, the Gaussian free field (GFF), is introduced and related to loop measure. The emphasis in the book is on discrete models, but the final chapter gives an introduction to the continuous objects: Brownian motion, Brownian loop measures and soups, Schramm-Loewner evolution (SLE), and the continuous Gaussian free field. A number of exercises scattered throughout the text will help a serious reader gain better understanding of the material.

Author : Thomas G. Power
Publisher : Psychology Press
ISBN 13 : 113569057X
Total Pages : 512 pages
Book Rating : 4.71/5 ( download)

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Download or read book Play and Exploration in Children and Animals written by Thomas G. Power and published by Psychology Press. This book was released on 1999-11 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: Play is a paradox. Why would the young of so many species--the very animals at greatest risk for injury and predation--devote so much time and energy to an activity that by definition has no immediate purpose? This question has long puzzled students of animal behavior, and has been the focus of considerable empirical investigation and debate. In this first comprehensive and state-of-the-art review of what we have learned from decades of research on exploration and play in children and animals, Power examines the paradox from all angles. Covering solitary activity as well as play with peers, siblings, and parents, he considers the nature, development, and functions of play, as well as the gender differences in early play patterns. A major purpose is to explore the relevance of the animal literature for understanding human behavior. The nature and amount of children's play varies significantly across cultures, so the author makes cross-cultural comparisons wherever possible. The scope is broad and the range multidisciplinary. He draws on studies by developmental researchers in psychology and other fields, ethologists, anthropologists, sociologists, sociolinguists, early childhood educators, and pediatricians. And he places research on play in the context of research on such related phenomena as prosocial behavior and aggression. Finally, Power points out directions for further inquiry and implications for those who work with young children and their parents. Researchers and students will find Play and Exploration in Children and Animals an invaluable summary of controversies, methods, and findings; practitioners and educators will find it an invaluable compendium of information relevant to their efforts to enrich play experiences.

Author : Jerry Burkhart
Publisher : Taylor & Francis
ISBN 13 : 1000500152
Total Pages : 273 pages
Book Rating : 4.58/5 ( download)

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Download or read book Advanced Common Core Math Explorations written by Jerry Burkhart and published by Taylor & Francis. This book was released on 2021-09-03 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stretch your students' mathematical imaginations to their limits as they solve challenging real-world and mathematical problems that extend concepts from the Common Core State Standards for Mathematics in Advanced Common Core Math Explorations: Probability and Statistics. Students will learn powerful mathematical ideas about data and chance as they make sense of real-world situations from science, sports, and everyday life. Each activity comes with extensive teacher support, including student handouts, discussion guides, detailed solutions, and suggestions for extending the investigations. Grades 5-8

Author : James V Lambers
Publisher : World Scientific
ISBN 13 : 9811227950
Total Pages : 691 pages
Book Rating : 4.50/5 ( download)

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Download or read book Explorations In Numerical Analysis: Python Edition written by James V Lambers and published by World Scientific. This book was released on 2021-01-14 with total page 691 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is intended to introduce advanced undergraduate and early-career graduate students to the field of numerical analysis. This field pertains to the design, analysis, and implementation of algorithms for the approximate solution of mathematical problems that arise in applications spanning science and engineering, and are not practical to solve using analytical techniques such as those taught in courses in calculus, linear algebra or differential equations.Topics covered include computer arithmetic, error analysis, solution of systems of linear equations, least squares problems, eigenvalue problems, nonlinear equations, optimization, polynomial interpolation and approximation, numerical differentiation and integration, ordinary differential equations, and partial differential equations. For each problem considered, the presentation includes the derivation of solution techniques, analysis of their efficiency, accuracy and robustness, and details of their implementation, illustrated through the Python programming language.This text is suitable for a year-long sequence in numerical analysis, and can also be used for a one-semester course in numerical linear algebra.

Author : Randall C. O'Reilly
Publisher : MIT Press
ISBN 13 : 9780262650540
Total Pages : 540 pages
Book Rating : 4.41/5 ( download)

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Download or read book Computational Explorations in Cognitive Neuroscience written by Randall C. O'Reilly and published by MIT Press. This book was released on 2000-08-28 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text, based on a course taught by Randall O'Reilly and Yuko Munakata over the past several years, provides an in-depth introduction to the main ideas in the computational cognitive neuroscience. The goal of computational cognitive neuroscience is to understand how the brain embodies the mind by using biologically based computational models comprising networks of neuronlike units. This text, based on a course taught by Randall O'Reilly and Yuko Munakata over the past several years, provides an in-depth introduction to the main ideas in the field. The neural units in the simulations use equations based directly on the ion channels that govern the behavior of real neurons, and the neural networks incorporate anatomical and physiological properties of the neocortex. Thus the text provides the student with knowledge of the basic biology of the brain as well as the computational skills needed to simulate large-scale cognitive phenomena. The text consists of two parts. The first part covers basic neural computation mechanisms: individual neurons, neural networks, and learning mechanisms. The second part covers large-scale brain area organization and cognitive phenomena: perception and attention, memory, language, and higher-level cognition. The second part is relatively self-contained and can be used separately for mechanistically oriented cognitive neuroscience courses. Integrated throughout the text are more than forty different simulation models, many of them full-scale research-grade models, with friendly interfaces and accompanying exercises. The simulation software (PDP++, available for all major platforms) and simulations can be downloaded free of charge from the Web. Exercise solutions are available, and the text includes full information on the software.

Author : Rodrigo Quian Quiroga
Publisher : CRC Press
ISBN 13 : 1439853312
Total Pages : 625 pages
Book Rating : 4.13/5 ( download)

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Download or read book Principles of Neural Coding written by Rodrigo Quian Quiroga and published by CRC Press. This book was released on 2013-05-06 with total page 625 pages. Available in PDF, EPUB and Kindle. Book excerpt: Understanding how populations of neurons encode information is the challenge faced by researchers in the field of neural coding. Focusing on the many mysteries and marvels of the mind has prompted a prominent team of experts in the field to put their heads together and fire up a book on the subject. Simply titled Principles of Neural Coding, this b

Author : Hujun Yin
Publisher : Springer
ISBN 13 : 3642326390
Total Pages : 882 pages
Book Rating : 4.94/5 ( download)

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Download or read book Intelligent Data Engineering and Automated Learning -- IDEAL 2012 written by Hujun Yin and published by Springer. This book was released on 2012-08-01 with total page 882 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 13th International Conference on Intelligent Data Engineering and Automated Learning, IDEAL 2012, held in Natal, Brazil, in August 2012. The 100 revised full papers presented were carefully reviewed and selected from more than 200 submissions for inclusion in the book and present the latest theoretical advances and real-world applications in computational intelligence.

Author : James G. March
Publisher : Stanford University Press
ISBN 13 : 0804758972
Total Pages : 480 pages
Book Rating : 4.70/5 ( download)

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Download or read book Explorations in Organizations written by James G. March and published by Stanford University Press. This book was released on 2008 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of recent papers authored or co-authored by James G. March explores contemporary issues in the study of organizations.

Author : Ronald W. Shonkwiler
Publisher : Springer Science & Business Media
ISBN 13 : 0387878378
Total Pages : 249 pages
Book Rating : 4.79/5 ( download)

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Download or read book Explorations in Monte Carlo Methods written by Ronald W. Shonkwiler and published by Springer Science & Business Media. This book was released on 2009-08-11 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: Monte Carlo methods are among the most used and useful computational tools available today, providing efficient and practical algorithims to solve a wide range of scientific and engineering problems. Applications covered in this book include optimization, finance, statistical mechanics, birth and death processes, and gambling systems. Explorations in Monte Carlo Methods provides a hands-on approach to learning this subject. Each new idea is carefully motivated by a realistic problem, thus leading from questions to theory via examples and numerical simulations. Programming exercises are integrated throughout the text as the primary vehicle for learning the material. Each chapter ends with a large collection of problems illustrating and directing the material. This book is suitable as a textbook for students of engineering and the sciences, as well as mathematics.

Author : John W. Kenelly
Publisher : Elsevier
ISBN 13 : 0080506143
Total Pages : 349 pages
Book Rating : 4.42/5 ( download)

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Download or read book Explorations With Texas Instruments TI-85 written by John W. Kenelly and published by Elsevier. This book was released on 1993-01-05 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: The TI-85 is the latest and most powerful graphing calculator produced by Texas Instruments. This book describes the use of the TI-85 in courses in precalculus, calculus, linear algebra, differential equations, business mathematics, probability, statistics and advanced engineering mathematics. The book features in-depth coverage of the calculator's use in specific course areas by distinguished experts in each field.