Mathematical Reports

Mathematical Reports

Author: Arthur Ziffer

Publisher: Author House

Published: 2014

Total Pages: 119

ISBN-13: 1496928431

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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.


Helping Children Learn Mathematics

Helping Children Learn Mathematics

Author: National Research Council

Publisher: National Academies Press

Published: 2002-07-31

Total Pages: 53

ISBN-13: 0309131987

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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.


Analogies Between Analogies

Analogies Between Analogies

Author: S. M. Ulam

Publisher: Univ of California Press

Published: 2023-11-15

Total Pages: 588

ISBN-13: 0520322924

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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

Semi-Riemannian Geometry With Applications to Relativity

Author: Barrett O'Neill

Publisher: Academic Press

Published: 1983-07-29

Total Pages: 483

ISBN-13: 0080570577

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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.


A Dictionary of Inequalities

A Dictionary of Inequalities

Author: Peter Bullen

Publisher: CRC Press

Published: 1998-08-21

Total Pages: 298

ISBN-13: 9780582327481

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The literature on inequalities is vast-in recent years the number of papers as well as the number of journals devoted to the subject have increased dramatically. At best, locating a particular inequality within the literature can be a cumbersome task. A Dictionary of Inequalities ends the dilemma of where to turn to find a result, a related inequality, or the references to the information you need. It provides a concise, alphabetical listing of each inequality-by its common name or its subject-with a short statement of the result, some comments, references to related inequalities, and a list of sources for further information. The author uses only the most elementary of mathematical terminology and does not offer proofs, thus making an interest in inequalities the only prerequisite for using the text. The author focuses on intuitive, physical forms of inequalities rather than their most general versions, and retains the beauty and importance of original versions rather than listing their later, abstract forms. He presents each in its simplest form with other renditions, such as for complex numbers and vectors, as extensions or under different headings. He has kept the book to a more manageable size by omitting inequalities in areas-such as elementary geometric and trigonometric inequalities-rarely used outside their fields. The end result is a current, concise, reference that puts the essential results on inequalities within easy reach. A Dictionary of Inequalities carries the beauty and attraction of the best and most successful dictionaries: on looking up a given item, the reader is likely to be intrigued and led by interest to others.


MATHEMATICAL COMBINATORICS, Vol. 1 / 2018

MATHEMATICAL COMBINATORICS, Vol. 1 / 2018

Author: Linfan Mao

Publisher: Infinite Study

Published: 2018

Total Pages: 161

ISBN-13: 159973558X

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The Mathematical Combinatorics (International Book Series) is a fully refereed international book series with ISBN number on each issue, sponsored by the MADIS of Chinese Academy of Sciences and published in USA quarterly comprising 110-160 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandache multi-spaces, Smarandache geometries, mathematical combinatorics, non-euclidean geometry and topology and their applications to other sciences.