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Thematische Bibliographien / Programming (mathematics)

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Auswahl der wissenschaftlichen Literatur zum Thema „Programming (mathematics)“

Autor: Grafiati

Veröffentlicht am 4. Juni 2021

Zuletzt aktualisiert am 29. Juli 2024

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Zeitschriftenartikel zum Thema "Programming (mathematics)"

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Turskienė, Sigita. "Kompiuterinių matematikos sistemų programavimo kalbų lyginamoji analizė." Lietuvos matematikos rinkinys 44 (December 17, 2004): 377–82. http://dx.doi.org/10.15388/lmr.2004.31946.

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The paper analyses possibilities of programming languages of computer mathematics systems. The summary table of operations of 5 programming languages is presented. The advantages and disadvantages between programming languages of computer mathematics systems (MAPLE, MATHEMATICA, MATLAB) and professional programming languages (C/C++, PASCAL) are presented, too. That makes easier the application of computer mathematics systems in practice.

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Tasic, Milan, Predrag Stanimirovic, Ivan Stanimirovic, Marko Petkovic, and Nebojsa Stojkovic. "Some useful MATHEMATICA teaching examples." Facta universitatis - series: Electronics and Energetics 18, no. 2 (2005): 329–44. http://dx.doi.org/10.2298/fuee0502329t.

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We show how a computer algebra system in MATHEMATICA can be used in several elementary courses in mathematics for students. We have also developed an application in programming language DELPHI for testing students in MATHEMATICA.

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Stigberg, Henrik, and Susanne Stigberg. "Teaching programming and mathematics in practice: A case study from a Swedish primary school." Policy Futures in Education 18, no. 4 (December 17, 2019): 483–96. http://dx.doi.org/10.1177/1478210319894785.

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Programming and computational thinking have emerged as compulsory skills in elementary school education. In 2018, Sweden has integrated programming in mathematics education with the rationale that it fosters problem solving and logical thinking skills and motivates students to learn mathematics. We investigated how teachers introduce programming in mathematics education in a Swedish primary school using an explorative case study. We followed four mathematics teachers during the first semester in which programming was mandatory. They taught second-, sixth- and ninth-grade students. Our contributions are threefold: we provide an account of how programming is taught in mathematics education; we discuss how teachers reflect on the challenge of teaching programming in mathematics; and we report on students’ understanding of programming and their view on the relationship between programming and mathematics.

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Kwon, Misun. "Analysis of Mathematical Elements for Programming Education Presented in Finnish 1st and 2nd Grade Elementary Mathematics Textbooks." Korean Society of Educational Studies in Mathematics - School Mathematics 25, no. 3 (September 30, 2023): 385–406. http://dx.doi.org/10.57090/sm.2023.09.25.3.385.

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Since 2016, Finland has been implementing programming education in elementary school mathematics. This study analyzed Finnish first and second grade elementary mathematics textbooks and tutorials that reflected programming education. Previous studies on programming were analyzed to extract mathematical elements for programming instruction, and based on the extracted sequence, rules, selection, variables, possibilities, logic elements, functions, and algorithm, the contents of elementary mathematics textbooks in Finland were analyzed. As a result of the analysis, in Finnish mathematics textbooks, activities suitable for programming learning were evenly presented by utilizing all content elements as a whole, and a separate lesson for programming was also organized. In addition, the basic content of programming suitable for the student level was presented mathematically, and the level was changed and presented as the grade level went up. Looking at each element, activities for variables and logic elements accounted for a large part, and students were provided with opportunities to learn various mathematical elements related to programming during the first and second grades of elementary school. Based on these results, this study is expected to provide significant resources for applying programming to mathematics education in Korea.

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Swanier, Cheryl, Cheryl Seals, and Elodie Billionniere. "Visual Programming: A Programming Tool For Increasing Mathematics Achivement." i-manager's Journal of Educational Technology 6, no. 2 (September 15, 2009): 1–5. http://dx.doi.org/10.26634/jet.6.2.784.

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Daher, Wajeeh, Nimer Baya'a, and Otman Jaber. "Mathematics Preservice Teachers’ Preparation in Designing Mathematics-Based Programming Activities Rich in Metacognitive Skills." International Journal of Emerging Technologies in Learning (iJET) 18, no. 06 (March 21, 2023): 71–82. http://dx.doi.org/10.3991/ijet.v18i06.36965.

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Programming problems enrich the environment of mathematics learning, adding the flavor of technology to these problems. This is especially true when this programming is Scratch based, where Scratch is being used to make students’ learning of mathematics more meaningful. This role of programming in the mathematics classroom points at the importance of preparing mathematics teachers for designing mathematics-based programming problems activities. The present research describes one attempt to prepare mathematics preservice teachers in designing mathematics-based programming problems activities that could be used in the classroom to teach both programming and mathematics concepts. Twenty-three preservice teachers participated in the research, where they worked in eight groups of 2-3 members in each group. Data collected through observations based on video recordings of the sessions in which the preservice teachers discussed with the pedagogical supervisors the designed mathematics activities. The preparation model comprises of five stages related to the educational environment and to the design notions. The results show special importance for the concepts of struggle and devolution in designing this kind of activities, in addition to the concept of equilibrium between the creative and imitative thinking. The results also show the useful application of metacognitive skills when designing the activities, especially when designing the directions given to the students for solving each of the programming activities.

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Freeman, T. L., A. L. Peressini, F. E. Sullivan, and J. J. Uhl. "The Mathematics of Nonlinear Programming." Mathematical Gazette 73, no. 464 (June 1989): 170. http://dx.doi.org/10.2307/3619709.

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Bar-On, Ehud. "A programming approach to mathematics." Computers & Education 10, no. 4 (January 1986): 393–401. http://dx.doi.org/10.1016/0360-1315(86)90015-1.

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Zotos, Kostas. "Object-oriented programming in Mathematics." Applied Mathematics and Computation 188, no. 2 (May 2007): 1562–66. http://dx.doi.org/10.1016/j.amc.2006.11.025.

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Lingefjärd, Thomas. "Empowering mathematics education through programming." Journal of Mathematics and Science Teacher 4, no. 1 (January 1, 2024): em053. http://dx.doi.org/10.29333/mathsciteacher/13847.

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One of my last assignments at the university of Gothenburg was to teach a sequence of three seminars in programming for prospective teachers (<i>n</i>=37). The three seminars are given in the introduction of this manuscript. Since this was a course for prospective upper secondary teacher of mathematics, it was decided that it should be a course in programming for learning mathematics. This manuscript is a research article but also a manuscript about programming in GeoGebra, Python, and Wolfram Alpha. The examples I shared with my students led me to write a book about programming. See the reference list.

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Dissertationen zum Thema "Programming (mathematics)"

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Rolandsson, Jakob. "Programming as Mathematics – A Curriculum Perspective." Thesis, Uppsala universitet, Matematiska institutionen, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-451806.

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Yung, Simon Yun Pui. "Definitive programming : a paradigm for exploratory programming." Thesis, University of Warwick, 1992. http://wrap.warwick.ac.uk/78859/.

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Exploratory software development is a method that applies to the development of programs whose requirement is initially unclear. In such a context, it is only through prototyping and experimenting on the prototypes that the requirement can be fully developed. A good exploratory software development method must have a short development cycle. This thesis describes our attempt to fulfil this demand. We address this issue in the programming language level. A novel programming paradigm - definitive (definition-based) programming - is developed. In definitive programming, a state is represented by a set of definitions (a definitive script) and a state transition is represented by a redefinition. By means of a definition, a variable is defined either by an explicit value or by a formula in terms of other variables. Unless this variable is redefined, the relationship between the variables within the definition persists. To apply this state representation principle, we have developed some definitive notations in which the underlying algebras used in formulating definitions are domain specific. We have also developed an agent-oriented specification language by which we can model state transitions over definitive scripts. The modelling principles of definitive programming rest on a solid foundation in observation and experiment that is essential for exploratory software development. This thesis describes how we may combine definitive notations and the agent oriented programming concept to produce software tools that are useful in exploratory software development. In this way, definitive programming can be considered as a paradigm for exploratory programming.

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Sharifi, Mokhtarian Faranak. "Mathematical programming with LFS functions." Thesis, McGill University, 1992. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=56762.

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Differentiable functions with a locally flat surface (LFS) have been recently introduced and studied in convex optimization. Here we extend this motion in two directions: to non-smooth convex and smooth generalized convex functions. An important feature of these functions is that the Karush-Kuhn-Tucker condition is both necessary and sufficient for optimality. Then we use the properties of linear LFS functions and basic point-to-set topology to study the "inverse" programming problem. In this problem, a feasible, but nonoptimal, point is made optimal by stable perturbations of the parameters. The results are applied to a case study in optimal production planning.

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Fuentes, Martinez Ana. "Teachers’ tactics when programming and mathematics converge." Licentiate thesis, Högskolan Väst, Avd för medier och design, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:hv:diva-16379.

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Teachers’ everyday practices are embedded in school contexts in which their teaching autonomy is constrained by rules, moral obligations, physical settings,and official directives. When a curricular revision mandated that programming was to be a part of mathematics in upper secondary education, teachers’ conditions changed. How teachers adapted to the new curriculum and how they navigated the tensions and contradictions that they encountered is in this thesis analyzed in terms of teachers’ tactics and policy strategies. The overall goal of the investigation is to contribute to a critical understanding of how mathematics teachers integrate programming in their professional practice and how this integration aligns and diverges from the intentions behind the reform. The empirical material is drawn from nine individual interviews with mathematics teachers that were already proficient in programming. The teachers’ unit plans and other lesson materials featuring programming activities served as a trigger point to delve into further reflections upon their own professional practices. To complete the scene, the policy documents were also examined. These included the mathematics curriculum, as well as related official documents and a collection of institutionally sanctioned programming exercises and demonstrations. Two tactical approaches were made apparent when mathematics teachers began to integrate computer programming in their subject: Dual teaching and Interspersed programming. The teacher’s use of dual teaching practices or interspersed programming are tactics shaped by and in response to the conditions of the new curriculum and their own preferences and views on student learning. These two tactics disclose different ontological commitments in relation to the strategies dictated by the curriculum and reflect a cardinal distinction between planning mathematics activities with elements of programming and planning programming activities with elements of mathematics. Of relevance for teachers and curriculum designers is the understanding of (a) how the notion of programming and mathematics as separate subjects oversimplifies teachers’ actual integration practices, and (b) how the curricular choices made by policy can shape the teaching tactics adopted by educators.

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Davidescu, Diana Maria. "Convexifiable smooth programming and applications." Thesis, McGill University, 2004. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=82216.

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This thesis is an introduction to the study of convexification problems involving smooth functions in the area of continuous mathematical programming. The results are applied to a real life problem in oil production. An improved model is formulated for the company which yields environmentally friendlier optimal solutions at the same profit level.

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Reeves, Laurence H. "Mathematical Programming Applications in Agroforestry Planning." DigitalCommons@USU, 1991. https://digitalcommons.usu.edu/etd/6495.

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Agroforestry as a sustainable production system has been recognized as a land use system with the potential to slow encroachment of agriculture onto forested lands in developing countries. However, the acceptance of nontraditional agroforestry systems has been hampered in some areas due to the risk-averse nature of rural agriculturalists. By explicitly recognizing risk in agroforestry planning, a wider acceptance of agroforestry is possible. This thesis consists of a collection of three papers that explore the potential of modern stock portfolio theory to reduce financial risk in agroforestry planning. The first paper presents a theoretical framework that incorporates modern stock portfolio theory through mathematical programming. This framework allows for the explicit recognition of financial risk by using a knowledge of past net revenue trends and fluctuations for various cropping systems, with the assumption that past trend behavior is indicative of future behavior. The paper demonstrates how financial risk can be reduced by selecting cropping systems with stable and/or negatively correlated net revenues, thereby reducing the variance of future net revenues. Agroforestry systems generally entail growing simultaneously some combination of plant and/or animal species. As a result, interactions between crops usually cause crop yields within systems to deviate from what would be observed under monocultural conditions, thus requiring some means of incorporating these interactions into mathematical models. The second paper presents two approaches to modeling such interactions, depending on the nature of the interaction. The continuous system approach is appropriate under conditions where yield interactions are linear between crops and allows for a continuous range of crop mixtures. The discrete system approach should be used where nonlinear interactions occur. Under this second approach, decision variables are defined as fixed crop mixtures with known yields. In the third paper, the techniques presented above were applied to a case study site in Costa Rica. Using MOTAD programming and a discrete system approach, a set of minimum-risk farm plans were derived for a hypothetical farm. For the region studied, results indicate that reductions in risk require substantial reductions in expected net revenue.

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Esche, Alexander. "Mathematical Programming and Magic| The Gathering(RTM)." Thesis, Northern Illinois University, 2018. http://pqdtopen.proquest.com/#viewpdf?dispub=10689404.

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<p> In this paper mathematical programming techniques were used to determine the optimal strategy for playing Magic: The Gathering<sup>®</sup>. Games with the cards Lightning Bolt, Mountain, and Vexing Devil were evaluated using the minimax algorithm to determine the winner when all information about the cards is assumed known to both players. Computation time was shortened through the use of an evaluation function, a random forest algorithm that had been trained on 1000 completed games. A winning percentage was established for each pair of decks where the number of creatures was less than eight. Using linear programming, the optimal mixed strategy was then calculated. By repeating the simulations, a standard deviation for the winning percentages was estimated. Techniques from robust optimization were then used to determine the optimal strategy under different possible variations. Last, an imperfect information player was constructed that made choices based on guessing the order of the cards in its deck and the composition of the opponent's deck, playing through the perfect information games of these guesses, and making the choice that won in most of these simulations. With decks of eight or fewer creatures, this imperfect information player played below or near a player who used an aggressive heuristic. When the number of possible creatures was increased to 16, the imperfect information player's performance was better than the aggressive heuristic.</p><p>

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Cregger, Michael L. "The general mixed-integer linear programming problem an empirical analysis /." Instructions for remote access. Click here to access this electronic resource. Access available to Kutztown University faculty, staff, and students only, 1993. http://www.kutztown.edu/library/services/remote_access.asp.

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Trujillo-Cortez, Refugio. "LFS functions in stable bilevel programming." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp01/MQ37171.pdf.

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Trujillo-Cortez, Refugio. "Stable convex parametric programming and applications." Thesis, McGill University, 2000. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=37856.

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This thesis is a study of stable perturbations in convex programming models. Stability of a general model is introduced as lower semicontinuity of the feasible set mapping. This stability is shown to be equivalent to the Robinson notion of stability and regularity. In the convex case, it is also equivalent to the full-rank Slater condition. Then, the relationships between various point-to-set mappings are studied for convex models and new implications between these mappings are established. Also, local and global optimality of parameters is studied. A new result here is a characterization of locally optimal parameters that does not require stable perturbations. This result is valid, in particular, for convex models with LFS constraints. The value of the model can be improved by one of several new formulations of the marginal value formula.<br>The results on stability are applied for bilevel convex models and an algorithm for solving these models, based on a marginal value formula, is suggested and then applied to a real-life problem in the petroleum industry.

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Bücher zum Thema "Programming (mathematics)"

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Liu, Xinyu. Mathematics in Programming. Singapore: Springer Nature Singapore, 2024. http://dx.doi.org/10.1007/978-981-97-2432-1.

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Dempe, Stephan. Foundations of bilevel programming. New York: Springer, 2011.

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Vajda, S. Mathematical programming. Mineola, N.Y: Dover Publications, 2009.

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Karmanov, V. G. Mathematical programming. Moscow: Mir Publishers, 1989.

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Williams, H. P. Model building in mathematical programming. 5th ed. Chichester, West Sussex: Wiley, 2013.

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D, Jones. Practical goal programming. New York: Springer, 2010.

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Craven, B. D. Fractional programming. Berlin: Heldermann, 1988.

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Reemtsen, Rembert. Semi-Infinite Programming. Boston, MA: Springer US, 1998.

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Stancu-Minasian, I. M. Fractional programming: Theory, methods, and applications. Dordrecht: Kluwer Academic Publishers, 1997.

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Stancu-Minasian, I. M. Fractional Programming: Theory, Methods and Applications. Dordrecht: Springer Netherlands, 1997.

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Buchteile zum Thema "Programming (mathematics)"

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Ullenboom, Christian. "Mathematics." In Java Programming Exercises, 30–41. Boca Raton: Chapman and Hall/CRC, 2024. http://dx.doi.org/10.1201/9781003495550-3.

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Ashford, Robert. "Linear Programming." In Business Mathematics, 246–69. London: Macmillan Education UK, 1988. http://dx.doi.org/10.1007/978-1-349-19038-6_12.

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Hoare, C. A. R. "Mathematics of Programming." In Program Verification, 135–54. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-011-1793-7_7.

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Mosca, Ettore, Ivan Merelli, and Luciano Milanesi. "Mathematics, Nonlinear Programming." In Encyclopedia of Systems Biology, 1188. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4419-9863-7_1025.

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Barbu, Viorel, and Teodor Precupanu. "Convex Programming." In Springer Monographs in Mathematics, 153–232. Dordrecht: Springer Netherlands, 2012. http://dx.doi.org/10.1007/978-94-007-2247-7_3.

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Nožička, František. "Linear Programming." In Survey of Applicable Mathematics, 1538–79. Dordrecht: Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-015-8308-4_37.

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Pedregal, Pablo. "Linear Programming." In Texts in Applied Mathematics, 23–66. New York, NY: Springer New York, 2004. http://dx.doi.org/10.1007/0-387-21680-4_2.

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Pedregal, Pablo. "Nonlinear Programming." In Texts in Applied Mathematics, 67–110. New York, NY: Springer New York, 2004. http://dx.doi.org/10.1007/0-387-21680-4_3.

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Enfield, Jacob. "Programming Fundamentals." In Mathematics of Game Development, 19–58. Boca Raton: CRC Press, 2024. http://dx.doi.org/10.1201/9781032701431-3.

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Junghenn, Hugo D. "Linear Programming." In Discrete Mathematics with Coding, 223–46. Boca Raton: Chapman and Hall/CRC, 2023. http://dx.doi.org/10.1201/9781003351689-12.

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Konferenzberichte zum Thema "Programming (mathematics)"

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Pacheco, Ana, Anabela Gomes, Joana Henriques, Ana Maria de Almeida, and António José Mendes. "Mathematics and programming." In the 9th International Conference. New York, New York, USA: ACM Press, 2008. http://dx.doi.org/10.1145/1500879.1500963.

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Förster, Klaus-Tycho. "Programming in Scratch and Mathematics." In SIGITE/RIIT '15: The 16th Annual Conference on Information Technology Education and the 4th Annual Conference on Research in Information Technology. New York, NY, USA: ACM, 2015. http://dx.doi.org/10.1145/2808006.2809636.

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Laitochová, Jitka, Martina Uhlířová, and Nikol Rusnoková. "PROSPECTIVE MATHEMATICS TEACHERS AND PROGRAMMING." In 13th International Conference on Education and New Learning Technologies. IATED, 2021. http://dx.doi.org/10.21125/edulearn.2021.1154.

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Babic, Snjezana, Divna Bjelanovic, and i. Marina Cicin-Sain. "Programming and Mathematics through Game." In 2021 44th International Convention on Information, Communication and Electronic Technology (MIPRO). IEEE, 2021. http://dx.doi.org/10.23919/mipro52101.2021.9597117.

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Berge, Runar Lie, Bjørnar Sæterås, and Andreas Brandsæter. "Integrated programming and mathematics in schools - A solid fundation for a future engineering education?" In SEFI 50th Annual conference of The European Society for Engineering Education. Barcelona: Universitat Politècnica de Catalunya, 2022. http://dx.doi.org/10.5821/conference-9788412322262.1394.

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The interest in programming in schools has the last decade increased, and many countries have introduced programming as part of the school curriculum. Teaching of programming to students in primary and secondary school is often focused on the computer sciences aspect of programming. The current study is a part of the recently initiated research project “Programming for understanding mathematics” which has a different emphasis; the project investigates how the mathematical competence of the students are affected by actively using programming in mathematics lessons. In this paper, a recognized analytical framework for analysing the cognitive demand of mathematical tasks is presented. We extend the framework to include the analysis of tasks that utilize programming, allowing us to distinguish between tasks that are demanding due to the mathematical content, but the programming aspect of the task is trivial, and tasks that are cognitive demanding due to complex programming, but the mathematics is simple. We use the extended framework to analyse tasks in four mathematics textbooks written for 16-17 year old students by two major publishers in Norway. The results show that the tasks provided in the textbooks mainly focus on elementary programming skills, and the tasks give limited experiences with cognitive demanding programming tasks.

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Ferreira, Bernardo, Lucas Souza, Laira Silva, Igor Felix, Leônidas Brandão, and Anarosa Brandão. "The Marriage of Mathematics and Programming." In XXX Simpósio Brasileiro de Informática na Educação (Brazilian Symposium on Computers in Education). Brazilian Computer Society (Sociedade Brasileira de Computação - SBC), 2019. http://dx.doi.org/10.5753/cbie.sbie.2019.1790.

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Wainwright, Roger L. "Introducing functional programming in discrete mathematics." In the twenty-third SIGCSE technical symposium. New York, New York, USA: ACM Press, 1992. http://dx.doi.org/10.1145/134510.134540.

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Foerster, Klaus-Tycho. "Integrating Programming into the Mathematics Curriculum." In SIGITE/RIIT 2016: The 17th Annual Conference on Information Technology Education and the 5th Annual Conference on Research in Information Technology. New York, NY, USA: ACM, 2016. http://dx.doi.org/10.1145/2978192.2978222.

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Razak, Mohd Rizal Bin, and Nor Zalina Binti Ismail. "Influence of mathematics in programming subject." In PROCEEDING OF THE 25TH NATIONAL SYMPOSIUM ON MATHEMATICAL SCIENCES (SKSM25): Mathematical Sciences as the Core of Intellectual Excellence. Author(s), 2018. http://dx.doi.org/10.1063/1.5041711.

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de Souza, Lucas Mendonca, Bernardo Martins Ferreira, Igor Moreira Felix, Leonidas de Oliveira Brandao, Anarosa Alves Franco Brandao, and Patricia Alves Pereira. "Mathematics and programming: marriage or divorce?" In 2019 IEEE World Conference on Engineering Education (EDUNINE). IEEE, 2019. http://dx.doi.org/10.1109/edunine.2019.8875849.

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Berichte der Organisationen zum Thema "Programming (mathematics)"

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Balyk, Nadiia, Svitlana Leshchuk, and Dariia Yatsenyak. Developing a Mini Smart House model. [б. в.], February 2020. http://dx.doi.org/10.31812/123456789/3741.

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The work is devoted to designing a smart home educational model. The authors analyzed the literature in the field of the Internet of Things and identified the basic requirements for the training model. It contains the following levels: command, communication, management. The authors identify the main subsystems of the training model: communication, signaling, control of lighting, temperature, filling of the garbage container, monitoring of sensor data. The proposed smart home educational model takes into account the economic indicators of resource utilization, which gives the opportunity to save on payment for their consumption. The hardware components for the implementation of the Mini Smart House were selected in the article. It uses a variety of technologies to conveniently manage it and use renewable energy to power it. The model was produced independently by students involved in the STEM project. Research includes sketching, making construction parts, sensor assembly and Arduino boards, programming in the Arduino IDE environment, testing the functioning of the system. Research includes sketching, making some parts, assembly sensor and Arduino boards, programming in the Arduino IDE environment, testing the functioning of the system. Approbation Mini Smart House researches were conducted within activity the STEM-center of Physics and Mathematics Faculty of Ternopil Volodymyr Hnatiuk National Pedagogical University, in particular during the educational process and during numerous trainings and seminars for pupils and teachers of computer science.

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Mamgasarian, Olivi L. Machine Learning via Mathematical Programming. Fort Belvoir, VA: Defense Technical Information Center, November 1999. http://dx.doi.org/10.21236/ada382583.

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3

Ho, James K. Nonprocedural Implementation of Mathematical Programming Algorithms. Fort Belvoir, VA: Defense Technical Information Center, December 1988. http://dx.doi.org/10.21236/ada203392.

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4

Shokaliuk, Svitlana V., Yelyzaveta Yu Bohunenko, Iryna V. Lovianova, and Mariya P. Shyshkina. Technologies of distance learning for programming basics lessons on the principles of integrated development of key competences. [б. в.], July 2020. http://dx.doi.org/10.31812/123456789/3888.

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In the era of the fourth industrial revolution – Industry 4.0 – developing key competences (digital, multilingual and mathematical competences in particular) is of paramount importance. The purpose of this work is to investigate the content of key competences of a secondary school student and to develop a method of teaching for the integrated development of multilingual and mathematical competences in the process of teaching Programming Basics with the help of distant technologies. The objectives of the research include generalizing and systematizing theoretical data on the structure and the content of key competences and the potential of informatics lessons for the development of separate components of multilingual and mathematical competences; generalizing and systematizing theoretical data on the ways of arranging distant support for informatics learning, Programming Basics in particular; to investigate the content and the methods of teaching Programming Basics in 7th-11th grades; to develop the e-learning Moodle course using Python for Programming Basics on the principles of integrated approach to developing separate components of multilingual and mathematical competence with determining some methodical special features while using it. The object of the study is to teach informatics to junior high school and high school students. The subject of the study is the means and the methods of realizing distant support in the process of teaching Programming Basics using Python on the principles of an integrated approach to developing multilingual and mathematical competences.

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5

Macal, C. M., and A. P. Hurter. Solution of mathematical programming formulations of subgame perfect equilibrium problems. Office of Scientific and Technical Information (OSTI), February 1992. http://dx.doi.org/10.2172/10134527.

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Goldfarb, Donald, and Garud Iyengar. Algorithms for Mathematical Programming with Emphasis on Bi-level Models. Office of Scientific and Technical Information (OSTI), May 2014. http://dx.doi.org/10.2172/1132080.

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7

Xu, Li. Fuzzy multiobjective mathematical programming in economic systems analysis: design and method. Portland State University Library, January 2000. http://dx.doi.org/10.15760/etd.471.

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Knighton, Shane A. A Network-Based Mathematical Programming Approach to Optimal Rostering of Continuous Heterogeneous Workforces. Fort Belvoir, VA: Defense Technical Information Center, May 2005. http://dx.doi.org/10.21236/ada433267.

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9

Goldfarb, D. Algorithms for mathematical programming. Annual technical progress report, June 15, 1993--June 14, 1994. Office of Scientific and Technical Information (OSTI), June 1994. http://dx.doi.org/10.2172/10159667.

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Rioux, Bertrand, Abdullah Al Jarboua, Frederic Murphy, and Axel Pierru. Implementing Alternative Pricing Policies in Economic Equilibrium Models Using the Extended Mathematical Programming Framework. King Abdullah Petroleum Studies and Research Center, March 2020. http://dx.doi.org/10.30573/ks--2020mp01.

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