Mathematical Reports


Book Description

The book consists of three parts. The first part gives an elementary derivation of the five basic equations of the discrete Kalman filter. The second part is a collection of reports on color matching with much use made of the theory of least squares. The third part shows how the discrete Kalman filter can be looked at as iterated least squares.




Mathematical Reports


Book Description




Analogies Between Analogies


Book Description

During his forty-year association with the Los Alamos National Laboratory, mathematician Stanislaw Ulam wrote many Laboratory Reports, usually in collaboration with colleagues. Some of them remain classified to this day. The rest are gathered in this volume and for the first time are easily accesible to mathematicians, physical scientists, and historians. The timeliness of these papers is remarkable. They contain seminal ideas in such fields as nonlinear stochastic processes, parallel computation, cellular automata, and mathematical biology. The collection is of historical interest as well, During and after World War II, the complexity of problems at the frontiers of science surpassed any technology that had ever existed. Electronic computing machines had to be developed and new computing methods had to be invented based on the most abstract ideas from the foundations of mathematics and theoretical physics. To these problems and others in physics, astronomy, and biology, Ulam was able to bring both general insights and specific conceptual contributions. His fertile ideas were far ahead of their time, and ranged over many branches of science. In fact, his mathematical versatility fulfilled the statement of his friend and mentor, the great Polish mathematician Stefan Banach, who claimed that the very best mathematicians see "analogies between analogies." Introduced by A. R. Bednarek and Francoise Ulam, these Los Alamos reports represent a unique view of one of the twentieth century's intellectual masters and scientific pioneers. This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1990.







Semi-Riemannian Geometry With Applications to Relativity


Book Description

This book is an exposition of semi-Riemannian geometry (also called pseudo-Riemannian geometry)--the study of a smooth manifold furnished with a metric tensor of arbitrary signature. The principal special cases are Riemannian geometry, where the metric is positive definite, and Lorentz geometry. For many years these two geometries have developed almost independently: Riemannian geometry reformulated in coordinate-free fashion and directed toward global problems, Lorentz geometry in classical tensor notation devoted to general relativity. More recently, this divergence has been reversed as physicists, turning increasingly toward invariant methods, have produced results of compelling mathematical interest.




Helping Children Learn Mathematics


Book Description

Results from national and international assessments indicate that school children in the United States are not learning mathematics well enough. Many students cannot correctly apply computational algorithms to solve problems. Their understanding and use of decimals and fractions are especially weak. Indeed, helping all children succeed in mathematics is an imperative national goal. However, for our youth to succeed, we need to change how we're teaching this discipline. Helping Children Learn Mathematics provides comprehensive and reliable information that will guide efforts to improve school mathematics from pre-kindergarten through eighth grade. The authors explain the five strands of mathematical proficiency and discuss the major changes that need to be made in mathematics instruction, instructional materials, assessments, teacher education, and the broader educational system and answers some of the frequently asked questions when it comes to mathematics instruction. The book concludes by providing recommended actions for parents and caregivers, teachers, administrators, and policy makers, stressing the importance that everyone work together to ensure a mathematically literate society.




Write for Mathematics


Book Description

"The strategies in Write for Mathematics helped my math students to not only write about mathematics but also to think about mathematics." -Lynda Ann DeLuca, Teacher and Math Coach Ann G. McGuinness Intermediate School, Endicott, NY "The integration of writing and mathematics is powerful instruction. This book provides ready-to-use strategies that will result in effective math instruction, and, more importantly, students will enjoy math class again. This is an outstanding resource." -Natalie R. Scavone, New Visions Teacher Education Preparation Instructor Cayuga-Onondaga Board of Cooperative Educational Services, NY Foster mathematical thinking and understanding by incorporating writing into your math instruction Research shows that engaging students in writing about mathematics can improve a learner′s overall math understanding. Addressing NCTM standards, Write for Mathematics, Second Edition, offers a wide range of practical writing strategies that can be used with students to deepen their understanding of key mathematical concepts. The process of incorporating writing into mathematics instruction need not seem daunting. This step-by-step handbook provides: Ten specific writing strategies that foster mathematical thinking and understanding Clear directions for using each strategy with students Application of the strategies to target NCTM standards A wide variety of examples at all levels Strategies that can be used with any mathematics curriculum A generous collection of reproducibles Students who write about mathematics develop deeper understandings, show increased interest in math, and reach higher achievement levels! Write for Mathematics, Second Edition, is an important resource for teachers who want to reach these goals.







Thomistic Metaphysics


Book Description

One of the major objectives of this book is to make Thomistic metaphysics – an inquiry into the act of existing, the act of to be, exercised by all beings to some degree – more understandable to the man of ordinary intellectual training. Therefore, the various problems of metaphysics and their solutions are presented in the simplest terms possible, with special emphasis on their significance for the contemporary mind.




Microsurveys in Discrete Probability


Book Description

This book contains eleven articles surveying emerging topics in discrete probability. The papers are based on talks given by experts at the DIMACS "Microsurveys in Discrete Probability" workshop held at the Institute for Advanced Study, Princeton, NJ, in 1997. This compilation of current research in discrete probability provides a unique overview that is not available elsewhere in book or survey form. Topics covered in the volume include: Markov chains (pefect sampling, coupling from the past, mixing times), random trees (spanning trees on infinite graphs, enumeration of trees and forests, tree-valued Markov chains), distributional estimates (method of bounded differences, Stein-Chen method for normal approximation), dynamical percolation, Poisson processes, and reconstructing random walk from scenery.