Relevant bibliographies by topics / Mathematical notation

Academic literature on the topic 'Mathematical notation'

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Published: 4 June 2021
Last updated: 30 July 2024

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Journal articles on the topic "Mathematical notation"

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Sokolowski, Andrzej. "Developing Covariational Reasoning Among Students Using Contexts of Formulas." Physics Educator 02, no. 04 (December 2020): 2050016. http://dx.doi.org/10.1142/s266133952050016x.

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Multiple studies have been conducted to assess students’ ability to apply covariational reasoning to sketching graphs in physics. This study is supported by research on developing students’ skills in sketching functions in mathematics. It attempts to evaluate physics students’ ability to apply these skills to identify critical algebraic attributes of physics formulas for their potential to be sketched. Rather than seeking formulas’ physical interpretation, this study is posited to challenge students’ skills to merge their mathematical knowledge within physics structures. A group of thirty ([Formula: see text]) first-year college-level physics students were provided with two physically identical equations that described the object’s position. However, one equation was expressed in functional mathematical notation, whereas the other in a standard formula notation. The students were asked to classify the symbols in each formula as variables or parameters and determine these formulas’ potential to be graphed in respective coordinates. The analysis revealed that 93% of these students considered function notation as possessing sketchable potential against 13% who envisioned such potential in the standard formula notation. Further investigations demystified students’ confusion about the classification of the symbols used in the formula notation. These results opened up a gate for discussing the effects of algebraic notations in physics on activating students’ covariational skills gained in mathematics courses. Suggestions for improving physics instructions stemming from this study are discussed.
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Yang, Seong Hyun. "A View on the Diversity of the Word and Mathematical Notation Expression Used in High School Mathematics Textbooks." Korean School Mathematics Society 20, no. 3 (September 30, 2017): 211–37. http://dx.doi.org/10.30807/ksms.2017.20.3.001.

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Depending on the type of textbook, the word and mathematical notation expression used in high school mathematics textbooks varied and there were also some differences on the mathematical definition and the content description methods. Not only the composition of textbooks but also various expressing ways of textbooks have significant impacts on teaching and learning of teacher and student. The diversity of expression had pros and cons like both sides of a coin. There is a positive aspect that we can pursue pedagogical diversity. Simultaneously there is a negative aspect that the possibility of acting as a learning burden exists in the viewpoint of the student and the equality of evaluation may be undermined. In this study, Preferentially we focused on analyzing the actual situation rather than judging what is more appropriate about the diversity of words and notation expressions used in mathematics textbooks which is based on the current curriculum. For this purpose, we analyzed 56 kinds of mathematics textbooks based on the 2009 revised mathematics curriculum, and presented four aspects(terms expressing, notations expression, mathematical definition, content description method) with examples about differences of the various expressions used in textbooks including ‘terms and notations’.
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Williams, Travis D. "Mathematical Enargeia: The Rhetoric of Early Modern Mathematical Notation." Rhetorica 34, no. 2 (2016): 163–211. http://dx.doi.org/10.1525/rh.2016.34.2.163.

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This article proposes and explicates a rhetorical model for the function of notational writing in sixteenth- and seventeenth-century European mathematics. Drawing on enargeia's requirement that both author and reader contribute to the full realization of a text, mathematical enargeia enables the transformation of images of mathematical imagination resulting from an encounter with mathematical writing into further written acts of mathematical creation. Mathematical enargeia provides readers with an ability to understand a text as if they created it themselves. Within the period's dominant reading of classical geometry as a synthetic presentation that suppressed, hid, or obscured analytic mathematical reality, notational mathematics found favor as a rhetorically unmediated expression of mathematical truth. Consequently, mathematical enargeia creates an operational and presentational link between mathematics' past and its future.
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Williams, Travis D. "Mathematical Enargeia: The Rhetoric of Early Modern Mathematical Notation." Rhetorica 34, no. 2 (March 2016): 163–211. http://dx.doi.org/10.1353/rht.2016.0017.

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Huuskonen, Taneli. "Polish Notation." Formalized Mathematics 23, no. 3 (September 1, 2015): 161–76. http://dx.doi.org/10.1515/forma-2015-0014.

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Abstract This article is the first in a series formalizing some results in my joint work with Prof. Joanna Golinska-Pilarek ([12] and [13]) concerning a logic proposed by Prof. Andrzej Grzegorczyk ([14]). We present some mathematical folklore about representing formulas in “Polish notation”, that is, with operators of fixed arity prepended to their arguments. This notation, which was published by Jan Łukasiewicz in [15], eliminates the need for parentheses and is generally well suited for rigorous reasoning about syntactic properties of formulas.
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DE TOFFOLI, SILVIA. "‘CHASING’ THE DIAGRAM—THE USE OF VISUALIZATIONS IN ALGEBRAIC REASONING." Review of Symbolic Logic 10, no. 1 (October 28, 2016): 158–86. http://dx.doi.org/10.1017/s1755020316000277.

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AbstractThe aim of this article is to investigate the roles of commutative diagrams (CDs) in a specific mathematical domain, and to unveil the reasons underlying their effectiveness as a mathematical notation; this will be done through a case study. It will be shown that CDs do not depict spatial relations, but represent mathematical structures. CDs will be interpreted as a hybrid notation that goes beyond the traditional bipartition of mathematical representations into diagrammatic and linguistic. It will be argued that one of the reasons why CDs form a good notation is that they are highly mathematically tractable: experts can obtain valid results by ‘calculating’ with CDs. These calculations, take the form of ‘diagram chases’. In order to draw inferences, experts move algebraic elements around the diagrams. It will be argued that these diagrams are dynamic. It is thanks to their dynamicity that CDs can externalize the relevant reasoning and allow experts to draw conclusions directly by manipulating them. Lastly, it will be shown that CDs play essential roles in the context of proof as well as in other phases of the mathematical enterprise, such as discovery and conjecture formation.
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Grabiner, Judith. "“Notation, Notation, Notation” or Book Review : Enlightening Symbols: A Short History of Mathematical Notation and Its Hidden Powers by Joseph Mazur." Journal of Humanistic Mathematics 5, no. 2 (July 2015): 151–60. http://dx.doi.org/10.5642/jhummath.201502.14.

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Wege, Theresa Elise, Sophie Batchelor, Matthew Inglis, Honali Mistry, and Dirk Schlimm. "Iconicity in mathematical notation: Commutativity and symmetry." Journal of Numerical Cognition 6, no. 3 (December 3, 2020): 378–92. http://dx.doi.org/10.5964/jnc.v6i3.314.

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Mathematical notation includes a vast array of signs. Most mathematical signs appear to be symbolic, in the sense that their meaning is arbitrarily related to their visual appearance. We explored the hypothesis that mathematical signs with iconic aspects – those which visually resemble in some way the concepts they represent – offer a cognitive advantage over those which are purely symbolic. An early formulation of this hypothesis was made by Christine Ladd in 1883 who suggested that symmetrical signs should be used to convey commutative relations, because they visually resemble the mathematical concept they represent. Two controlled experiments provide the first empirical test of, and evidence for, Ladd’s hypothesis. In Experiment 1 we find that participants are more likely to attribute commutativity to operations denoted by symmetric signs. In Experiment 2 we further show that using symmetric signs as notation for commutative operations can increase mathematical performance.
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Bier, Agnieszka, and Zdzisław Sroczyński. "Rule based intelligent system verbalizing mathematical notation." Multimedia Tools and Applications 78, no. 19 (July 4, 2019): 28089–110. http://dx.doi.org/10.1007/s11042-019-07889-3.

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Perkins, Isabel, and Alfinio Flores. "Mathematical Notations and Procedures of Recent Immigrant Students." Mathematics Teaching in the Middle School 7, no. 6 (February 2002): 346–51. http://dx.doi.org/10.5951/mtms.7.6.0346.

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Mathematics is often referred to as a universal language. Compared with the differences in language and culture faced by students who are recent immigrants, the differences in mathematical notation and procedures seem to be minor. Nevertheless, immigrant students confront noticeable differences between the way that mathematical ideas are represented in their countries of origin and the manner that they are represented in the United States. If not addressed, the differences in notation and procedures can add to the difficulties that immigrants face during their first years in a new country.
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Dissertations / Theses on the topic "Mathematical notation"

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Coleman, Edwin. "The role of notation in mathematics." Title page, table of contents and summary only, 1988. http://web4.library.adelaide.edu.au/theses/09PH/09phc6921.pdf.

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Tolmie, Julie, and julie tolmie@techbc ca. "Visualisation, navigation and mathematical perception: a visual notation for rational numbers mod1." The Australian National University. School of Mathematical Sciences, 2000. http://thesis.anu.edu.au./public/adt-ANU20020313.101505.

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There are three main results in this dissertation. The first result is the construction of an abstract visual space for rational numbers mod1, based on the visual primitives, colour, and rational radial direction. Mathematics is performed in this visual notation by defining increasingly refined visual objects from these primitives. In particular, the existence of the Farey tree enumeration of rational numbers mod1 is identified in the texture of a two-dimensional animation. ¶ The second result is a new enumeration of the rational numbers mod1, obtained, and expressed, in abstract visual space, as the visual object coset waves of coset fans on the torus. Its geometry is shown to encode a countably infinite tree structure, whose branches are cosets, nZ+m, where n, m (and k) are integers. These cosets are in geometrical 1-1 correspondence with sequences kn+m, (of denominators) of rational numbers, and with visual subobjects of the torus called coset fans. ¶ The third result is an enumeration in time of the visual hierarchy of the discrete buds of the Mandelbrot boundary by coset waves of coset fans. It is constructed by embedding the circular Farey tree geometrically into the empty internal region of the Mandelbrot set. In particular, coset fans attached to points of the (internal) binary tree index countably infinite sequences of buds on the (external) Mandelbrot boundary.
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Tolmie, Julie. "Visualisation, navigation and mathematical perception : a visual notation for rational numbers mod 1." View thesis entry in Australian Digital Theses Program, 2000. http://thesis.anu.edu.au/public/adt-ANU20020313.101505/index.html.

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Godwin, William Henry. "Formalizing graphical notations." n.p, 1998. http://ethos.bl.uk/.

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Loftus, John A. "Powers of words in language families." Diss., Online access via UMI:, 2007.

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Meyer, Bronwin Colleen. "The equal sign: Teachers’ specialised content knowledge and Learners’ misconceptions." Thesis, Cape Peninsula University of Technology, 2016. http://hdl.handle.net/20.500.11838/2369.

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Thesis (MEd (Education))--Cape Peninsula University of Technology, 2016.
Numerical and algebraic equations require understanding of the equal sign as an equivalence relation. Teachers and learners, however, often have an operational, rather than a relational, understanding of the equal sign. This conception is viewed as a misconception. This study investigates the extent to which Grade 6 learners at a particular school have this and other misconceptions regarding equality, with the equal sign as focus. It also investigates this school’s Grade 1 to 6 teachers’ specialised content knowledge (SCK) regarding equality, again focusing on the equal sign. Ultimately the study wishes to establish whether there might be a possible relationship between the level of these teachers’ SCK of the equal sign and learners’ misconceptions of the equal sign. In particular, it tries to answer the question whether teachers’ SCK of the equal sign could possibly promote or prevent the forming of such misconceptions in learners, as well as whether teachers’ SCK of the equal sign could possibly help them identify learners’ misconceptions and help learners form the correct conceptions. This research project is framed within an interpretive paradigm. It focuses on one school taking the form of a theory-led case study in which a mixed method approach is used. Data collection methods include teacher questionnaires followed by two focus group interviews with teachers, based on data collected from questionnaires. In addition, data is collected through a series of lesson observations on number concepts and assessment. Grade 6 learners answered a set of questions structured in the form of a test to investigate their understanding of equality and the equal sign. Six learners were purposefully selected, based on their answers to the questions, and interviewed. Although this school is a high-performing academic school, results indicate that few learners have a flexible operational or basic relational view of the equal sign. The same group of learners that struggle with closure seems to struggle with the misconception of using all the numbers in an equation to solve a particular equation. The majority of Grade 6 learners cannot define the equal sign correctly. According to results, the nature of Grade 1- 6 teachers’ SCK of the equal sign shows that teachers lack skills to prevent, reduce or correct misconceptions about the equal sign.
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Dagiene, Valentina, and Inga Zilinskiene. "Localization of Learning Objects in Mathematics." Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79623.

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Mathematics learning seems to be a demanding and time-consuming task for many learners. Information and communication technology (ICT) is an attractive tool of learning for students at any level and it can provide an effective atmosphere for understanding mathematics. The question is how to combine mathematics teaching contents, approaches, curricula, and syllabus with new media. The key issue in European educational policy (and other countries as well) is exchange and sharing digital learning resources (learning objects) among countries. In order to accumulate the practice of various countries and use the best digital resources created by different countries, it is necessary to localize learning objects (LO). The paper deals with some problems connected with localization of LO, developed for mathematics education, and presents some solution. Software localization is mainly referred to as language translation (e.g., translation of user interface texts and help documents). However, there are many other important elements depending on the country and people who will use the localized software. In this paper, the main attention is paid to localization of learning objects used for teaching and learning mathematics.
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Jones, Charles H. "TELEMETRY AND JUGGLING." International Foundation for Telemetering, 2000. http://hdl.handle.net/10150/608297.

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International Telemetering Conference Proceedings / October 23-26, 2000 / Town & Country Hotel and Conference Center, San Diego, California
One of the beauties of mathematics is its ability to demonstrate the relationship between apparently unrelated subjects. And this is not only an aesthetic attribute. The insight obtained by seeing relations where they are not obvious often leads to elegant solutions to difficult problems. This paper will demonstrate a mathematical relation between telemetry and juggling. Any given pulse code modulation (PCM) format can be mapped onto a juggling pattern. The Inter-Range Instrumentation Group (IRIG) 106 Class I PCM formats are a subset of all juggling patterns while the Class II PCM formats are equivalent to the set of all juggling patterns (within some mathematically precise definitions). There are actually quite a few mathematical results regarding juggling patterns. This paper will also discuss how these topics relate to tessellations, bin packing, PCM format design, and dynamic spectrum allocation. One of the shortcomings of human nature is the tendency to get caught up in a particular topic or viewpoint. This is true of the telemetry community as well. It is hoped that this paper will increase the awareness that there are a variety of areas of theory outside of telemetry that may be applicable to the field.
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Araujo, Renarte Dantas de. "A linguagem matemática para uso em sites de busca ou em ferramentas para portadores de necessidades especiais." Universidade Federal da Paraíba, 2015. http://tede.biblioteca.ufpb.br:8080/handle/tede/7668.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
This paper deals with some peculiarities involving mathematical writing that generate many communication problems through different perspectives. In a time where the Internet is increasingly used and where it is common to see people on the streets carrying tablet computers, smartphones and even laptops, it is unacceptable that there is no simple and common knowledge way to insert a mathematic equation on a web search. Initially we address the interaction between people with special needs, especially those who make use of applications or devices for easy communication, then treat the virtual communication applied to the form of distance education, whether instantaneous or not instantaneous. Following deal about differences between Mathematics written in Portuguese and other languages as well as inconsistencies in mathematical notation observed in Brazil. Then treat the common text input forms used in Information and Communication Technologies to finish with a rough draft agreement that meets the needs exposed at work.
Este trabalho aborda algumas peculiaridades envolvendo a escrita matemática que geram problemas de comunicação diversos através de diferentes perspectivas. Em uma época onde a Internet é cada vez mais usada e na qual é comum ver pessoas nas ruas portando tablets, smartphones e mesmo computadores portáteis, é inaceitável que não exista uma forma simples e de conhecimento comum para se inserir uma equação matemática em um site de busca.Inicialmente abordamos a interação entre portadores de necessidades especiais, principalmente os que façam uso de aplicativos ou dispositivos para facilitar sua comunicação, em seguida tratamos da comunicação virtual aplicada à modalidade de educação à distância, quer seja instantânea ou não instantânea. Na sequência tratamos sobre divergências entre a escrita matemática na língua portuguesa e outras línguas bem como inconsistências na notação matemática observadas no Brasil. Tratamos então das formas de inserção de texto comuns usadas nas Tecnologias da Informação e Comunicação para finalizar com uma proposta rudimentar de convenção que atenda às necessidades expostas durante o trabalho.
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Borg, Philip. "Using the computer as a tool for constructivist teaching : a case study of Grade 7 students developing representations and interpretations of mathematical notation when using the software Grid Algebra." Thesis, Loughborough University, 2017. https://dspace.lboro.ac.uk/2134/32717.

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The aim of this research was to investigate how I engaged in constructivist teaching (CT) when helping a group of low-performing Grade 7 students to develop new meanings of notation as they started to learn formal algebra. Data was collected over a period of one scholastic year, in which I explored the teacher-student dynamics during my mathematics lessons, where students learnt new representations and interpretations of notation with the help of the computer software Grid Algebra. Analysing video recordings of my lessons, I observed myself continuously changing my teaching purpose as I negotiated between the mathematics I intended to teach and the mathematics being constructed by my students. These shifts of focus and purpose were used to develop a conceptual framework called Mathematics-Negotiation-Learner (M-N-L). Besides serving as a CT model, the M-N-L framework was found useful to determine the extent to which I managed to engage in CT during the lessons and also to identify moments where I lost my sensitivity to students constructions of knowledge. The effectiveness of my CT was investigated by focusing on students learning, for which reason I developed the analytical framework called CAPS (Concept-Action-Picture-Symbol). The CAPS framework helped me to analyse how students developed notions about properties of operational notation, the structure and order of operations in numerical and algebraic expressions, and the relational property of the equals sign. Grid Algebra was found to be a useful tool in helping students to enrich their repertoire of representations and to develop new interpretations of notation through what I defined as informal- and formal-algebraic activities. All students managed to transfer these representations and interpretations of notation to pen-and-paper problems, where they successfully worked out traditionally set substitution-and-evaluation tasks.
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Books on the topic "Mathematical notation"

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Cajori, Florian. A history of mathematical notations. New York: Dover Publications, 1993.

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Chrisomalis, Stephen. Numerical notation: A comparative history. Cambridge: Cambridge University Press, 2010.

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Chrisomalis, Stephen. Numerical notation: A comparative history. New York: Cambridge University Press, 2010.

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Schulte, Mary Leontius. Writing the history of mathematical notation: 1483-1700. Boston: Docent Press, 2015.

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Allen, Nancy Kelly. All about math symbols. Vero Beach, Florida: Rourke Educational Media, 2014.

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Brizuela, Bárbara M. Mathematical development in young children: Exploring notations. New York: Teachers College Press, 2004.

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Iaccarino, Bruno. L' antibabele: Il processo scientifico nacque quando le ricerche matematiche incominciarono ad utilizzare un unico linguaggio. Napoli: Edizioni scientifiche italiane, 1999.

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Pask, Colin, and Colin Pask. Math for the frightened: Facing scary symbols and everything else that freaks you out about mathematics. Amherst, N.Y: Prometheus Books, 2011.

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Krämer, Sybille, and Sybille Krämer. Berechenbare Vernuft: Kalkül und Rationalismus im 17. Jahrhundert. Berlin: W. de Gruyter, 1991.

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Peppas, Lynn. Math words and symbols. New York: Crabtree Pub., 2010.

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Book chapters on the topic "Mathematical notation"

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Moore, Emily, and Harriet Pollatsek. "Notation." In The Student Mathematical Library, 273–76. Providence, Rhode Island: American Mathematical Society, 2013. http://dx.doi.org/10.1090/stml/067/15.

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Zettl, Anton. "Notation." In Mathematical Surveys and Monographs, 293–94. Providence, Rhode Island: American Mathematical Society, 2010. http://dx.doi.org/10.1090/surv/121/15.

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Blostein, Dorothea, and Richard Zanibbi. "Processing Mathematical Notation." In Handbook of Document Image Processing and Recognition, 679–702. London: Springer London, 2014. http://dx.doi.org/10.1007/978-0-85729-859-1_21.

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Anglin, W. S. "Modern Mathematical Notation." In Mathematics: A Concise History and Philosophy, 137–39. New York, NY: Springer New York, 1994. http://dx.doi.org/10.1007/978-1-4612-0875-4_23.

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Yafaev, D. "Basic notation." In Mathematical Surveys and Monographs, 1–4. Providence, Rhode Island: American Mathematical Society, 2010. http://dx.doi.org/10.1090/surv/158/01.

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Lochak, Pierre, and Claude Meunier. "Introduction and Notation." In Applied Mathematical Sciences, 1–9. New York, NY: Springer New York, 1988. http://dx.doi.org/10.1007/978-1-4612-1044-3_1.

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Etesami, Seyed Rasoul. "Notation and Mathematical Preliminaries." In Potential-Based Analysis of Social, Communication, and Distributed Networks, 17–24. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-54289-8_2.

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Tartar, Luc. "Abbreviations and Mathematical Notation." In Lecture Notes of the Unione Matematica Italiana, 451–58. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-05195-1_36.

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Godehardt, Erhard. "Mathematical Symbols and Notation." In Graphs as Structural Models, 1–4. Wiesbaden: Vieweg+Teubner Verlag, 1988. http://dx.doi.org/10.1007/978-3-322-96310-9_1.

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Dong, Qiao-Li, Yeol Je Cho, Songnian He, Panos M. Pardalos, and Themistocles M. Rassias. "Notation and Mathematical Foundations." In The Krasnosel'skiĭ-Mann Iterative Method, 21–28. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-91654-1_2.

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Conference papers on the topic "Mathematical notation"

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Bier, Agnieszka, and Zdzisław Sroczyński. "Towards semantic search for mathematical notation." In 2018 Federated Conference on Computer Science and Information Systems. IEEE, 2018. http://dx.doi.org/10.15439/2018f155.

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Zhao, Yanjie, Tetsuya Sakurai, Hiroshi Sugiura, and Tatsuo Torii. "A methodology of parsing mathematical notation for mathematical computation." In the 1996 international symposium. New York, New York, USA: ACM Press, 1996. http://dx.doi.org/10.1145/236869.237087.

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Jo, Hwiyeol, Dongyeop Kang, Andrew Head, and Marti A. Hearst. "Modeling Mathematical Notation Semantics in Academic Papers." In Findings of the Association for Computational Linguistics: EMNLP 2021. Stroudsburg, PA, USA: Association for Computational Linguistics, 2021. http://dx.doi.org/10.18653/v1/2021.findings-emnlp.266.

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Davila, Kenny. "Appearance-Based Retrieval of Mathematical Notation in Documents and Lecture Videos." In SIGIR '16: The 39th International ACM SIGIR conference on research and development in Information Retrieval. New York, NY, USA: ACM, 2016. http://dx.doi.org/10.1145/2911451.2911477.

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Kumar, Bhawnesh, Umesh Kumar Tiwari, Santosh Kumar, Harendra Singh Negi, and Kiran Kumain. "Two dimensional successive transformations in computer graphics: Mathematical and matrix notation." In INTERNATIONAL SCIENTIFIC AND PRACTICAL CONFERENCE “TECHNOLOGY IN AGRICULTURE, ENERGY AND ECOLOGY” (TAEE2022). AIP Publishing, 2022. http://dx.doi.org/10.1063/5.0103814.

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Vovk, Anatolii, and Denys Girnyk. "Web-based notation of mathematical text preserving semantics for scientific and educational communication." In 2013 IEEE 7th International Conference on Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications (IDAACS). IEEE, 2013. http://dx.doi.org/10.1109/idaacs.2013.6663029.

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Sargent, Murray. "Efficient entry of mathematical equations." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1986. http://dx.doi.org/10.1364/oam.1986.fm4.

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Mathematical text includes patterns such as fractions and bracketed expressions that require careful placement of arguments. The typist could estimate the size of these arguments as on an IBM Selectric typewriter, moving the cursor to desired places on the screen and typing characters. Although simple in principle, this method requires many keystrokes to type formulas and makes it hard even to achieve positioning of the characters accurate to the low resolution computer screen. Over the years I have developed a linear format for equations that proves to be both much more typist efficient as well as providing the highest accuracy available on the target printer, e.g., 1/300" on a laser printer. In technical documents, fractions are often written in a single line with the numerator written first followed by a slash and then the denominator. My linear equation notation generalizes this concept to handle arbitrary mathematical formulas. Text is entered and edited in the linear format. Both on graphics preview and on printing, a text filter recognizes legal mathematical expressions, automatically expanding fractions, brackets, braces, parentheses, square roots, etc., to built-up form precisely fitting their arguments.
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Genfang, Chen, Zhang Wenjun, and Wang Qiuqiu. "Pick-up the Musical Information from Digital Musical Score Based on Mathematical Morphology and Music Notation." In 2009 First International Workshop on Education Technology and Computer Science. IEEE, 2009. http://dx.doi.org/10.1109/etcs.2009.261.

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Milinković, Nenad, and Sanja Maričić. "Nepoznata i promenljiva – problem učenja rane algebre." In Nauka i obrazovanje – izazovi i perspektive. University of Kragujevac, Faculty of Edaucatin in Uzice, 2022. http://dx.doi.org/10.46793/noip.245m.

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Abstract:
The paper draws attention to the difficulties associated with the introduction of symbols and symbolic notation in junior grades of primary school. In this context, the paper draws special attention to the proper understanding of the concepts of unknown and variable at this age and also point to a wide range of problems related to understanding letters as symbols used to denote an unknown or variable in early algebra. The shaping of a real-world context problem at different levels of abstraction is exemplified with the formation of the concepts of unknown andvariable. In this process, real-world situations represent a source of developing mathematical concepts, tools and procedures in which students can apply their mathematical knowledge at a later stage because it gradually becomes more general and formalized and therefore less contextrelated.
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Hendry, Holly, Mark Chattington, Ana Cavalcanti, and Cade Mccall. "Verification of a search-and-rescue drone with humans in the loop." In 14th International Conference on Applied Human Factors and Ergonomics (AHFE 2023). AHFE International, 2023. http://dx.doi.org/10.54941/ahfe1003753.

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In this presentation we use an example of a search-and-rescue drone, used by mountain rescue teams, to illustrate our approach to develop mathematical models and use them to verify behaviour that depends on human interactions with the drone. The design and development of human-in-the-loop robotic systems, such as the search-and-rescue drone, requires knowledge of the human, software, and hardware components of the system. The verification of these systems require knowledge of those same three components. Through this example we will demonstrate how a Hierarchical Task Analysis can be used to develop conformant sequence diagrams that can capture use cases of interest for verification. We will discuss the notation for our sequence diagrams, which is a variation of UML sequence diagrams tailored to capture time properties and with a view of the system that includes the software, the hardware, and human stakeholders.Our sequence diagram notation integrates within an existing verification framework, namely RoboStar, which provides domain-specific notations to model and verify both control software and robotic platforms. In the presentation, we show the kind of property and verification that we can carry out using our sequence diagrams and RoboStar technology. The presentation will also cover leading tools for modelling and verification of human-in-the-loop robotic systems, namely Circus, Ivy, PVSio-web and how they handle human behaviour within the system design. We will compare our approach with that supported by these tools.Verification is a technique used to prove that the system design and development meets the requirements specified; there are many forms of verification including formal verification, simulation, and testing. Formal verification is a tried and tested method to improve confidence in the correctness of a system, its ability to satisfy design requirements. Due to its application during design time, this confidence can be gained prior to the investing of time and resources into system development. Formal verification outputs mathematical proof artefacts that can be used in safety-case development. This verification technique requires formal models of system behaviour and formal models of the properties to be proved. To perform formal verification on a human-in-the-loop system, the formal model of the system behaviour needs to include a model of the expected human interaction. Whilst the data required for the generation of such a model can be provided by evidence from the fields of Human-Computer Interaction, Psychology, Human-Robot Interaction or Human Factors, this data needs to be gathered in a formal model for verification. On the other hand, requiring professionals with the knowledge of human behaviour to also have the expertise on formal verification is unrealistic. Our sequence diagrams are accessible and readable as a way to capture and communicate expected human behaviour. Moreover, it is possible to generate mathematical models for verification automatically from the sequence diagrams.
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Reports on the topic "Mathematical notation"

1

Chun, Kee S. Mathematical Methods of Three-Dimensional Eye Rotations Based Upon Spacecraft Dynamics Notation. Fort Belvoir, VA: Defense Technical Information Center, February 1999. http://dx.doi.org/10.21236/ada361385.

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