Moments In Mathematics

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Moments in Mathematics

Author : Henry J. Landau
Publisher : American Mathematical Soc.
ISBN 13 : 9780821801147
Total Pages : 170 pages
Book Rating : 4.8/5 (11 download)

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Book Synopsis Moments in Mathematics by : Henry J. Landau

Download or read book Moments in Mathematics written by Henry J. Landau and published by American Mathematical Soc.. This book was released on 1987 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: Function theory, spectral decomposition of operators, probability, approximation, electrical and mechanical inverse problems, prediction of stochastic processes, the design of algorithms for signal-processing VLSI chips--these are among a host of important theoretical and applied topics illuminated by the classical moment problem. To survey some of these ramifications and the research which derives from them, the AMS sponsored the Short Course Moments in Mathematics at the Joint Mathematics Meetings, held in San Antonio, Texas, in January 1987. This volume contains the six lectures presented during that course. The papers are likely to find a wide audience, for they are expository, but nevertheless lead the reader to topics of current research. In his paper, Henry J. Landau sketches the main ideas of past work related to the moment problem by such mathematicians as Caratheodory, Herglotz, Schur, Riesz, and Krein and describes the way the moment problem has interconnected so many diverse areas of research. J. H. B. Kemperman examines the moment problem from a geometric viewpoint which involves a certain natural duality method and leads to interesting applications in linear programming, measure theory, and dilations. Donald Sarason first provides a brief review of the theory of unbounded self-adjoint operators then goes on to sketch the operator-theoretic treatment of the Hamburger problem and to discuss Hankel operators, the Adamjan-Arov-Krein approach, and the theory of unitary dilations. Exploring the interplay of trigonometric moment problems and signal processing, Thomas Kailath describes the role of Szego polynomials in linear predictive coding methods, parallel implementation, one-dimensional inverse scattering problems, and the Toeplitz moment matrices. Christian Berg contrasts the multi-dimensional moment problem with the one-dimensional theory and shows how the theory of the moment problem may be viewed as part of harmonic analysis on semigroups. Starting from a historical survey of the use of moments in probability and statistics, Persi Diaconis illustrates the continuing vitality of these methods in a variety of recent novel problems drawn from such areas as Wiener-Ito integrals, random graphs and matrices, Gibbs ensembles, cumulants and self-similar processes, projections of high-dimensional data, and empirical estimation.

Great Moments in Mathematics Before 1650

Author : Howard Eves
Publisher : American Mathematical Soc.
ISBN 13 : 1614442142
Total Pages : 286 pages
Book Rating : 4.6/5 (144 download)

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Book Synopsis Great Moments in Mathematics Before 1650 by : Howard Eves

Download or read book Great Moments in Mathematics Before 1650 written by Howard Eves and published by American Mathematical Soc.. This book was released on 1983-12-31 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: Great Moments in Mathematics: Before 1650 is the product of a series of lectures on the history of mathematics given by Howard Eves. He presents here, in chronological order, 20 ``great moments in mathematics before 1650'', which can be appreciated by anyone who enjoys mathematics. These wonderful lectures could be used as the basis of a course on the history of mathematics but can also serve as enrichment to any mathematics course. Included are lectures on the Pythagorean Theorem, Euclid's Elements, Archimedes (on the sphere), Diophantus, Omar Khayyam, and Fibonacci.

Moments in Mathematics Coaching

Author : Kristine Reed Woleck
Publisher : Corwin Press
ISBN 13 : 1412965845
Total Pages : 185 pages
Book Rating : 4.4/5 (129 download)

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Book Synopsis Moments in Mathematics Coaching by : Kristine Reed Woleck

Download or read book Moments in Mathematics Coaching written by Kristine Reed Woleck and published by Corwin Press. This book was released on 2010-03-09 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using a case-based approach, Moments in Mathematics Coaching helps readers examine the possibilities of their position and develop a range of images of the work of mathematics coaching. The cases and author narrative illustrate how to implement specific coaching strategies and make transparent to the reader the reflection and decision-making elements of coaching. In this way the author, an experienced mathematics coach and coach-educator, effectively models the reflective nature of the work and the power of such reflection for continual growth. The book communicates the challenges and successes of mathematics coaching and provides a wide range of strategies, tips, and guidelines. This resource may be used by individuals or by a book study group of mathematics coaches.

Great Moments in Mathematics

Author : Howard Eves
Publisher : American Mathematical Soc.
ISBN 13 : 1614442150
Total Pages : 278 pages
Book Rating : 4.6/5 (144 download)

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Book Synopsis Great Moments in Mathematics by : Howard Eves

Download or read book Great Moments in Mathematics written by Howard Eves and published by American Mathematical Soc.. This book was released on 1998-12-31 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Great Moments in Mathematics: After 1650

Author : Howard Eves
Publisher : American Mathematical Soc.
ISBN 13 : 0883853116
Total Pages : 278 pages
Book Rating : 4.8/5 (838 download)

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Book Synopsis Great Moments in Mathematics: After 1650 by : Howard Eves

Download or read book Great Moments in Mathematics: After 1650 written by Howard Eves and published by American Mathematical Soc.. This book was released on 2020-07-31 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: What a splendid addition this is to the Dolciani Mathematical Exposition series! This second set of lectures on great moments in mathematics (after 1650) is a fascinating collection of pivotal points in the historical development of mathematics...The four lectures devoted to the liberation of geometry and algebra are of particular interest. The lectures should be required reading for all teachers of mathematics. —Herbert Fremont, The Mathematics Teacher Eves is never less than tantalizing and usually inspiring...each 'great moment' has detailed exercises following it, as these have been carefully chosen to illustrate the depth of the ideas in question. —C. W. Kilmister, The London Times, Higher Education Supplement As is usual with Eves' work, the books are well written and entertaining. They give an historical background to many of the best known mathematical results, and, in addition, provide interesting pieces of information about the mathematicians involved. Eves includes relevant exercises at the end of each chapter. These are a good source of different, interesting problems, and when combined with the material in the chapter, could form the basis for a mathematical project...Eves' book provides an interesting, well-written, and enjoyable account. You won't be disappointed. —David Parrott, The Australian Mathematics Teacher

Moments in Mathematics Coaching

Author : Kristine Reed Woleck
Publisher : Corwin Press
ISBN 13 : 1452295972
Total Pages : 185 pages
Book Rating : 4.4/5 (522 download)

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Book Synopsis Moments in Mathematics Coaching by : Kristine Reed Woleck

Download or read book Moments in Mathematics Coaching written by Kristine Reed Woleck and published by Corwin Press. This book was released on 2010-03-09 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: "A must-read for all mathematics teacher coaches. Woleck brings us into her coaching life by sharing these cases from her work. Through the engaging details of these personal stories, she skillfully leads us into considering various coaching models, essential coaching skills, and effective coaching practices. Focus questions at the end of each chapter add an incentive for readers to deepen their own practices and use this book as the basis for study groups." —Euthecia Hancewicz, Mathematics Teacher Support Specialist Mathematics Educator Support Services, Westhampton, MA "Woleck provides an instructive and insightful analysis of what makes coaching a powerful and capacity-building resource for schools. This highly engaging and informative account details how effective coaching skills develop and become refined through research-based study, daily practice, and ongoing reflection." —Mary Monroe Kolek, Deputy Superintendent New Canaan Public Schools, CT Follow a mathematics coach through real cases from actual school situations! Kristine Reed Woleck reflects on specific cases or "moments" from her years as a mathematics coach, unpacking and examining for readers the critical elements of mathematics teaching, learning, and coaching. This accessible, practical resource discusses what effective coaching looks like and how beginning and veteran mathematics coaches in Grades K–5 can bring about meaningful improvements in mathematics instruction. The real-life cases illustrate how to Incorporate key elements of coaching into practice Build trusting relationships with teachers Make effective decisions throughout the coaching cycle Reference data and the curriculum as coaching tools Use reflection to link coaching concepts to actual practice

Moments, Positive Polynomials and Their Applications

Author : Jean-Bernard Lasserre
Publisher : World Scientific
ISBN 13 : 1848164467
Total Pages : 384 pages
Book Rating : 4.8/5 (481 download)

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Book Synopsis Moments, Positive Polynomials and Their Applications by : Jean-Bernard Lasserre

Download or read book Moments, Positive Polynomials and Their Applications written by Jean-Bernard Lasserre and published by World Scientific. This book was released on 2010 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. The generalized moment problem. 1.1. Formulations. 1.2. Duality theory. 1.3. Computational complexity. 1.4. Summary. 1.5. Exercises. 1.6. Notes and sources -- 2. Positive polynomials. 2.1. Sum of squares representations and semi-definite optimization. 2.2. Nonnegative versus s.o.s. polynomials. 2.3. Representation theorems : univariate case. 2.4. Representation theorems : mutivariate case. 2.5. Polynomials positive on a compact basic semi-algebraic set. 2.6. Polynomials nonnegative on real varieties. 2.7. Representations with sparsity properties. 2.8. Representation of convex polynomials. 2.9. Summary. 2.10. Exercises. 2.11. Notes and sources -- 3. Moments. 3.1. The one-dimensional moment problem. 3.2. The multi-dimensional moment problem. 3.3. The K-moment problem. 3.4. Moment conditions for bounded density. 3.5. Summary. 3.6. Exercises. 3.7. Notes and sources -- 4. Algorithms for moment problems. 4.1. The overall approach. 4.2. Semidefinite relaxations. 4.3. Extraction of solutions. 4.4. Linear relaxations. 4.5. Extensions. 4.6. Exploiting sparsity. 4.7. Summary. 4.8. Exercises. 4.9. Notes and sources. 4.10. Proofs -- 5. Global optimization over polynomials. 5.1. The primal and dual perspectives. 5.2. Unconstrained polynomial optimization. 5.3. Constrained polynomial optimization : semidefinite relaxations. 5.4. Linear programming relaxations. 5.5. Global optimality conditions. 5.6. Convex polynomial programs. 5.7. Discrete optimization. 5.8. Global minimization of a rational function. 5.9. Exploiting symmetry. 5.10. Summary. 5.11. Exercises. 5.12. Notes and sources -- 6. Systems of polynomial equations. 6.1. Introduction. 6.2. Finding a real solution to systems of polynomial equations. 6.3. Finding all complex and/or all real solutions : a unified treatment. 6.4. Summary. 6.5. Exercises. 6.6. Notes and sources -- 7. Applications in probability. 7.1. Upper bounds on measures with moment conditions. 7.2. Measuring basic semi-algebraic sets. 7.3. Measures with given marginals. 7.4. Summary. 7.5. Exercises. 7.6. Notes and sources -- 8. Markov chains applications. 8.1. Bounds on invariant measures. 8.2. Evaluation of ergodic criteria. 8.3. Summary. 8.4. Exercises. 8.5. Notes and sources -- 9. Application in mathematical finance. 9.1. Option pricing with moment information. 9.2. Option pricing with a dynamic model. 9.3. Summary. 9.4. Notes and sources -- 10. Application in control. 10.1. Introduction. 10.2. Weak formulation of optimal control problems. 10.3. Semidefinite relaxations for the OCP. 10.4. Summary. 10.5. Notes and sources -- 11. Convex envelope and representation of convex sets. 11.1. The convex envelope of a rational function. 11.2. Semidefinite representation of convex sets. 11.3. Algebraic certificates of convexity. 11.4. Summary. 11.5. Exercises. 11.6. Notes and sources -- 12. Multivariate integration 12.1. Integration of a rational function. 12.2. Integration of exponentials of polynomials. 12.3. Maximum entropy estimation. 12.4. Summary. 12.5. Exercises. 12.6. Notes and sources -- 13. Min-max problems and Nash equilibria. 13.1. Robust polynomial optimization. 13.2. Minimizing the sup of finitely many rational cunctions. 13.3. Application to Nash equilibria. 13.4. Exercises. 13.5. Notes and sources -- 14. Bounds on linear PDE. 14.1. Linear partial differential equations. 14.2. Notes and sources

Creativity of an Aha! Moment and Mathematics Education

Author :
Publisher : BRILL
ISBN 13 : 9004446435
Total Pages : 491 pages
Book Rating : 4.0/5 (44 download)

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Book Synopsis Creativity of an Aha! Moment and Mathematics Education by :

Download or read book Creativity of an Aha! Moment and Mathematics Education written by and published by BRILL. This book was released on 2021-05-25 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: Creativity of an Aha!Moment and Mathematics Education introduces bisociation, the theory of Aha! moment creativity into Mathematics Education. It establishes relationships between bisociation and constructivist theories of learning laying down the basis for the new theory integrating creativity with learning.

The Problem of Moments

Author : James Alexander Shohat
Publisher : American Mathematical Soc.
ISBN 13 : 0821815016
Total Pages : 160 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis The Problem of Moments by : James Alexander Shohat

Download or read book The Problem of Moments written by James Alexander Shohat and published by American Mathematical Soc.. This book was released on 1943-12-31 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book was first published in 1943 and then was reprinted several times with corrections. It presents the development of the classical problem of moments for the first 50 years, after its introduction by Stieltjes in the 1890s. In addition to initial developments by Stieltjes, Markov, and Chebyshev, later contributions by Hamburger, Nevanlinna, Hausdorff, Stone, and others are discussed. The book also contains some results on the trigonometric moment problem and a chapter devoted to approximate quadrature formulas.

The Moment Problem

Author : Konrad Schmüdgen
Publisher : Springer
ISBN 13 : 3319645463
Total Pages : 530 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis The Moment Problem by : Konrad Schmüdgen

Download or read book The Moment Problem written by Konrad Schmüdgen and published by Springer. This book was released on 2017-11-09 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: This advanced textbook provides a comprehensive and unified account of the moment problem. It covers the classical one-dimensional theory and its multidimensional generalization, including modern methods and recent developments. In both the one-dimensional and multidimensional cases, the full and truncated moment problems are carefully treated separately. Fundamental concepts, results and methods are developed in detail and accompanied by numerous examples and exercises. Particular attention is given to powerful modern techniques such as real algebraic geometry and Hilbert space operators. A wide range of important aspects are covered, including the Nevanlinna parametrization for indeterminate moment problems, canonical and principal measures for truncated moment problems, the interplay between Positivstellensätze and moment problems on semi-algebraic sets, the fibre theorem, multidimensional determinacy theory, operator-theoretic approaches, and the existence theory and important special topics of multidimensional truncated moment problems. The Moment Problem will be particularly useful to graduate students and researchers working on moment problems, functional analysis, complex analysis, harmonic analysis, real algebraic geometry, polynomial optimization, or systems theory. With notes providing useful background information and exercises of varying difficulty illustrating the theory, this book will also serve as a reference on the subject and can be used for self-study.

Matrices, Moments and Quadrature with Applications

Author : Gene H. Golub
Publisher : Princeton University Press
ISBN 13 : 1400833884
Total Pages : 376 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Matrices, Moments and Quadrature with Applications by : Gene H. Golub

Download or read book Matrices, Moments and Quadrature with Applications written by Gene H. Golub and published by Princeton University Press. This book was released on 2009-12-07 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This computationally oriented book describes and explains the mathematical relationships among matrices, moments, orthogonal polynomials, quadrature rules, and the Lanczos and conjugate gradient algorithms. The book bridges different mathematical areas to obtain algorithms to estimate bilinear forms involving two vectors and a function of the matrix. The first part of the book provides the necessary mathematical background and explains the theory. The second part describes the applications and gives numerical examples of the algorithms and techniques developed in the first part. Applications addressed in the book include computing elements of functions of matrices; obtaining estimates of the error norm in iterative methods for solving linear systems and computing parameters in least squares and total least squares; and solving ill-posed problems using Tikhonov regularization. This book will interest researchers in numerical linear algebra and matrix computations, as well as scientists and engineers working on problems involving computation of bilinear forms.

The Creative Use of Odd Moments

Author : Doug French
Publisher :
ISBN 13 : 9780906588628
Total Pages : 80 pages
Book Rating : 4.5/5 (886 download)

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Book Synopsis The Creative Use of Odd Moments by : Doug French

Download or read book The Creative Use of Odd Moments written by Doug French and published by . This book was released on 2007 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Items, with minor amendments, are in the same form as when they were originally published in Mathematics in school between 1993 and 2001"--Intro.

The Moment of Proof

Author : Donald C. Benson
Publisher : Oxford University Press, USA
ISBN 13 : 9780195139198
Total Pages : 346 pages
Book Rating : 4.1/5 (391 download)

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Book Synopsis The Moment of Proof by : Donald C. Benson

Download or read book The Moment of Proof written by Donald C. Benson and published by Oxford University Press, USA. This book was released on 2000 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: A brilliant introduction to the pleasures of mathematical thinking, this book attempts to convey to general readers the feeling of eureka--the joy of discovery--that mathematicians feel when they first encounter an elegant truth. 92 line illustrations.

In the Moment

Author : Jen Munson
Publisher :
ISBN 13 : 9780325098692
Total Pages : 160 pages
Book Rating : 4.0/5 (986 download)

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Book Synopsis In the Moment by : Jen Munson

Download or read book In the Moment written by Jen Munson and published by . This book was released on 2018-09-06 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: Conferring in math supports students' learning How do we support all students' mathematical sense-making and move their thinking forward in the midst of problem solving? Talking to students about their work, while they work, is a powerful way of supporting learning. We often engage in these conversations with our readers and writers, and these interactions are just as needed in mathematics. What does it look like to talk with students about their mathematical thinking so that their thinking grows? Practical, research-based guidance for getting started In the Moment offers research-based guidance for conferring with your students in math. Jen Munson explains how, in just a few minutes, a math conference provides opportunities for supporting productive struggle, helping students grow their ideas, and differentiating instruction. You'll learn about: the process of conferring: eliciting, interpreting, and nudging creating the conditions for conferring in your classroom responding to your students' thinking in the moment of a conference addressing unique challenges teachers face when conferring in math using conferring as formative assessment. Enhanced with online videos showing real math conferences and teacher reflections, this comprehensive, classroom-tested approach to conferring helps you step into your students' mathematical lives to support their learning, communication, and participation. It provides the guidance and support needed to get started with conferring and see it become a crucial part of your teaching.

Wiener Chaos: Moments, Cumulants and Diagrams

Author : Giovanni Peccati
Publisher : Springer Science & Business Media
ISBN 13 : 8847016797
Total Pages : 281 pages
Book Rating : 4.8/5 (47 download)

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Book Synopsis Wiener Chaos: Moments, Cumulants and Diagrams by : Giovanni Peccati

Download or read book Wiener Chaos: Moments, Cumulants and Diagrams written by Giovanni Peccati and published by Springer Science & Business Media. This book was released on 2011-04-06 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: The concept of Wiener chaos generalizes to an infinite-dimensional setting the properties of orthogonal polynomials associated with probability distributions on the real line. It plays a crucial role in modern probability theory, with applications ranging from Malliavin calculus to stochastic differential equations and from probabilistic approximations to mathematical finance. This book is concerned with combinatorial structures arising from the study of chaotic random variables related to infinitely divisible random measures. The combinatorial structures involved are those of partitions of finite sets, over which Möbius functions and related inversion formulae are defined. This combinatorial standpoint (which is originally due to Rota and Wallstrom) provides an ideal framework for diagrams, which are graphical devices used to compute moments and cumulants of random variables. Several applications are described, in particular, recent limit theorems for chaotic random variables. An Appendix presents a computer implementation in MATHEMATICA for many of the formulae.

The Theory of Canonical Moments with Applications in Statistics, Probability, and Analysis

Author : Holger Dette
Publisher : John Wiley & Sons
ISBN 13 : 9780471109914
Total Pages : 368 pages
Book Rating : 4.1/5 (99 download)

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Book Synopsis The Theory of Canonical Moments with Applications in Statistics, Probability, and Analysis by : Holger Dette

Download or read book The Theory of Canonical Moments with Applications in Statistics, Probability, and Analysis written by Holger Dette and published by John Wiley & Sons. This book was released on 1997-09-08 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new material is concerned with the theory and applications of probability, statistics and analysis of canonical moments. It provides a powerful tool for the determination of optimal experimental designs, for the calculation of the main characteristics of random walks, and for other moment problems appearing in probability and statistics.

The Mathematics of Juggling

Author : Burkard Polster
Publisher : Springer Science & Business Media
ISBN 13 : 0387227482
Total Pages : 240 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis The Mathematics of Juggling by : Burkard Polster

Download or read book The Mathematics of Juggling written by Burkard Polster and published by Springer Science & Business Media. This book was released on 2006-05-26 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: As a juggler the author likes to finish his performances with a stunt that combines props and techniques from a variety of juggling disciplines. Imagine him idling on a giraffe unicycle, while balancing a spinning basketball on a mouth stick, and toss-juggling a sword, a toilet plunger, and a rubber chicken. As a mathematician he is also interested in the treasure trove of beautiful mathematics used to model the different activities in a juggler's repertoire. In this book he provides an intellectually stimulating collection of mostly self-contained mathematical essays that introduce the reader to many elegant results and techniques from a wide range of mathematical disciplines such as combinatorics, graph theory, knot theory, mechanics, differential equations, control theory, and robotics. "The Mathematics of Juggling" is the first comprehensive account summarizing and expanding the results in the literature on juggling tricks and skills, as well as the mathematics behind these tricks and skills. Anybody who is not put off by the word "mathematics" in the title of this book should have a good time reading it.