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Counting In The City (Math Around Us)
by Tracey StefforaThis title uses simple text and vivid images to give readers concrete examples through which they can further develop number sense from zero to ten.
Counting Lattice Paths Using Fourier Methods (Applied and Numerical Harmonic Analysis)
by Shaun Ault Charles KiceyThis monograph introduces a novel and effective approach to counting lattice paths by using the discrete Fourier transform (DFT) as a type of periodic generating function. Utilizing a previously unexplored connection between combinatorics and Fourier analysis, this method will allow readers to move to higher-dimensional lattice path problems with ease. The technique is carefully developed in the first three chapters using the algebraic properties of the DFT, moving from one-dimensional problems to higher dimensions. In the following chapter, the discussion turns to geometric properties of the DFT in order to study the corridor state space. Each chapter poses open-ended questions and exercises to prompt further practice and future research. Two appendices are also provided, which cover complex variables and non-rectangular lattices, thus ensuring the text will be self-contained and serve as a valued reference.Counting Lattice Paths Using Fourier Methods is ideal for upper-undergraduates and graduate students studying combinatorics or other areas of mathematics, as well as computer science or physics. Instructors will also find this a valuable resource for use in their seminars. Readers should have a firm understanding of calculus, including integration, sequences, and series, as well as a familiarity with proofs and elementary linear algebra.
Counting Populations, Understanding Societies: Towards a Interpretative Demography (Demographic Transformation and Socio-Economic Development #1)
by Véronique PetitThe core aim of this book is to determine how anthropology and demography can be used in conjunction in the field of population and development. The boundaries of demography are not as clearly defined or as stable as one might think, especially in view of the tension between a formal demography centered on the 'core of procedures and references' and a more open form of demography, generally referred to as Population Studies. Many rapprochements, missed opportunities and isolated attempts marked the disciplinary history of anthropology and demography, both disciplines being founded on distinct and highly differentiated traditions and practices. Moreover, the role and the place assigned to epistemology differ significantly in ethnology and demography. Yet, anthropology and demography provide complementary models and research instruments and this book shows that neither discipline can afford to overlook their respective contributions. Based on research conducted in West Africa over more than twenty years, it is a defense of field demography that makes case for a continuum ranging from the initial conception of fieldwork and research to its effective implementation and to data analysis. Changes in behaviors relating to fertility, poverty or migration cannot be interpreted without invoking the cultural factor at some stage. Representations in their collective and individual dimensions also fit into the extended explanatory space of demography.
Counting Pumpkins
by Ellen SenisiJoin two friends counting pumpkins— and find a surprise at the end!
Counting Statistics for Dependent Random Events: With a Focus on Finance
by Silvia Romagnoli Enrico BernardiThis book on counting statistics presents a novel copula-based approach to counting dependent random events. It combines clustering, combinatorics-based algorithms and dependence structure in order to tackle and simplify complex problems, without disregarding the hierarchy of or interconnections between the relevant variables. These problems typically arise in real-world applications and computations involving big data in finance, insurance and banking, where experts are confronted with counting variables in monitoring random events.In this new approach, combinatorial distributions of random events are the core element. In order to deal with the high-dimensional features of the problem, the combinatorial techniques are used together with a clustering approach, where groups of variables sharing common characteristics and similarities are identified and the dependence structure within groups is taken into account. The original problems can then be modeled using new classes of copulas, referred to here as clusterized copulas, which are essentially based on preliminary groupings of variables depending on suitable characteristics and hierarchical aspects.The book includes examples and real-world data applications, with a special focus on financial applications, where the new algorithms’ performance is compared to alternative approaches and further analyzed. Given its scope, the book will be of interest to master students, PhD students and researchers whose work involves or can benefit from the innovative methodologies put forward here. It will also stimulate the empirical use of new approaches among professionals and practitioners in finance, insurance and banking.
Counting Surfaces: CRM Aisenstadt Chair lectures (Progress in Mathematical Physics #70)
by Bertrand EynardThe problem of enumerating maps (a map is a set of polygonal "countries" on a world of a certain topology, not necessarily the plane or the sphere) is an important problem in mathematics and physics, and it has many applications ranging from statistical physics, geometry, particle physics, telecommunications, biology, . . . etc. This problem has been studied by many communities of researchers, mostly combinatorists, probabilists, and physicists. Since 1978, physicists have invented a method called "matrix models" to address that problem, and many results have been obtained. Besides, another important problem in mathematics and physics (in particular string theory), is to count Riemann surfaces. Riemann surfaces of a given topology are parametrized by a finite number of real parameters (called moduli), and the moduli space is a finite dimensional compact manifold or orbifold of complicated topology. The number of Riemann surfaces is the volume of that moduli space. More generally, an important problem in algebraic geometry is to characterize the moduli spaces, by computing not only their volumes, but also other characteristic numbers called intersection numbers. Witten's conjecture (which was first proved by Kontsevich), was the assertion that Riemann surfaces can be obtained as limits of polygonal surfaces (maps), made of a very large number of very small polygons. In other words, the number of maps in a certain limit, should give the intersection numbers of moduli spaces. In this book, we show how that limit takes place. The goal of this book is to explain the "matrix model" method, to show the main results obtained with it, and to compare it with methods used in combinatorics (bijective proofs, Tutte's equations), or algebraic geometry (Mirzakhani's recursions). The book intends to be self-contained and accessible to graduate students, and provides comprehensive proofs, several examples, and gives the general formula for the enumeration of maps on surfaces of any topology. In the end, the link with more general topics such as algebraic geometry, string theory, is discussed, and in particular a proof of the Witten-Kontsevich conjecture is provided. <
Counting and Measuring: An Approach to Number Education in the Infant School
by Eileen M. ChurchillThe teaching of numbers in the primary grades is seen in this book as the foundation of the beginnings of mathematical understanding. Mathematics is taken to be a language, and the aim of its teaching is to make the pupil, so to speak, bilingual, or so to increase his understanding that he is able to translate a concrete numerical problem into the symbolic language of calculation. For a child taught along these lines, how much easier, for example, would be the transition from arithmetic to algebra!<P><P>Miss Churchill is fully conversant with the works of Piaget, Cuisenaire, Cassirer and other leading thinkers in educational philosophy, psychology, and linguistics. She has synthesized their concepts with her own experience and research at Leeds University, and, though written within the contexts of British education, her book should also have a marked influence on the teaching of young children in North America.
Counting at the Store (The World Around You)
by Christianne JonesPiles of tart apples. Cans of delicious soup. Rows of crunchy carrots. The grocery store is full of tasty foods and other items to count. The interactive, rhyming text and colorful photographs will have young learners counting along with every page in this picture book.
Counting on Community
by Innosanto NagaraCounting on Community is Innosanto Nagara's follow-up to his hit ABC book, A is for Activist. Counting up from one stuffed piñata to ten hefty hens--and always counting on each other--children are encouraged to recognize the value of their community, the joys inherent in healthy eco-friendly activities, and the agency they posses to make change. A broad and inspiring vision of diversity is told through stories in words and pictures. And of course, there is a duck to find on every page!
Counting on Mom
by Odd DotA beautifully illustrated picture book that encourages readers to count and celebrate all the moms around them!1 mom waking, 2 moms eating, 3 moms walking . . .Moms are all around us! This simple counting book encourages readers to count and celebrate all the amazing moms around them--the heroes kids count on everyday! Moms playing; moms relaxing; moms helping each other and their kids. It's a joyful opportunity to celebrate all that moms are and do! With sweet animal characters and charming art, this is the perfect gift book for new moms and at Mother's Day and all year long.
Counting on Snow
by Maxwell NewhouseMaxwell Newhouse, folk artist extraordinaire, has created a unique counting book. The premise is simple. He invites children to count with him from ten crunching caribou down to one lonely moose, by finding other northern animals - from seals to wolves to snowy owls - as they turn the pages. But as the animals appear, so does the snow, until it's a character too, obliterating light and dark, sky and earth. A gorgeous exploration of the isolation and the beauty of northern winter, Maxwell Newhouse has created a deceptively simple picture book that can be enjoyed by all ages.
Counting with Symmetric Functions (Developments in Mathematics #43)
by Anthony Mendes Jeffrey RemmelThis monograph provides a self-contained introduction to symmetric functions and their use in enumerative combinatorics. It is the first book to explore many of the methods and results that the authors present. Numerous exercises are included throughout, along with full solutions, to illustrate concepts and also highlight many interesting mathematical ideas. The text begins by introducing fundamental combinatorial objects such as permutations and integer partitions, as well as generating functions. Symmetric functions are considered in the next chapter, with a unique emphasis on the combinatorics of the transition matrices between bases of symmetric functions. Chapter 3 uses this introductory material to describe how to find an assortment of generating functions for permutation statistics, and then these techniques are extended to find generating functions for a variety of objects in Chapter 4. The next two chapters present the Robinson-Schensted-Knuth algorithm and a method for proving Pólya's enumeration theorem using symmetric functions. Chapters 7 and 8 are more specialized than the preceding ones, covering consecutive pattern matches in permutations, words, cycles, and alternating permutations and introducing the reciprocity method as a way to define ring homomorphisms with desirable properties. Counting with Symmetric Functions will appeal to graduate students and researchers in mathematics or related subjects who are interested in counting methods, generating functions, or symmetric functions. The unique approach taken and results and exercises explored by the authors make it an important contribution to the mathematical literature.
Counting-Out Rhymes: A Dictionary
by Roger D. Abrahams Lois RankinEeny, meeny, figgledy, fig. Delia, dolia, dominig,Ozy, pozy doma-nozy,Tee, tau, tut,Uggeldy, buggedy, boo!Out goes you. (no. 129)You can stand,And you can sit,But, if you play,You must be it. (no. 577)Counting-out rhymes are used by children between the ages of six and eleven as a special way of choosing it and beginning play. They may be short and simple ("O-U-T spells out/And out goes you") or relatively long and complicated; they may be composed of ordinary words, arrant nonsense, or a mixture of the two. Roger D. Abrahams and Lois Rankin have gathered together a definitive compendium of counting-out rhymes in English reported to 1980. These they discovered in over two hundred sources from the nineteenth and twentieth centuries, including rhymes from England, Scotland, Ireland, Australia, New Zealand, and the United States. Representative texts are given for 582 separate rhymes, with a comprehensive listing of sources and variants for each one, as well as information on each rhyme's provenience, date, and use. Cross-references are provided for variants whose first lines differ from those of the representative texts. Abrahams's introduction discusses the significance of counting-out rhymes in children's play. Children's folklore and speech play have attracted increasing attention in recent years. Counting-Out Rhymes will be a valuable resource for researchers in this field.
Counting: How We Use Numbers To Decide What Matters
by Deborah Stone“Deborah Stone’s mind-altering insight is that the numbers we use to capture the human experience are themselves a form of creative story-telling. They shouldn’t end the conversation, but spark a deeper and richer one. Counting deserves five stars for showing why five stars can never tell the whole story.” —Jacob S. Hacker, co-author of Let Them Eat Tweets: How the Right Rules in an Age of Extreme Inequality What do people do when they count? What do numbers really mean? We all know that people can lie with statistics, but in this groundbreaking work, eminent political scientist Deborah Stone uncovers a much deeper problem. With help from Dr. Seuss and Cookie Monster, she explains why numbers can’t be objective: in order to count, one must first decide what counts. Every number is the ending to a story built on cultural assumptions, social conventions, and personal judgments. And yet, in this age of big data and metric mania, numbers shape almost every facet of our lives: whether we get hired, fired, or promoted; whether we get into college or out of prison; how our opinions are gathered and portrayed to politicians; or how government designs health and safety regulations. In warm and playful prose, Counting explores what happens when we measure nebulous notions like merit, race, poverty, pain, or productivity. When so much rides on numbers, they can become instruments of social welfare, justice, and democracy—or not. The citizens of Flint, Michigan, for instance, used numbers to prove how their household water got contaminated and to force their government to take remedial action. In stark contrast, the Founding Fathers finessed an intractable conflict by counting each slave as three-fifths of a person in the national census. They set a terrible precedent for today’s politicians who claim to solve moral and political dilemmas with arithmetic. Suffused with moral reflection and ending with a powerful epilogue on COVID-19’s dizzying statistics, Counting will forever change our relationship with numbers.
Coupled Heat and Mass Transfer in Binary Mixtures at Supercritical Pressures (Springer Theses)
by Zhan-Chao HuSupercritical pressure fluids have been exploited in many engineering fields, where binary mixtures are frequently encountered. This book focuses on the coupled heat and mass transfer in them, where the coupling comes from cross-diffusion effects (i.e., Soret and Dufour effects) and temperature-dependent boundary reactions. Under this configuration, three main topics are discussed: relaxation and diffusion problems, hydrodynamic stability, and convective heat and mass transfer. This book reports a series of new phenomena, novel mechanisms, and an innovative engineering design in hydrodynamics and transport phenomena of binary mixtures at supercritical pressures. This book covers not only current research progress but also basic knowledge and background. It is very friendly to readers new to this field, especially graduate students without a deep theoretical background.
Coupled Mathematical Models for Physical and Biological Nanoscale Systems and Their Applications: Banff International Research Station, Banff, Canada, 28 August - 2 September 2016 (Springer Proceedings in Mathematics & Statistics #232)
by Roderick Melnik Luis L. Bonilla Efthimios KaxirasThis volume gathers selected contributions from the participants of the Banff International Research Station (BIRS) workshop Coupled Mathematical Models for Physical and Biological Nanoscale Systems and their Applications, who explore various aspects of the analysis, modeling and applications of nanoscale systems, with a particular focus on low dimensional nanostructures and coupled mathematical models for their description. Due to the vastness, novelty and complexity of the interfaces between mathematical modeling and nanoscience and nanotechnology, many important areas in these disciplines remain largely unexplored. In their efforts to move forward, multidisciplinary research communities have come to a clear understanding that, along with experimental techniques, mathematical modeling and analysis have become crucial to the study, development and application of systems at the nanoscale. The conference, held at BIRS in autumn 2016, brought together experts from three different communities working in fields where coupled mathematical models for nanoscale and biosystems are especially relevant: mathematicians, physicists (both theorists and experimentalists), and computational scientists, including those dealing with biological nanostructures. Its objectives: summarize the state-of-the-art; identify and prioritize critical problems of major importance that require solutions; analyze existing methodologies; and explore promising approaches to addressing the challenges identified. The contributions offer up-to-date introductions to a range of topics in nano and biosystems, identify important challenges, assess current methodologies and explore promising approaches. As such, this book will benefit researchers in applied mathematics, as well as physicists and biologists interested in coupled mathematical models and their analysis for physical and biological nanoscale systems that concern applications in biotechnology and medicine, quantum information processing and optoelectronics.
Covariance and Gauge Invariance in Continuum Physics: Application to Mechanics, Gravitation, and Electromagnetism (Progress in Mathematical Physics #73)
by Lalaonirina R. RakotomananaThis book presents a Lagrangian approach model to formulate various fields of continuum physics, ranging from gradient continuum elasticity to relativistic gravito-electromagnetism. It extends the classical theories based on Riemann geometry to Riemann-Cartan geometry, and then describes non-homogeneous continuum and spacetime with torsion in Einstein-Cartan relativistic gravitation. It investigates two aspects of invariance of the Lagrangian: covariance of formulation following the method of Lovelock and Rund, and gauge invariance where the active diffeomorphism invariance is considered by using local Poincaré gauge theory according to the Utiyama method. Further, it develops various extensions of strain gradient continuum elasticity, relativistic gravitation and electromagnetism when the torsion field of the Riemann-Cartan continuum is not equal to zero. Lastly, it derives heterogeneous wave propagation equations within twisted and curved manifolds and proposes a relation between electromagnetic potential and torsion tensor.
Covariant Electrodynamics: A Concise Guide
by John M. CharapA notoriously difficult subject, covariant electrodynamics is nonetheless vital for understanding relativistic field theory. John M. Charap’s classroom-tested introduction to the mathematical foundations of the topic presents the material in an approachable manner.Charap begins with a historical overview of electrodynamics and a discussion of the preliminary mathematics one needs in order to grasp the advanced and abstract concepts underlying the theory. He walks the reader through Maxwell’s four equations, explaining how they were developed and demonstrating how they are applied. From there, Charap moves through the other components of electrodynamics, such as Lorentz transformations, tensors, and charged particle behavior. At each point, he carefully works through the mathematics, applies the concepts to simple physical systems, and provides historical context that makes clear the connections among the theories and the mathematicians responsible for developing them. A concluding chapter reviews the history of electrodynamics and points the way for independent testing of the theory.Thorough, evenly paced, and intuitive, this friendly introduction to high-level covariant electrodynamics is a handy and helpful addition to any physicist’s toolkit.
Covariant Techniques in Quantum Field Theory (SpringerBriefs in Physics)
by Enrique Álvarez Jesús AneroThe purpose of this book is to illustrate some of the most important techniques which are helpful in combinatorial problems when computing quantum effects in covariant theories, like general relativity. In fact, most of the techniques find application also in broader contexts, such as low energy effective (chiral) Lagrangians or even in specific problems in condensed matter. Some of the topics covered are: the background field approach and the heat kernel ideas. The arguments are explained in some detail and the presentation is meant for young researchers and advanced students who are starting working in the field. As prerequisite the reader should have attended a course in quantum field theory including Feynman’s path integral. In the Appendix a nontrivial calculation of one-loop divergences in Einstein-Hilbert gravity is explained step-by-step.
Covering Walks in Graphs (SpringerBriefs in Mathematics)
by Ping Zhang Futaba FujieCovering Walks in Graphs is aimed at researchers and graduate students in the graph theory community and provides a comprehensive treatment on measures of two well studied graphical properties, namely Hamiltonicity and traversability in graphs. This text looks into the famous Kӧnigsberg Bridge Problem, the Chinese Postman Problem, the Icosian Game and the Traveling Salesman Problem as well as well-known mathematicians who were involved in these problems. The concepts of different spanning walks with examples and present classical results on Hamiltonian numbers and upper Hamiltonian numbers of graphs are described; in some cases, the authors provide proofs of these results to illustrate the beauty and complexity of this area of research. Two new concepts of traceable numbers of graphs and traceable numbers of vertices of a graph which were inspired by and closely related to Hamiltonian numbers are introduced. Results are illustrated on these two concepts and the relationship between traceable concepts and Hamiltonian concepts are examined. Describes several variations of traceable numbers, which provide new frame works for several well-known Hamiltonian concepts and produce interesting new results.
Covers and Envelopes in the Category of Complexes of Modules
by J.R. Garcia RozasOver the last few years, the study of complexes has become increasingly important. To date, however, most of the research is scattered throughout the literature or available only as lecture notes. Covers and Envelopes in the Category of Complexes of Modules collects these scattered notes and results into a single, concise volume that provides an account of recent developments in the theory and presents several new and important ideas.The author introduces the theory of complexes of modules using only elementary tools-making the field more accessible to non-specialists. He focuses the study on envelopes and covers in this category with respect to some well established and important classes of complexes. He places particular emphasis on DG-injective and DG-projective complexes and flat and DG-flat covers.Other topics covered include Zorn's Lemma for categories, preserving and reflecting covers by functors, orthogonality in the category of complexes, Gorenstein injective and projective complexes, and pure sequences of complexes.Along with its value as a collection of recent work in the field, Covers and Envelopes in the Category of Complexes of Modules presents powerful new ideas that will undoubtedly advance homological methods. Mathematicians-especially researchers in module theory and homological algebra-will welcome this volume as a reference guide and for its new and important results.
Covid By Numbers: Making Sense of the Pandemic with Data (Pelican Books)
by David Spiegelhalter Anthony Masters'I couldn't imagine a better guidebook for making sense of a tragic and momentous time in our lives. Covid by Numbers is comprehensive yet concise, impeccably clear and always humane' Tim HarfordHow many people have died because of COVID-19? Which countries have been hit hardest by the virus? What are the benefits and harms of different vaccines? How does COVID-19 compare to the Spanish flu? How have the lockdown measures affected the economy, mental health and crime?This year we have been bombarded by statistics - seven day rolling averages, rates of infection, excess deaths. Never have numbers been more central to our national conversation, and never has it been more important that we think about them clearly. In the media and in their Observer column, Professor Sir David Spiegelhalter and RSS Statistical Ambassador Anthony Masters have interpreted these statistics, offering a vital public service by giving us the tools we need to make sense of the virus for ourselves and holding the government to account.In Covid by Numbers, they crunch the data on a year like no other, exposing the leading misconceptions about the virus and the vaccine, and answering our essential questions. This timely, concise and approachable book offers a rare depth of insight into one of the greatest upheavals in history, and a trustworthy guide to these most uncertain of times.
Cox Rings
by Ivan Arzhantsev Ulrich Derenthal Jürgen Hausen Antonio LafaceCox rings are significant global invariants of algebraic varieties, naturally generalizing homogeneous coordinate rings of projective spaces. This book provides a largely self-contained introduction to Cox rings, with a particular focus on concrete aspects of the theory. Besides the rigorous presentation of the basic concepts, other central topics include the case of finitely generated Cox rings and its relation to toric geometry; various classes of varieties with group actions; the surface case; and applications in arithmetic problems, in particular Manin's conjecture. The introductory chapters require only basic knowledge in algebraic geometry. The more advanced chapters also touch on algebraic groups, surface theory, and arithmetic geometry. Each chapter ends with exercises and problems. These comprise mini-tutorials and examples complementing the text, guided exercises for topics not discussed in the text, and, finally, several open problems of varying difficulty.
Coyotes All Around
by Stuart J. MurphyClever Coyote thinks it's time for lunch -- and also time to show her friends how, with some simple rounding, she can add up numbers in her head. If only she were as good at hunting as she is at math!