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Novelty, Information and Surprise (Information Science and Statistics)
by Günther PalmThis revised edition offers an approach to information theory that is more general than the classical approach of Shannon. Classically, information is defined for an alphabet of symbols or for a set of mutually exclusive propositions (a partition of the probability space Ω) with corresponding probabilities adding up to 1. The new definition is given for an arbitrary cover of Ω, i.e. for a set of possibly overlapping propositions. The generalized information concept is called novelty and it is accompanied by two concepts derived from it, designated as information and surprise, which describe "opposite" versions of novelty, information being related more to classical information theory and surprise being related more to the classical concept of statistical significance. In the discussion of these three concepts and their interrelations several properties or classes of covers are defined, which turn out to be lattices. The book also presents applications of these concepts, mostly in statistics and in neuroscience.
Novice Mathematics Teachers’ Professional Learning: A Multi-Case Study in Shanghai (Perspektiven der Mathematikdidaktik)
by Xiaoli LuThis book investigates three novice high school mathematics teachers’ professional learning processes in the early stages of their careers at schools in Shanghai, China. Teacher professional learning is examined as a complex and dynamic system that connects both cognitive and situated perspectives on learning theory. Inspiring mathematics teachers to adopt student-focused pedagogies is challenging, particularly in China where tensions in teacher-centred, content-focused and examination-oriented practices are predominant. The three novice teachers who participated in this study brought different beliefs and knowledge derived from their different individual experiences to bear on their teaching practices. However, they were strongly influenced by the environments in which they taught and mainly adopted a professional learning approach to teacher-centred practices, despite reporting that they favoured student-centred teaching practices. The study also observed professional learning towards student-centred pedagogical aspects in a single teacher case with mentorship support, indicating that student-centred pedagogies may be promoted within the constraints of the existing dominant teaching practice.
Nuclear Computational Science
by Yousry Azmy Enrico SartoriNuclear engineering has undergone extensive progress over the years. In the past century, colossal developments have been made and with specific reference to the mathematical theory and computational science underlying this discipline, advances in areas such as high-order discretization methods, Krylov Methods and Iteration Acceleration have steadily grown. Nuclear Computational Science: A Century in Review addresses these topics and many more; topics which hold special ties to the first half of the century, and topics focused around the unique combination of nuclear engineering, computational science and mathematical theory. Comprising eight chapters, Nuclear Computational Science: A Century in Review incorporates a number of carefully selected issues representing a variety of problems, providing the reader with a wealth of information in both a clear and concise manner. The comprehensive nature of the coverage and the stature of the contributing authors combine to make this a unique landmark publication. Targeting the medium to advanced level academic, this book will appeal to researchers and students with an interest in the progression of mathematical theory and its application to nuclear computational science.
The Nuclear Environmentalist
by Juan José Gomez CadenasThis book explains how society will face an energy crisis in the coming decades owing to increasing scarcity of fossil fuels and climate change impacts. It carefully explores this coming crisis and concisely examines all of the major technologies related to energy production (fossil fuels, renewables, and nuclear) and their impacts on our society and environment. The author argues that it is wrong to pit alternatives to fossil fuels against each other and proposes that nuclear energy, although by no means free of problems, can be a viable source of reliable and carbon-free electricity. He concludes by calling for a diversified and rational mix of electricity generation in order to mitigate the effects of the energy crisis. Throughout, the book is spiced with science, history, and anecdotes in a way that ensures rewarding reading without loss of rigor.
Nuclear Lattice Effective Field Theory: An Introduction (Lecture Notes in Physics #957)
by Timo A. Lähde Ulf-G. MeißnerThis primer begins with a brief introduction to the main ideas underlying Effective Field Theory (EFT) and describes how nuclear forces are obtained from first principles by introducing a Euclidean space-time lattice for chiral EFT. It subsequently develops the related technical aspects by addressing the two-nucleon problem on the lattice and clarifying how it fixes the numerical values of the low-energy constants of chiral EFT. In turn, the spherical wall method is introduced and used to show how improved lattice actions render higher-order corrections perturbative. The book also presents Monte Carlo algorithms used in actual calculations. In the last part of the book, the Euclidean time projection method is introduced and used to compute the ground-state properties of nuclei up to the mid-mass region. In this context, the construction of appropriate trial wave functions for the Euclidean time projection is discussed, as well as methods for determining the energies of the low-lying excitations and their spatial structure. In addition, the so-called adiabatic Hamiltonian, which allows nuclear reactions to be precisely calculated, is introduced using the example of alpha-alpha scattering. In closing, the book demonstrates how Nuclear Lattice EFT can be extended to studies of unphysical values of the fundamental parameters, using the triple-alpha process as a concrete example with implications for the anthropic view of the Universe. Nuclear Lattice Effective Field Theory offers a concise, self-contained, and introductory text suitable for self-study use by graduate students and newcomers to the field of modern computational techniques for atomic nuclei and nuclear reactions.
Nuclear Structure with Coherent States
by Apolodor Aristotel RadutaThis book covers the essential features of a large variety of nuclear structure properties, both collective and microscopic in nature. Most of results are given in an analytical form thus giving deep insight into the relevant phenomena. Using coherent states as variational states, which allows a description in the classical phase space, or provides the generating function for a boson basis, is an efficient tool to account, in a realistic fashion, for many complex properties. A detailed comparison with all existing nuclear structure models provides readers with a proper framework and, at the same time, demonstrates the prospects for new developments. The topics addressed are very much of current concern in the field. The book will appeal to practicing researchers and, due to its self-contained account, can also be successfully read and used by new graduate students.
Nucleation Theory
by V. I. KalikmanovOne of the most striking phenomena in condensed matter physics is the occurrence of abrupt transitions in the structure of a substance at certain temperatures or pressures. These are first order phase transitions, and examples such as the freezing of water are familiar in everyday life. The conditions at which the transformation takes place can sometimes vary. For example, the freezing point of water is not always 0°C, but the liquid can be supercooled considerably if it is pure enough and treated carefully. The reason for this phenomenon is nucleation. This monograph covers all major available routes of theoretical research of nucleation phenomena (phenomenological models, semi-phenomenological theories, density functional theories, microscopic and semi-microscopic approaches), with emphasis on the formation of liquid droplets from a metastable vapor. Also, it illustrates the application of these various approaches to experimentally relevant problems. In spite of the familiarity of the involved phenomena, it is still impossible to calculate nucleation accurately, as the properties and the kinetics of the daughter phase are insufficiently well known. Existing theories based upon classical nucleation theory have on the whole explained the trends in behavior correctly. However they often fail spectacularly to account for new data, in particular in the case of binary or, more generally, multi-component nucleation. The current challenge of this book is to go beyond such classical models and provide a more satisfactory theory by using density functional theory and microscopic computer simulations in order to describe the properties of small clusters. Also, semi-phenomenological models are proposed, which attempt to relate the properties of small clusters to known properties of the bulk phases. This monograph is an introduction as well as a compendium to researchers in soft condensed matter physics and chemical physics, graduate and post-graduate students in physics and chemistry starting on research in the area of nucleation, and to experimentalists wishing to gain a better understanding of the efforts being made to account for their data.
Nuestras manzanas favoritas / Our Favorite Apples (Storytelling Math)
by Grace Lin¡Libro de cartón grueso ahora disponible en español-inglés bilingüe! La ganadora del Honor de Caldecott, Grace Lin, celebra las matemáticas para todos los niños, ¡en todas partes!Board book now available in bilingual Spanish-English! Caldecott Honor winner Grace Lin celebrates math for every kid, everywhere!Manny, Olivia y Mei van a recoger manzanas y clasifican sus manzanas rojas, verdes y amarillas por colores. Pero luego encuentran una manzana que tiene los tres colores. ¿Qué deberían hacer? Una exploración juguetona de la clasificación, la categorización y la amistad.Storytelling Math celebra a los niños usando las matemáticas en sus aventuras diarias mientras juegan, construyen y descubren el mundo que les rodea. Historias alegres y actividades manuales hacen que sea fácil para los niños y sus adultos explorar las matemáticas cotidianas juntos. Desarrollado en colaboración con expertos en matemáticas de TERC, una organización educativa con enfoque en ciencia, tecnología, ingeniería y matemáticas (STEM, por sus siglas en inglés), bajo una subvención de la Fundación Heising-Simons.Manny, Olivia, and Mei go apple picking and sort their red, green, and yellow apples by color. But then they find an apple that&’s all three colors. What should they do? A playful exploration of sorting, classifying, and friendship.Storytelling Math celebrates children using math in their daily adventures as they play, build, and discover the world around them. Joyful stories and hands-on activities make it easy for kids and their grown-ups to explore everyday math together. Developed in collaboration with math experts at STEM education nonprofit TERC, under a grant from the Heising-Simons Foundation.
Null Set
by Ted MathysNull Set collects the slightly obsessive possibilities that rise when we give them the space--odd jobs, trouble-making, and farm boy rambling, all in dialogue with mathematics, or William Faulkner, or other poets.From "Hypotenuse":HYPOTENUSEI write three, erase it, blow rubbershavings from the desk. Write its notation,erase it, blow shavings. Then three 3serased, shavings blown, persistfor the nonce, three of nothing, nowhereattending to discrete objects for counting,themselves objects at any rate. To kiss,sleep, and focus we know to closeour eyes, imagine. I do, see nothing.
Numb and Number: How to Avoid Being Mystified by the Mathematics of Modern Life
by William HartstonLike it or not, our lives are dominated by mathematics. Our daily diet of news regales us with statistical forecasts, opinion polls, risk assessments, inflation figures, weather and climate predictions and all sorts of political decisions and advice backed up by supposedly accurate numbers. Most of us do not even pause and question such figures even to ask what they really mean and whether they raise more questions than they answer. We let the figures wash over us with no more than a glance. In this simple guide for anyone numbed by numbers, William Hartston explains with clarity and humor how to steer a safe path through the minefield of mathematics that surrounds us.
Numbed!
by David LubarWhen Logan’s class takes a trip to a math museum, his mischievous friend Benedict is sure it will be a boring day—until he discovers a robot and its creator in an off-limits area. The robot proves feisty, and soon both boys get zapped. They realize only later that they’d left the museum without their math skills. To get back the knowledge they need for school—not to mention buying food at the mall, divvying up dinner at home, and much more—they’ll have to get back to the museum and pass a series of math challenges. Being “numbed” teaches Logan and Benedict just how useful, and even fun, math can be.
Number: The Language of Science
by Tobias DantzigNumber is an eloquent, accessible tour de force that reveals how the concept of number evolved from prehistoric times through the twentieth century. Renowned professor of mathematics Tobias Dantzig shows that the development of math—from the invention of counting to the discovery of infinity—is a profoundly human story that progressed by “trying and erring, by groping and stumbling.” He shows how commerce, war, and religion led to advances in math, and he recounts the stories of individuals whose breakthroughs expanded the concept of number and created the mathematics that we know today.
Number: Activities for Children with Mathematical Learning Difficulties
by Mel LeverFirst Published in 2003. Routledge is an imprint of Taylor & Francis, an informa company.
Number Activities For Early Learners: Ideas for Parents and Pre-School Teachers
by Jan ConaglenThis e-book outlines interesting and age appropriate activities that can be carried out by parents and preschool teachers. It uses concrete materials so young children can visualize concepts, predict outcomes and display confidence, whilst learning from the suggested tasks.It will provide parents and preschool teachers with an insight into the importance of early basic mathematical knowledge.It will help develop the understanding and application of more complex skills that the student requires for later learning.The activities suggested are suitable for 3 years - 6 years old. This is usually preschool children up to second year at school.
Number Corner: Student Book
by Math Learning CenterThe Number Corner 2nd Edition Grade 3 Student Book provides students with opportunities to solve problems, conduct investigations, and practice skills in the context of familiar Number Corner Grade 3 lessons.
Number Corner, Grade 2, Student Book, Spanish Edition
by The Math Learning CenterNIMAC-sourced textbook
Number Corner Second Edition Grade 5 Student Book
by The Math Learning CenterA mathematics textbook
Number-Crunching: Taming Unruly Computational Problems from Mathematical Physics to Science Fiction
by Paul J. NahinMore stimulating mathematics puzzles from bestselling author Paul NahinHow do technicians repair broken communications cables at the bottom of the ocean without actually seeing them? What's the likelihood of plucking a needle out of a haystack the size of the Earth? And is it possible to use computers to create a universal library of everything ever written or every photo ever taken? These are just some of the intriguing questions that best-selling popular math writer Paul Nahin tackles in Number-Crunching. Through brilliant math ideas and entertaining stories, Nahin demonstrates how odd and unusual math problems can be solved by bringing together basic physics ideas and today's powerful computers. Some of the outcomes discussed are so counterintuitive they will leave readers astonished.Nahin looks at how the art of number-crunching has changed since the advent of computers, and how high-speed technology helps to solve fascinating conundrums such as the three-body, Monte Carlo, leapfrog, and gambler's ruin problems. Along the way, Nahin traverses topics that include algebra, trigonometry, geometry, calculus, number theory, differential equations, Fourier series, electronics, and computers in science fiction. He gives historical background for the problems presented, offers many examples and numerous challenges, supplies MATLAB codes for all the theories discussed, and includes detailed and complete solutions.Exploring the intimate relationship between mathematics, physics, and the tremendous power of modern computers, Number-Crunching will appeal to anyone interested in understanding how these three important fields join forces to solve today's thorniest puzzles.
Number Fields (Universitext)
by Daniel A. MarcusRequiring no more than a basic knowledge of abstract algebra, this text presents the mathematics of number fields in a straightforward, pedestrian manner. It therefore avoids local methods and presents proofs in a way that highlights the important parts of the arguments. Readers are assumed to be able to fill in the details, which in many places are left as exercises.
A Number for your Thoughts: Facts and Speculations About Numbers from Euclid to the Latest Computers
by M. E. LinesWhy do we count the way we do? What is a prime number or a friendly, perfect, or weird one? How many are there and who has found the largest yet known? What is the Baffling Law of Benford and can you really believe it? Do most numbers you meet in every day life really begin with a 1, 2, or 3? What is so special about 6174? Can cubes, as well as squares, be magic? What secrets lie hidden in decimals? How do we count the infinite, and is one infinity really larger than another? These and many other fascinating questions about the familiar 1, 2, and 3 are collected in this adventure into the world of numbers. Both entertaining and informative, A Number for Your Thoughts: Facts and Speculations about Numbers from Euclid to the Latest Computers contains a collection of the most interesting facts and speculations about numbers from the time of Euclid to the most recent computer research. Requiring little or no prior knowledge of mathematics, the book takes the reader from the origins of counting to number problems that have baffled the world's greatest experts for centuries, and from the simplest notions of elementary number properties all the way to counting the infinite.
Number Freak
by Derrick NiedermanNumber fanatic Derrick Niederman has a mission - to bring numbers to life. In Number Freak he explores the unique properties of the most fascinating numbers from 1 to 200, wherever they may crop up: from mathematics to sport, from history to the natural world, from language to pop culture. Packed with illustrations, amusing facts, puzzles, brainteasers and anecdotes, Number Freak is an enthralling and thought-provoking numerical voyage through the history of mathematics, investigating problems of logic, geometry and arithmetic along the way. Entertaining and accessible, it is a must for trivia addicts, maths-lovers and arithmophiles.
Number One Puppy
by Zachary WilsonA story about a little girl going to a dog pound to choose a pet.
Number Properties GRE Math Strategy Guide 2nd Edition
by Manhattan Gre StaffUpdated for the revised GRE, the Number Properties Guide provides a comprehensive analysis of the properties and rules of integers tested on the GRE to help you learn, practice, and master everything from prime products to perfect squares. Each chapter builds comprehensive content understanding by providing rules, strategies and in-depth examples of how the GRE tests a given topic and how you can respond accurately and quickly. The Guide contains both "Check Your Skills" questions in the chapters that test your understanding as you go and "In-Action" problems of increasing difficulty, all with detailed answer explanations.
Number Savvy: From the Invention of Numbers to the Future of Data
by George SciadasThis book is written for the love of numbers. It tells their story, shows how they were invented and used to quantify our world, and explains what quantitative data mean for our lives. It aspires to contribute to overall numeracy through a tour de force presentation of the production, use, and evolution of data. Understanding our physical world, our economies, and our societies through quantification has been a persistent feature of human evolution. This book starts with a narrative on why and how our ancestors were driven to the invention of number, which is then traced to the eventual arrival at our number system. This is followed by a discussion of how numbers were used for counting, how they enabled the measurement of physical quantities, and how they led to the estimation of man-made and abstract notions in the socio-economic domain. As data don’t fall like manna from the sky, a unique feature of this book is that it explains from a teacher’s perspective how they’re really conceived in our minds, how they’re actually produced from individual observations, and how this defines their meaning and interpretation. It discusses the significance of standards, the use of taxonomies, and clarifies a series of misconceptions regarding the making of data. The book then describes the switch to a new research paradigm and its implications, highlights the arrival of microdata, illustrates analytical uses of data, and closes with a look at the future of data and our own role in it.