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Books on the topic 'Numerical representations'

Author: Grafiati

Published: 4 June 2021

Last updated: 26 April 2022

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1

Blackett, Norman. Developing understanding of trigonometry in boys and girls using a computer to link numerical and visual representations. typescript, 1990.

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2

Canada. Defence Research Establishment Atlantic. Numerical Representation of Hulls with Knuckles. s.n, 1986.

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3

Myers, Cory S. Signal representation for symbolic and numerical processing. Massachusetts Institute of Technology, Research Laboratory of Electronics, 1986.

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4

Walmsley, N. The numerical representation of pump-turbine performance characteristics. typescript, 1986.

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5

Emanuel, Kerry A., and David J. Raymond, eds. The Representation of Cumulus Convection in Numerical Models. American Meteorological Society, 1993. http://dx.doi.org/10.1007/978-1-935704-13-3.

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6

Stone, Dan N. Numeric and linguistic information representation in multiattribute choice. College of Commerce and Business Administration, University of Illinois at Urbana-Champaign, 1989.

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7

Madej, Łukasz. Development of the modelling strategy for the strain localization simulation based on the digital material representation. AGH University of Science and Technology Press, 2010.

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8

Pawlak, Zdzisław. Rough sets: Theoretical aspects of reasoning about data. Kluwer Academic Publishers, 1991.

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9

David, Hutchison. Transactions on Computational Science V: Special Issue on Cognitive Knowledge Representation. Springer Berlin Heidelberg, 2009.

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10

Spadacini, Lorenzo. Regole elettorali e integrità numerica delle Camere: La mancata assegnazione di alcuni seggi alla Camera nella 14. legislatura. Promodis Italia, 2003.

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11

Kutyniok, Gitta. Shearlets: Multiscale Analysis for Multivariate Data. Birkhäuser Boston, 2012.

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12

Hersh, Reuben. Peter Lax, mathematician: An illustrated memoir. American Mathematical Society, 2015.

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13

Mass.) AMS Special Session on Radon Transforms and Geometric Analysis (2012 Boston. Geometric analysis and integral geometry: AMS special session in honor of Sigurdur Helgason's 85th birthday, radon transforms and geometric analysis, January 4-7, 2012, Boston, MA ; Tufts University Workshop on Geometric Analysis on Euclidean and Homogeneous Spaces, January 8-9, 2012, Medford, MA. Edited by Quinto, Eric Todd, 1951- editor of compilation, Gonzalez, Fulton, 1956- editor of compilation, Christensen, Jens Gerlach, 1975- editor of compilation, and Tufts University. Workshop on Geometric Analysis on Euclidean and Homogeneous Spaces. American Mathematical Society, 2013.

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14

Davies, Nigel Howard. Numerical representations of fluid mixing. 1993.

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15

Tzelgov, Joseph, Dana Ganor-Stern, Arava Kallai, and Michal Pinhas. Primitives and Non-primitives of Numerical Representations. Edited by Roi Cohen Kadosh and Ann Dowker. Oxford University Press, 2014. http://dx.doi.org/10.1093/oxfordhb/9780199642342.013.019.

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Primitives of numerical representation are numbers holistically represented on the mental number line (MNL). Non-primitives are numbers generated from primitives in order to perform specific tasks. Primitives can be automatically retrieved from long-term memory (LTM). Using the size congruency effect in physical comparisons as a marker of automatic retrieval, and its modulation by intrapair numerical distance as an indication of alignment along the MNL, we identify single-digits, but not two-digit numbers, as primitives. By the same criteria, zero is a primitive, but negative numbers are not p

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16

Representation Theory and Numerical AF-Invariants. American Mathematical Society, 2004.

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17

Mesinger, Fedor, Miodrag Rančić, and R. James Purser. Numerical Methods in Atmospheric Models. Oxford University Press, 2018. http://dx.doi.org/10.1093/acrefore/9780190228620.013.617.

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The astonishing development of computer technology since the mid-20th century has been accompanied by a corresponding proliferation in the numerical methods that have been developed to improve the simulation of atmospheric flows. This article reviews some of the numerical developments concern the ongoing improvements of weather forecasting and climate simulation models. Early computers were single-processor machines with severely limited memory capacity and computational speed, requiring simplified representations of the atmospheric equations and low resolution. As the hardware evolved and mem

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18

Lindemann, Oliver, and Martin H. Fischer. Cognitive Foundations of Human Number Representations and Mental Arithmetic. Edited by Roi Cohen Kadosh and Ann Dowker. Oxford University Press, 2014. http://dx.doi.org/10.1093/oxfordhb/9780199642342.013.61.

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The chapters in this section of the volume reveal the striking variety of human numerical cognition. The section comprises four chapters that focus on different aspects of the representation of numerical knowledge, as well as three chapters that examine the several cognitive processes involved in the manipulation of numbers during simple mental arithmetic. They show how chronometric analyses, in combination with clever experimental designs, can reveal the cognitive processes and representations underlying this impressive collection of cognitive skills. Our goal in this overview chapter is to h

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19

Castronovo, Julie. Numbers in the Dark. Edited by Roi Cohen Kadosh and Ann Dowker. Oxford University Press, 2014. http://dx.doi.org/10.1093/oxfordhb/9780199642342.013.036.

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How do we represent numbers in the dark? Is vision necessary in the elaboration of numerical representations and skills? These questions are of great interest, as for a long time, the role of vision has been implicitly and explicitly stressed in the acquisition and development of numerical representations and skills. Over the last few years, several researchers have directly addressed this question by studying the impact of early visual deprivation on numerical representations and skills. Different numerical processes have been investigated in blind people: numerical comparison, parity judgeme

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20

Gebuis, Titia, and Bert Reynvoet. Number Representations and their Relation with Mathematical Ability. Edited by Roi Cohen Kadosh and Ann Dowker. Oxford University Press, 2014. http://dx.doi.org/10.1093/oxfordhb/9780199642342.013.035.

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In this chapter we review research on the processes that underlie the development of mathematical abilities. It is proposed that numerical deficiencies might arise from domain specific problems. The approximate number system that supports reasoning with non-symbolic numbers, on the one hand, and the symbolic number system on the other hand were put forth as possible candidates. To gain insight into the two different systems, we will describe the development of non-symbolic and symbolic number processing and introduce the two main theories about numerical deficiencies: the approximate number sy

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21

Brannon, Elizabeth M., and Joonkoo Park. Phylogeny and Ontogeny of Mathematical and Numerical Understanding. Edited by Roi Cohen Kadosh and Ann Dowker. Oxford University Press, 2015. http://dx.doi.org/10.1093/oxfordhb/9780199642342.013.57.

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This navigator chapter situates the chapters that comprise the section on the phylogeny and ontogeny of mathematical and numerical understanding. How is number represented in the absence of language? What are the key questions that arise as we map out the continuities and discontinuities between non-human and human numerical cognition? What can we learn from studying individual differences in numerical cognition? How do the initial representations of quantity in the infant give rise to the uniquely human mathematical mind? Can we use the knowledge we are gaining about how the preverbal mind re

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22

Lancellotti, Vito. Advanced Theoretical and Numerical Electromagnetics. Volume 2: Field representations and the Method of Moments. Institution of Engineering and Technology, 2021. http://dx.doi.org/10.1049/sbew560g.

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23

Andres, Michael, and Mauro Pesenti. Finger-based representation of mental arithmetic. Edited by Roi Cohen Kadosh and Ann Dowker. Oxford University Press, 2014. http://dx.doi.org/10.1093/oxfordhb/9780199642342.013.028.

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Human beings are permanently required to process the world numerically and, consequently, to perform computations to adapt their behaviour and they have developed various calculation strategies, some of them based on specific manipulations of the fingers. In this chapter, we argue that the way we express physically numerical concepts by raising fingers while counting leads to embodied representations of numbers and calculation procedures in the adult brain. To illustrate this, we focus on number and finger interactions in the context of simple arithmetic operations. We show that the fixed orde

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24

Sarnecka, Barbara W., Meghan C. Goldman, and Emily B. Slusser. How Counting Leads to Children’s First Representations of Exact, Large Numbers. Edited by Roi Cohen Kadosh and Ann Dowker. Oxford University Press, 2014. http://dx.doi.org/10.1093/oxfordhb/9780199642342.013.011.

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Young children initially learn to ‘count’ without understanding either what counting means, or what numerical quantities the individual number words pick out. Over a period of many months, children assign progressively more sophisticated meanings to the number words, linking them to discrete objects, to quantification, to numerosity, and so on. Eventually, children come to understand the logic of counting. Along with this knowledge comes an implicit understanding of the successor function, as well as of the principle of equinumerosity, or exact equality between sets. Thus, when children arrive

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25

Representations, Wavelets, and Frames: A Celebration of the Mathematical Work of Lawrence W. Baggett (Applied and Numerical Harmonic Analysis). Birkhäuser, 2008.

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26

Nedelec, Jean-Claude. Acoustic and Electromagnetic Equations: Integral Representations For Harmonic Problems. Springer, 2010.

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27

Nuerk, Hans-Christoph, Korbinian Moeller, and Klaus Willmes. Multi-digit Number Processing. Edited by Roi Cohen Kadosh and Ann Dowker. Oxford University Press, 2014. http://dx.doi.org/10.1093/oxfordhb/9780199642342.013.021.

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Only recently the focus in numerical cognition research has considered multi-digit number processing as a relatively new and yet understudied domain in mathematical cognition. In this chapter: (i) we argue that single-digit number processing is not sufficient to understand multi-digit number processing; (ii) provide an overview on which representations and effects have been investigated for multi-digit numbers; (iii) suggest a conceptual distinction between place-identification, place-value activation, and place-value computation; (iv) identify language influences on multi-digit number process

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28

Covarrubias Díaz, Felipe. Evaluación de la Contribución de las Capacidades Numéricas Básicas y de la Memoria de Trabajo al Rendimiento Aritmético en Niños de Edad Escolar. Universidad Autónoma de Chile, 2019. http://dx.doi.org/10.32457/20.500.12728/88642019mnc12.

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Introduction: There are several causes and explanations of the cognitive mechanisms that underlie the deficits of mathematical learning difficulties. Several studies have evaluated the relations among general domain cognitive abilities (like intellectual coefficient and working memory (WM)) or cognitive abilities of specific domain; However, there are a few studies that evaluate simultaneously the contribution of cognitive variables of both domains to the arithmetic efficiency. Aim: The present study aims to simultaneously evaluate the unique contribution of the basic numerical capacities (BNC

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29

(Editor), Ulrich Trottenberg, and W. Hackbusch (Editor), eds. Multigrid Methods, Koeln-Porz, Frg, 1981: Proceedings (Lecture Notes in Mathematics). Springer, 1986.

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30

Boudreau, Joseph F., and Eric S. Swanson. Interpolation and extrapolation. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198708636.003.0004.

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This chapter deals with two related problems occurring frequently in the physical sciences: first, the problem of estimating the value of a function from a limited number of data points; and second, the problem of calculating its value from a series approximation. Numerical methods for interpolating and extrapolating data are presented. The famous Lagrange interpolating polynomial is introduced and applied to one-dimensional and multidimensional problems. Cubic spline interpolation is introduced and an implementation in terms of Eigen classes is given. Several techniques for improving the conv

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31

1955-, Emanuel Kerry A., and Raymond David J, eds. The representation of cumulus convection in numerical models. American Meteorological Society, 1993.

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32

The Representation of Cumulus Convection in Numerical Models. Amer Meteorological Society, 1994.

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33

Institute for Computer Applications in Science and Engineering., ed. Multiresolution representation and numerical algorithms: A brief review. Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1994.

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34

Walker, James C. G. Numerical Adventures with Geochemical Cycles. Oxford University Press, 1991. http://dx.doi.org/10.1093/oso/9780195045208.001.0001.

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The dynamic, evolving Earth, and the mathematical representation of its geochemical changes are the subject of this timely, helpful handbook. Global warming, changes in the ocean, and the effects of fossil fuel combustion are just a few of the phenomena that make the development of geochemical models critical. But what computational methods will help to accurately carry out this task? This new text teaches the methodology of computational simulation of environmental change. The author presents interesting applications of his methods to describe the response of the ocean and atmosphere to the i

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35

Salillas, Elena, and Carlo Semenza. Mapping the Brain for Math. Edited by Roi Cohen Kadosh and Ann Dowker. Oxford University Press, 2014. http://dx.doi.org/10.1093/oxfordhb/9780199642342.013.046.

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Brain stimulation techniques allow for the search of crucial areas for a given function. Not always convergent with neuroimaging, TMS studies have targeted parietal areas critical for quantity representation, spatio-numerical links, numerical and non-numerical quantity, finger gnosis and calculation. TMS data indicate the intraparietal sulcus and surrounding areas in the left and right hemisphere as crucial for quantity processing, although left hemisphere might be dominant. Bilateral parietal loci are essential for calculation and bilateral parietal areas are behind the spatio-numerical link,

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36

Wolff, J. E. The Metaphysics of Quantities. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198837084.001.0001.

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This book articulates and defends a new and original answer to two questions: What are physical quantities and what makes them quantitative? This novel position—substantival structuralism—says that quantitativeness is an irreducible feature of particular attributes, and quantitative attributes are best understood as substantival structured spaces. Physical quantities like mass, momentum, or temperature play an important role in formulating laws of nature and in testing scientific theories. It is therefore important to have a clear philosophical understanding of what makes these attributes spec

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37

Thomas, Nehrkorn, Grassotti Christopher, and United States. National Aeronautics and Space Administration., eds. Distortion representation of forecast errors for model skill assessment and objective analysis: Technical report. National Aeronautics and Space Administration, 1997.

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38

(Editor), David J. Raymond, ed. The Representation of Cumulus Convection in Numerical Models (Meteorological Monographs (Amer Meteorological Soc)). American Meteorological Society, 1994.

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39

Boudreau, Joseph F., and Eric S. Swanson. Encapsulation and the C++ class. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198708636.003.0002.

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Built-in datatypes and C++ classes are introduced in this chapter, and discussed in relation to the important notion of encapsulation, which refers to the separation between the internal representation of the datatype and the operations to which it responds. Encapsulation later becomes an important consideration in the design of custom C++ classes that programmers develop themselves. It is illustrated with built-in floating-point datatypes float and double and with the complex class from the C++ standard library. While a sophisticated programmer is aware of the internal representation of data

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40

Transforms and Fast Algorithms for Signal Analysis and Representation (Applied and Numerical Harmonic Analysis). Birkhauser, 2003.

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41

1940-, Smith Robert E., and United States. National Aeronautics and Space Administration., eds. Software systems for surface modeling and grid generation: Proceedings of a workshop sponsored by the National Aeronautics and Space Administration, Washington, D.C., and held at Langley Research Center, Hampton, Virginia, April 28-30, 1992. National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Program, 1992.

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42

Johnson, Niki. Marginalization of Women and Male Privilege in Political Representation in Uruguay. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780190851224.003.0010.

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Niki Johnson shows that despite Uruguay being an institutionalized democracy, women have struggled to make numerical progress in politics. Formal and informal institutions that are inherently ridden with political biases limit women’s representation. Small district and party magnitudes along with male-biased candidate selection rules hindered women’s entry into office until the adoption of a gender quota, which was applied minimally by the main parties. Even with a quota, they still do not prioritize gender as a criterion for political office. Johnson points out that substantive representation

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43

Rusconi, Elena, and Carlo Umiltà. Mathematics and TMS. Edited by Charles M. Epstein, Eric M. Wassermann, and Ulf Ziemann. Oxford University Press, 2012. http://dx.doi.org/10.1093/oxfordhb/9780198568926.013.0033.

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This article introduces the relationship between mathematical cognition and transcranial magnetic stimulation (TMS). The mental number line is located in the parietal lobe. Studies employing TMS have explored issues related to the mental number line. This article reviews the studies centered on the magnitude code. The results show that even though the parietal activation is nearly always present in both hemispheres, it is often asymmetric, being greater in the right hemisphere when quantification of nonverbal and nonsymbolic material is required. Neuropsychological studies confirm the relation

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44

Kutyniok, Gitta, and Demetrio Labate. Shearlets: Multiscale Analysis for Multivariate Data. Springer, 2012.

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45

The Expected Knowledge: What can we know about anything and everything? Sivashanmugam Palaniappan, 2012.

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