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Data publikacji: 25 maja 2024

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1

1946-, Soderstrand Michael A., red. Residue number system arithmetic: Modern applications in digital signal processing. New York: Institute of Electrical and Electronics Engineers, 1986.

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Omondi, Amos R. Residue number systems: Theory and implementation. London: Imperial College Press, 2007.

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A, Soderstrand Michael, red. Residue number system arithmetic: Modern applications in digital signal processing. NewYork: IEEE Press, 1986.

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4

Moduli spaces and arithmetic dynamics. Providence, R.I: American Mathematical Society, 2012.

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Contemporary's number power: Fractions, decimals, and percents. Lincolnwood, Ill: Contemporary Books, 2000.

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Contemporary's number power: Addition, subtraction, multiplication, and division. Lincolnwood, Ill., USA: Contemporary Books, 2000.

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Howett, Jerry. Contemporary's number power: A real world approach to math. Chicago, Ill: McGraw-Hill/Wright Group, 2000.

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Jamīl, T̤āriq. Complex Binary Number System: Algorithms and Circuits. India: Springer India, 2013.

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9

Elliptic curves, modular forms, and their L-functions. Providence, R.I: American Mathematical Society, 2011.

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Contemporary's number power 2: Fractions, decimals and percents. Chicago: Contemporary Books, 1988.

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Graham, Jullien, i Muscedere Roberto, red. Multiple-base number system: Theory and applications. Boca Raton: CRC Press, 2012.

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Ed, Muller A. M., red. Computer-assisted instruction in arithmetic/mathematics with the TOAM system in a number of primary schools. Pretoria: Human Sciences Research Council, 1987.

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The geometric and arithmetic volume of Shimura varieties of orthogonal type. Providence, Rhode Island, USA: American Mathematical Society, 2014.

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14

V, Kokotović Petar, Khalil Hassan K. 1950- i IEEE Control Systems Society, red. Singular perturbations in systems and control. New York: IEEE Press, 1986.

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Fermat's last theorem. Providence, Rhode Island: American Mathematical Society, 2013.

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Tschinkel, Yuri, Carlo Gasbarri, Steven Lu i Mike Roth. Rational points, rational curves, and entire holomorphic curves on projective varieties: CRM short thematic program, June 3-28, 2013, Centre de Recherches Mathematiques, Universite de Montreal, Quebec, Canada. Providence, Rhode Island: American Mathematical Society, 2015.

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Cojocaru, Alina Carmen, Chantal David i F. Pappalardi. Scholar, a scientific celebration highlighting open lines of arithmetic research: Conference in honour of M. Ram Murty's mathematical legacy on his 60th birthday, October 15-17, 2013, Centre de Recherches Mathematiques, Universite de Montreal, Quebec, Canada. Redaktor Murty Maruti Ram editor. Providence, Rhode Island: American Mathematical Society, 2015.

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18

Trends in number theory: Fifth Spanish meeting on number theory, July 8-12, 2013, Universidad de Sevilla, Sevilla, Spain. Providence, Rhode Island: American Mathematical Society, 2015.

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Alladi, Krishnaswami, Frank Garvan i Ae Ja Yee. Ramanujan 125: International conference to commemorate the 125th anniversary of Ramanujan's birth, Ramanujan 125, November 5--7, 2012, University of Florida, Gainesville, Florida. Providence, Rhode Island: American Mathematical Society, 2014.

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20

On certain L-functions: Conference in honor of Freydoon Shahidi on certain L-functions, Purdue Univrsity, West Lafayette, Indiana, July 23-27, 2007. Providence, R.I: American Mathematical Society, 2011.

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21

Skavantzos, Alexander. The polynomial residue number system and its applications. 1987.

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Griffin, Michael F. The residue number system, complex residue number systems, and digital signal processing. 1988.

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23

Residue Number Systems: Theory and Implementation (Advances in Computer Science and Engineering Texts) (Advances in Computer Science and Engineering Texts). Imperial College Press, 2007.

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Thurston, H. A. The Number System. Dover Publications, 2007.

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25

Zhou, Xing. Number Theory - Modular Arithmetic: Math for Gifted Students. Createspace Independent Publishing Platform, 2017.

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26

Picken, David Kennedy. Number System of Arithmetic and Algebra. Creative Media Partners, LLC, 2018.

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27

Roberts, J. B. Real Number System in an Algebraic Setting. Dover Publications, Incorporated, 2018.

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Roberts, J. B. Real Number System in an Algebraic Setting. Dover Publications, Incorporated, 2018.

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29

Number Power Consumer Math. Ntc Pub Group, 1994.

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Mumford, Jeanette, Jane Crowden i Fay Turner. Cambridge Mathematics Direct 4 Numbers and the Number System Solutions (Cambridge Mathematics Direct). Cambridge University Press, 2000.

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Russell, Susan Jo, Virginia Bastable i Deborah Schifter. Number and Operations, Part 1: Building A System of Tens Casebook. National Council of Teachers of Mathematics, 2016.

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32

Jullien, Graham, Vassil Dimitrov i Roberto Muscedere. Multiple-Base Number System: Theory and Applications. Taylor & Francis Group, 2017.

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Dimitrov, Vassil. Multiple-Base Number System: Theory and Applications. Taylor & Francis Group, 2012.

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34

Luebering, J. E., Michael J. Cominskey, Anthony L. Green, Hope Lourie Kilcoyne, Nelson Sá, Nicole Russo i Cindy Reiman. The number system and common and decimal fractions. Redaktor John Strazzabosco, writer of supplementary textual content. 2015.

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Mult-e-Maths KS2 Numbers and the Number System Teacher's Notes (Mult-e-Maths). Cambridge-Hitachi, 2005.

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Zelniker, Glenn. Algebraic and number theoretic computing: Advances and applications in VLSI signal processing. 1991.

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Jullien, Graham, Vassil Dimitrov i Roberto Muscedere. Multiple-Base Number System: Theory and Applications. Taylor & Francis Group, 2017.

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38

Jullien, Graham, Vassil Dimitrov i Roberto Muscedere. Multiple-Base Number System: Theory and Applications. Taylor & Francis Group, 2017.

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Jullien, Graham, Vassil Dimitrov i Roberto Muscedere. Multiple-Base Number System: Theory and Applications. Taylor & Francis Group, 2017.

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40

Jullien, Graham, Vassil Dimitrov i Roberto Muscedere. Multiple-Base Number System: Theory and Applications. Taylor & Francis Group, 2017.

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41

Stein, Dorothy. Introduction to Binary Arithmetic: 3000 Solved Examples That Demonstrate Conversion to the Decimal Number System. Independently Published, 2021.

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42

(Editor), Sandy Cowling, Jane Crowden (Editor), Andrew King (Editor) i Jeanette Mumford (Editor), red. Cambridge Mathematics Direct 5 Numbers and the Number System Teacher's Handbook (Cambridge Mathematics Direct). Cambridge University Press, 2001.

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43

Hizzani, Mohammad. Design of a Modular Multiplier for Public-Key Cryptography Applications Using Residue Number System and Signed-Digit Representation. Independently published, 2019.

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44

Soderstrand, Michael A. Residue Number System Arithmetic: Modern Applications in Digital Signal Processing/Pbn, Pc01982 (Ieee Press Selected Reprint Series). Ieee, 1986.

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45

Gilmore, Camilla. Approximate Arithmetic Abilities in Childhood. Redaktorzy Roi Cohen Kadosh i Ann Dowker. Oxford University Press, 2014. http://dx.doi.org/10.1093/oxfordhb/9780199642342.013.006.

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This article reviews recent research exploring children’s abilities to perform approximate arithmetic with non-symbolic and symbolic quantities, and considers what role this ability might play in mathematics achievement. It has been suggested that children can use their approximate number system (ANS) to solve approximate arithmetic problems before they have been taught exact arithmetic in school. Recent studies provide evidence that preschool children can add, subtract, multiply, and divide non-symbolic quantities represented as dot arrays. Children can also use their ANS to perform simple approximate arithmetic with non-symbolic quantities presented in different modalities (e.g. sequences of tones) or even with symbolic representations of number. This article reviews these studies, and consider whether children’s performance can be explained through the use of alternative non-arithmetical strategies. Finally, it discusses the potential role of this ability in the learning of formal symbolic mathematics.

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McCrink, Koleen, i Wesley Birdsall. Numerical Abilities and Arithmetic in Infancy. Redaktorzy Roi Cohen Kadosh i Ann Dowker. Oxford University Press, 2014. http://dx.doi.org/10.1093/oxfordhb/9780199642342.013.038.

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Numerical Abilities and Arithmetic in Infancy. In this chapter, infants’ capacity to represent and manipulate numerical amounts via a precise system for small numbers (the object-tracking system) and an imprecise system for large numbers (the Approximate Number System, or ANS) is detailed. Of particular interest is the presence of an untrained ability to calculate arithmetic outcomes as a result of mathematical operations. The evidence for addition, subtraction, ordering, multiplication, and division in infancy is reviewed and links to other domains such as statistical learning are explored.

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Perfectoid Spaces: Lectures from the 2017 Arizona Winter School. American Mathematical Society, 2019.

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Kedlaya, Kiran S., Debargha Banerjee, Ehud de Shalit i Chitrabhanu Chaudhuri. Perfectoid Spaces. Springer Singapore Pte. Limited, 2022.

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LeFevre, Jo-Anne, Emma Wells i Carla Sowinski. Individual Differences in Basic Arithmetical Processes in Children and Adults. Redaktorzy Roi Cohen Kadosh i Ann Dowker. Oxford University Press, 2014. http://dx.doi.org/10.1093/oxfordhb/9780199642342.013.005.

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This chapter describes the four main sources of individual differences in arithmetic that have been identified through research with children and adults. Numerical quantitative knowledge invokes basic cognitive processes that are either numerically specific or are recruited to be used in quantitative tasks (e.g. subitizing, discrimination acuity for approximate quantities). Attentional skills, including executive attention and various aspects of working memory are important, especially for more complex procedures. Linguistic knowledge is used within arithmetic to learn number system rules and structures, specific number words, and in developing and executing counting processes. Strategic abilities, which may reflect general planning and awareness skills, are involved in selecting procedures and solving problems adaptively. Other important sources of individual differences include automaticity of knowledge related to practice, experiences outside school, and the specific language spoken. Suggestions are made for further research that would be helpful in establishing a full picture of individual differences in arithmetic.

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Uittenhove, Kim, i Patrick Lemaire. Numerical Cognition during Cognitive Aging. Redaktorzy Roi Cohen Kadosh i Ann Dowker. Oxford University Press, 2014. http://dx.doi.org/10.1093/oxfordhb/9780199642342.013.045.

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This chapter provides an overview of age-related changes and stabilities in numerical cognition. For each component (i.e. approximate and exact number system, quantification, and arithmetic) of numerical cognition, we review changes in participants’ performance during normal and pathological aging in a wide variety of tasks (e.g. number comparison, subitizing, counting, and simple or complex arithmetic problem-solving). We discuss both behavioral and neural mechanisms underlying these performance variations. Moreover, we highlight the importance of taking into account strategic variations. Indeed, investigating strategy repertoire (i.e. how young and older adults accomplish numerical cognitive tasks), selection (i.e. how participants choose strategies on each problem), execution (i.e. how strategies are implemented once selected), and distribution (i.e. how often participants use each available strategy) enables to determine sources of aging effects and individual differences in numerical cognition. Finally, we discuss potential future research to further our understanding of age-related changes in numerical cognition.

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