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Journal articles on the topic 'Counting and numbers'

Author: Grafiati

Published: 4 June 2021

Last updated: 28 July 2025

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1

Kortezov, Ivaylo. "Double Counting and Fibonacci Numbers." Mathematics and Informatics 67, no. 3 (2024): 336–50. https://doi.org/10.53656/math2024-3-7-dou.

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The article proposes a double counting method for proving combinatorial identities involving Fibonacci numbers. The method is easily remembered by the students. It allows them to apply it creatively in many situations, by (re)discovering the results by themselves and asking meaningful questions. The method is mainly oriented towards preparation for mathematical competitions.

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2

Bulley, Michael. "Counting Numbers." Cogito 4, no. 1 (1990): 41–47. http://dx.doi.org/10.5840/cogito19904114.

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3

De Koninck, Jean-Marie, and Florian Luca. "Counting the number of economical numbers." Publicationes Mathematicae Debrecen 68, no. 1-2 (2006): 97–113. http://dx.doi.org/10.5486/pmd.2006.3171.

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4

Goddard, Cliff. "The conceptual semantics of numbers and counting." Functions of Language 16, no. 2 (2009): 193–224. http://dx.doi.org/10.1075/fol.16.2.02god.

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This study explores the conceptual semantics of numbers and counting, using the natural semantic metalanguage (NSM) technique of semantic analysis (Wierzbicka 1996; Goddard & Wierzbicka (eds.) 2002). It first argues that the concept of a number in one of its senses (number1, roughly, “number word”) and the meanings of low number words, such as one, two, and three, can be explicated directly in terms of semantic primes, without reference to any counting procedures or practices. It then argues, however, that the larger numbers, and the productivity of the number sequence, depend on the conce

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5

Baumann, P. "Counting on numbers." Analysis 69, no. 3 (2009): 446–48. http://dx.doi.org/10.1093/analys/anp061.

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6

Lobeck, Martin A. "Counting the numbers." Nature 358, no. 6385 (1992): 365. http://dx.doi.org/10.1038/358365a0.

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7

Howard, P. J. A. "Counting the numbers." Nature 358, no. 6385 (1992): 365. http://dx.doi.org/10.1038/358365b0.

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8

Manitius, L. G. "Counting the numbers." Nature 358, no. 6385 (1992): 365. http://dx.doi.org/10.1038/358365c0.

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9

Hansell, D. P. "Counting the numbers." Nature 358, no. 6385 (1992): 365. http://dx.doi.org/10.1038/358365d0.

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10

De Koninck, J. M., N. Doyon, and I. Kátai. "Counting the number of twin Niven numbers." Ramanujan Journal 17, no. 1 (2008): 89–105. http://dx.doi.org/10.1007/s11139-008-9127-z.

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11

Trehearne, Andrew. "Counting on big numbers." International Journal of Surgery 7, no. 5 (2009): 413–15. http://dx.doi.org/10.1016/j.ijsu.2009.08.001.

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12

Carbó-Dorca, Ramon. "Mersenne Numbers, Recursive Generation of Natural Numbers, and Counting the Number of Prime Numbers." Applied Mathematics 13, no. 06 (2022): 538–43. http://dx.doi.org/10.4236/am.2022.136034.

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13

Read, Dwight. "Learning natural numbers is conceptually different than learning counting numbers." Behavioral and Brain Sciences 31, no. 6 (2008): 667–68. http://dx.doi.org/10.1017/s0140525x08005840.

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AbstractHow children learn number concepts reflects the conceptual and logical distinction between counting numbers, based on a same-size concept for collections of objects, and natural numbers, constructed as an algebra defined by the Peano axioms for arithmetic. Cross-cultural research illustrates the cultural specificity of counting number systems, and hence the cultural context must be taken into account.

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14

K. Volkov, Alexeï. "Large Numbers and Counting Rods." Extrême orient Extrême occident 16, no. 16 (1994): 71–92. http://dx.doi.org/10.3406/oroc.1994.991.

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15

Moree, Pieter. "Counting divisors of Lucas numbers." Pacific Journal of Mathematics 186, no. 2 (1998): 267–84. http://dx.doi.org/10.2140/pjm.1998.186.267.

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16

Almada, Carlos. "On counting the rational numbers." International Journal of Mathematical Education in Science and Technology 41, no. 8 (2010): 1096–101. http://dx.doi.org/10.1080/0020739x.2010.500695.

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17

Kimberling, Clark. "Path-Counting and Fibonacci Numbers." Fibonacci Quarterly 40, no. 4 (2002): 328–38. http://dx.doi.org/10.1080/00150517.2002.12428634.

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18

Kuba, Gerald. "Counting Fields of Complex Numbers." American Mathematical Monthly 116, no. 6 (2009): 541–46. http://dx.doi.org/10.1080/00029890.2009.11920971.

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19

Kuba, Gerald. "Counting Fields of Complex Numbers." American Mathematical Monthly 116, no. 6 (2009): 541–46. http://dx.doi.org/10.4169/193009709x470452.

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20

Adair, Aaron. "Counting on the Census Numbers." HIPHIL Novum 10, no. 1 (2025): 2–21. https://doi.org/10.7146/hn.v10i1.152021.

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Censuses of the Israelites found in Numbers have been mulled over because of both their large values and the particulars of those values. Efforts to fit the large numbers of Israelites escaping Egypt into something historically plausible or suggest a lexical development focus on reinterpreting the standard counter for “thousands”, elep (אלף). The most recent attempts use mathematical models, but the results have not been rigorously tested. A statistical evaluation finds the efforts wanting, and the underlying numbers are most likely artificial. The origin of the census values is then proposed,

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21

Saian, Pratyaksa Ocsa Nugraha. "Parallel Counting Sort: A Modified of Counting Sort Algorithm." International Journal of Information Technology and Business 1, no. 1 (2018): 10–15. http://dx.doi.org/10.24246/ijiteb.112018.10-15.

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Sorting is one of a classic problem in computer engineer. One well-known sorting algorithm is a Counting Sort algorithm. Counting Sort had one problem, it can’t sort a positive and negative number in the same input list. Then, Modified Counting Sort created to solve that’s problem. The algorithm will split the numbers before the sorting process begin. This paper will tell another modification of this algorithm. The algorithm called Parallel Counting Sort. Parallel Counting Sort able to increase the execution time about 70% from Modified Counting Sort, especially in a big dataset (around 1000 a

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22

Kaufhold, Annemarie E., Johannes Hirschberger, Sven Reese, Gesine Foerster, and Jutta Hein. "A comparison of manual counting of rabbit reticulocytes with ADVIA 2120i analyzer counting." Journal of Veterinary Diagnostic Investigation 30, no. 3 (2018): 337–41. http://dx.doi.org/10.1177/1040638717750428.

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We compared manual counting of reticulocytes in rabbits with automatic counting using an ADVIA 2120i analyzer. Reproducibility and the influence of different anticoagulants (EDTA and Li-heparin) were also examined. Blood samples of 331 rabbits (method comparison, n = 289; reproducibility, n = 33; comparison of anticoagulants, n = 9) were tested. The reticulocyte numbers of each specimen were manually determined twice for method comparison. Passing–Bablok regressions, Bland–Altman plots, and the coefficient of variation (CV) were used to evaluate statistical significance. Good correlation (rs =

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23

De Koninck, Jean-Marie, Nicolas Doyon, A. Arthur Bonkli Razafindrasoanaivolala, and William Verreault. "Bounds for the counting function of the Jordan-Pólya numbers." Archivum Mathematicum, no. 3 (2020): 141–52. http://dx.doi.org/10.5817/am2020-3-141.

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24

Hewson, Claire. "‘Numbers everywhere’." Early Years Educator 21, no. 4 (2019): S11—S12. http://dx.doi.org/10.12968/eyed.2019.21.4.s11.

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Make counting fun by linking it to the picture book Bear Counts. Children will be motivated to count spontaneously as part of indoor and outdoor activities that promote flexible mathematical thinking.

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25

Calegari, Frank, and Zili Huang. "Counting Perron numbers by absolute value." Journal of the London Mathematical Society 96, no. 1 (2017): 181–200. http://dx.doi.org/10.1112/jlms.12061.

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26

Zhang, Zhenxiang. "Counting Carmichael numbers with small seeds." Mathematics of Computation 80, no. 273 (2010): 437–42. http://dx.doi.org/10.1090/s0025-5718-2010-02382-8.

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27

McKay, Brendan D., and Stanisław P. Radziszowski. "Subgraph Counting Identities and Ramsey Numbers." Journal of Combinatorial Theory, Series B 69, no. 2 (1997): 193–209. http://dx.doi.org/10.1006/jctb.1996.1741.

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28

Suárez Suri, Pedro Roberto. "Counting prime numbers in arithmetic sequences." Minerva 4, no. 10 (2023): 122–34. http://dx.doi.org/10.47460/minerva.v4i10.111.

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This paper presents the theoretical elements that support the calculation of the prime number counting function, π(x), based on properties of the sequences (6n-1) and (6n+1), n ≥ 1. As a result, Sufficient primality criteria are exposed for the terms of both sequences that support a deterministic computational algorithm that reduces the number of operations in calculating the function π(x) by exonerating all multiples of 3 from the analysis. In analyzing the primality of a particular term, the divisions by factor 3 are excluded. Such an algorithm can be applied to the search for prime numbers

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29

Ganayim, Deia, Shireen Ganayim, Ann Dowker, and Sinan Olkun. "Transcoding Errors of Two-Digit Numbers From Arabic Digits Into Verbal Numbers and From Verbal Numbers Into Arabic Digits by Arab First Graders." Journal of Cognitive Education and Psychology 20, no. 2 (2021): 161–78. http://dx.doi.org/10.1891/jcep-d-20-00007.

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The study focuses on the effect of the lexical-syntactic structure on the patterns of errors by Arab first graders in tasks involving reading two-digit number and writing two-digit numbers to dictation. Children made few change or omission errors, indicating that they had little problem with the lexical aspects of the counting system. However, they made frequent substitution errors (e.g., 23 for 32), especially in the number reading task, and especially for numbers that depended strongly on the numerical syntactic structure. Such errors were less common for decade numbers and for the 11–19 num

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30

Harries, Judith. "Christmas and counting…" Early Years Educator 23, no. 5 (2021): S10—S11. http://dx.doi.org/10.12968/eyed.2021.23.5.s10.

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This is the second article in the series exploring traditional nursery rhymes as a resource for activities throughout the early years curriculum. It features rhymes that involve numbers, counting and other mathematical concepts such as shapes, time, money and of course, Christmas.

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31

Andres, Michael, Samuel Di Luca, and Mauro Pesenti. "Finger counting: The missing tool?" Behavioral and Brain Sciences 31, no. 6 (2008): 642–43. http://dx.doi.org/10.1017/s0140525x08005578.

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AbstractRips et al. claim that the principles underlying the structure of natural numbers cannot be inferred from interactions with the physical world. However, in their target article they failed to consider an important source of interaction: finger counting. Here, we show that finger counting satisfies all the conditions required for allowing the concept of numbers to emerge from sensorimotor experience through a bottom-up process.

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32

Russo, James. "Skip-counting battle." Teaching Children Mathematics 22, no. 8 (2016): 512. http://dx.doi.org/10.5951/teacchilmath.22.8.0512.

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Student teams battle one another by skip counting by different numbers and switching their counts when the teacher shouts, “Switch!” This game promotes numerical fluency, numerical pattern recognition, and addition/multiplication operations. Postscript items are designed as rich grab-and-go resources that teachers can quickly incorporate into their classroom repertoire with little effort and maximum impact.

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33

Coclanis, P. A. "History by the Numbers: Why Counting Matters." OAH Magazine of History 7, no. 2 (1992): 5–8. http://dx.doi.org/10.1093/maghis/7.2.5.

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34

Sutherland, Ewan. "Counting customers, subscribers and mobile phone numbers." info 11, no. 2 (2009): 6–23. http://dx.doi.org/10.1108/14636690910941858.

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35

Nickerson, Raymond S. "Counting, Computing, and the Representation of Numbers." Human Factors: The Journal of the Human Factors and Ergonomics Society 30, no. 2 (1988): 181–99. http://dx.doi.org/10.1177/001872088803000206.

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36

Benjamin, Arthur T., and Curtis R. Heberle. "Counting on r -Fibonacci Numbers." Fibonacci Quarterly 52, no. 2 (2014): 121–28. http://dx.doi.org/10.1080/00150517.2014.12427902.

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37

Masser, David, and Jeffrey D. Vaaler. "Counting algebraic numbers with large height II." Transactions of the American Mathematical Society 359, no. 1 (2006): 427–45. http://dx.doi.org/10.1090/s0002-9947-06-04115-8.

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38

Seddon, J. A., H. E. Jenkins, L. Liu, et al. "Counting children with tuberculosis: why numbers matter." International Journal of Tuberculosis and Lung Disease 19, no. 12 (2015): 9–16. http://dx.doi.org/10.5588/ijtld.15.0471.

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39

Rotman, Brian. "Counting information: A note on physicalized numbers." Minds and Machines 6, no. 2 (1996): 229–38. http://dx.doi.org/10.1007/bf00391287.

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40

BURYKIN, ALEXIS A., and SARDANA I. SHARINA. "WORD BUILDING PATTERNS OF NUMERALS IN TUNGUS-MANCHU LANGUAGES." Theoretical and Applied Linguistics, no. 3 (2021): 52–68. http://dx.doi.org/10.22250/2410-7190_2021_7_3_52_68.

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The article discusses the reconstruction of the archetype of cardinal numbers, word formation of the categories of numbers in the Tungus-Manchu languages. Based on the available data on languages, 15 categories are analyzed: cardinal, ordinal, multiples, dividing, distributive, restrictive, collective, numerals for counting days, numerals for counting animals, numerals for counting households, numerals for counting fingers, numerals for counting pairs of objects, numerals for counting places and directions, numerals for counting various objects, numerals for counting the years of an animal. It

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41

Kline, Kate. "Early Childhood Corner: Kindergarten Is More Than Counting." Teaching Children Mathematics 5, no. 2 (1998): 84–87. http://dx.doi.org/10.5951/tcm.5.2.0084.

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Teachers of primary-grade children realize the importance of helping their students develop an understanding of number relationships. It is important to encourage the kind of thinking that allows children to readily decompose numbers into parts and know how to put parts together to make a whole. This thinking sets the foundation for working with larger numbers, using reasoning to approach computation, and developing sophisticated mental strategies. Parker (1998) describes the importance of building what she calls “fluency with small numbers.” She defines fluency as being able to take apart and

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42

Markovits, Stefanie. "But Who’s Counting? Plotting Age in Trollope." Genre 53, no. 2 (2020): 111–34. http://dx.doi.org/10.1215/00166928-8562656.

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Anthony Trollope is unusually concerned with numbers: consider both the famous obsession with productivity and the figures that organize his serial fictions, what Mary Hamer has called his “writing by numbers.” Yet while such numerals control his narrative flow, forming the remarkable torrents of his romans fleuve, this essay focuses on ones that appear as such within his novels: those used to designate his characters’ ages. Age has long been recognized as a central Trollopian concern, but exploring formally Trollope’s habitual use of age-related integers reveals Trollope’s practice of countin

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43

Bernik, Vasily I., Friedrich Götze, and Nikolai I. Kalosha. "Counting algebraic numbers in short intervals with rational points." Journal of the Belarusian State University. Mathematics and Informatics, no. 1 (April 12, 2019): 4–11. http://dx.doi.org/10.33581/2520-6508-2019-1-4-11.

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In 2012 it was proved that real algebraic numbers follow a nonuniform but regular distribution, where the respective definitions go back to H. Weyl (1916) and A. Baker and W. Schmidt (1970). The largest deviations from the uniform distribution occur in neighborhoods of rational numbers with small denominators. In this article the authors are first to specify a gene ral condition that guarantees the presence of a large quantity of real algebraic numbers in a small interval. Under this condition, the distribution of real algebraic numbers attains even stronger regularity properties, indicating

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44

Ryoti, Don E. "Computer Corner." Arithmetic Teacher 34, no. 9 (1987): 46–48. http://dx.doi.org/10.5951/at.34.9.0046.

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Students need to count objects and to group objects for an understanding of the number system. Students also need to learn the sequence of names for the counting numbers. The computer can be used to illustrate how the digits change. The following programs print the successive counting numbers from 1 through a number that the user enters.

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45

Ramachandran, Vembu, and Roopkumar Rajakumar. "An analytical formula for Bell numbers." Notes on Number Theory and Discrete Mathematics 30, no. 4 (2024): 797–802. http://dx.doi.org/10.7546/nntdm.2024.30.4.797-802.

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46

PANHOLZER, ALOIS, and HELMUT PRODINGER. "ASYMPTOTIC RESULTS FOR THE NUMBER OF PATHS IN A GRID." Bulletin of the Australian Mathematical Society 85, no. 3 (2011): 446–55. http://dx.doi.org/10.1017/s0004972711002759.

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AbstractIn two recent papers, Albrecht and White [‘Counting paths in a grid’, Austral. Math. Soc. Gaz.35 (2008), 43–48] and Hirschhorn [‘Comment on “Counting paths in a grid”’, Austral. Math. Soc. Gaz.36 (2009), 50–52] considered the problem of counting the total number Pm,n of certain restricted lattice paths in an m×n grid of cells, which appeared in the context of counting train paths through a rail network. Here we give a precise study of the asymptotic behaviour of these numbers for the square grid, extending the results of Hirschhorn, and furthermore provide an asymptotic equivalent of t

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47

Demeyere, Nele, Pia Rotshtein, and Glyn W. Humphreys. "The Neuroanatomy of Visual Enumeration: Differentiating Necessary Neural Correlates for Subitizing versus Counting in a Neuropsychological Voxel-based Morphometry Study." Journal of Cognitive Neuroscience 24, no. 4 (2012): 948–64. http://dx.doi.org/10.1162/jocn_a_00188.

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This study is the first to assess lesion–symptom relations for subitizing and counting impairments in a large sample of neuropsychological patients (41 patients) using an observer-independent voxel-based approach. We tested for differential effects of enumerating small versus large numbers of items while controlling for hemianopia and visual attention deficits. Overall impairments in the enumeration of any numbers (small or large) were associated with an extended network, including bilateral occipital and fronto-parietal regions. Within this network, severe impairments in accuracy when enumera

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48

MA, SHI-MEI. "COUNTING PERMUTATIONS BY NUMBERS OF EXCEDANCES, FIXED POINTS AND CYCLES." Bulletin of the Australian Mathematical Society 85, no. 3 (2011): 415–21. http://dx.doi.org/10.1017/s0004972711002760.

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AbstractIn this paper we present a combinatorial proof of an identity involving the two kinds of Stirling numbers and the numbers of permutations with prescribed numbers of excedances and cycles. Several recurrence relations related to the numbers of excedances, fixed points and cycles are also obtained.

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49

Gryszka, Karol. "Binomial formulas via divisors of numbers." Notes on Number Theory and Discrete Mathematics 27, no. 4 (2021): 122–28. http://dx.doi.org/10.7546/nntdm.2021.27.4.122-128.

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50

Fuadiah, Nyiayu Fahriza, Didi Suryadi, and Turmudi Turmudi. "Some Difficulties in Understanding Negative Numbers Faced by Students: A Qualitative Study Applied at Secondary Schools in Indonesia." International Education Studies 10, no. 1 (2016): 24. http://dx.doi.org/10.5539/ies.v10n1p24.

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This study revealed how students’ understanding of negative numbers and identified their difficulties related with the concept of integer and its counting operation as part of identifying epistemological obstacles about negative numbers. Even though teachers have explained counting operation procedure of integer, but there was concept misunderstanding among students. The concept difference between what was comprehended by respondents in their learning process and knowledge science has resulted in wrong perceptions about the negative numbers. In this article, the authors explained how these mis

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