| 1. |
- Belova, Anna, et al.
(författare)
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Meshfree methods in option pricing
- 2012
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Konferensbidrag (refereegranskat)abstract
- A meshfree approximation scheme based on the radial basis function (RBF) methods is presented for the numerical solution of the options pricing model. This work deals with the valuation of the European, Asian and American options. The option prices are modeled by the Black-Scholes equation. The θ-method is used to discretize the equation with respect to time. Next, the option price is approximated in space with RBF. In case of American options a penalty method is used, i.e. the free boundary is removed by adding a small and continuous penalty term to the Black-Scholes equation. Finally, we present a comparison of analytical and finite difference solutions and numerical results. © 2012 MANT.
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| 2. |
- Bråting, Kajsa, 1975-, et al.
(författare)
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Geometri för lärare
- 2013
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Bok (populärvet., debatt m.m.)
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| 3. |
- Markdahl, Johan, et al.
(författare)
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Towards Almost Global Synchronization on the Stiefel Manifold
- 2018
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Ingår i: 2018 IEEE Conference on Decision and Control (CDC), Miami Beach, FL, USA, Dec. 17-19, 2018. - Miami Beach, Florida : IEEE. ; , s. 496-501
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Konferensbidrag (refereegranskat)abstract
- The Kuramoto model evolves on the circle, i.e., the 1-sphere S1. A graph G is referred to as S1 -synchronizing if the Kuramoto model on G synchronizes almost globally. This paper generalizes the Kuramoto model and the concept of synchronizing graphs to the Stiefel manifold St (p, n). Previous work on generalizations of the Kuramoto model have largely been influenced by results and techniques that pertain to the original model. It was recently shown that all connected graphs are Sn -synchronizing for all n ≥ 2. However, that does not hold for n = 1. Previous results on generalized models may thus have been overly conservative. The n-sphere is a special case of the Stiefel manifold, namely St(1, n+1). As such, it is natural to ask for the extent to which the results on Sn can be extended to the Stiefel manifold. This paper shows that all connected graphs are St(p, n) -synchronizing provided the pair (p, n) satisfies p ≤ [2n/3]-1. © Copyright 2019 IEEE - All rights reserved.
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| 4. |
- Sollervall, Håkan
(författare)
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Affordances and their mediating artifacts as instruments for the collaborative design of innovative mathematical learning activities
- 2012
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- The unfolding of an affordance, as an opportunity for action, during a learningactivity requires the learner to interact with mediating artifacts. The design of alearning activity involves appropriating affordances and embedding them in theactivity in such a manner that the learner is invited to unfold the affordances,through interaction with their mediating artifacts in accordance with pre-definedhypothetical learning trajectories. In this paper, the notion of affordances is usedexplicitly in the discussion of two previous research efforts. We argue that thenotion of affordances, which was tacitly used in these efforts and aligns well withthe methodology of scenario-based design, may be used as an instrument for thecollaborative design of innovative mathematical learning activities.
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| 5. |
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| 6. |
- Sollervall, Håkan, et al.
(författare)
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Blending mobile technologies and traditional resources in mathematical learning activities
- 2012
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Ingår i: Workshop Proceedings of the 20th International Conference on Computers in Education (ICCE) 2012. - Singapore : Asia-Pacific Society for Computers in Education. - 9789810746506 ; , s. 2-10
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Konferensbidrag (refereegranskat)abstract
- Designing curriculum-based learning activities involves identifying andimplementing affordances that provide opportunities for students to engage in actionsdirected at achieving specific learning objectives. These affordances may be mediated byinformation and communication technologies (ICT) or traditional resources, peers orteachers, or other contextual features of the learning environment. The learning objectivesguide the designer’s choice of affordances, whose deployment on specific artifacts is basedon assessing the available artifacts’ mediating capabilities. Such a design approach putshigh demands on the designer’s technological, pedagogical and content knowledge. In thispaper, we discuss how we have addressed these demands by adopting a flexible co-designapproach that invites the creative blending of mobile technologies and augmented realitywith traditional resources, for the purpose of designing innovative mathematical learningactivities with high relevance for teachers’ practice and the mathematics curriculum.
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| 7. |
- Sollervall, Håkan, 1962-
(författare)
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Collaborative mathematical inquiry with augmented reality
- 2012
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Ingår i: Research and Practice of Technology Enhanced Learning. - Singapore : World Scientific. - 1793-2068. ; 7:3, s. 153-173
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we describe and reflect on the design of a mathematical learning activity developed in collaboration between teachers, researchers and technical developers. By making use of augmented reality (AR) as a technology supporting augmentation of a real-world projection with computergene- rated images, we have designed an activity that promotes unique action and learning trajectories. These trajectories require the learners to engage in interactive-constructive actions that involve and stimulate the development of their self-regulatory skills by inviting them to vary and coordinate across the contextual affordances of the technologies and the physical resources in the classroom. Our learning activity is designed as a collaborative guided inquiry, implemented in a regular classroom and involved mathematical problem solving in relation to the geometric concept of scale. In order to successfully complete the activity, the learners are challenged to coordinate affordances from three distinct referential contexts by involving physical and virtual artifacts. In the design process, we identify critical aspects of the activity and embed affordances for corresponding scaffolding actions which turn out to play a crucial role when the activity is implemented with a group of four 15-year-old students. Although the AR technology has served us well in developing this particular activity, this specific technology appears to have limited applicability in mathematics education beyond geometry. We recommend that future research efforts move beyond AR and consider the broader context of embodied design with tangible user interfaces, that have recently shown great potential for the design of innovative activities for the learning of mathematics.
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| 8. |
- Sollervall, Håkan
(författare)
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Euklides i mobilen
- 2012
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Ingår i: Dokumentation av Matematikbiennalen 2012. ; , s. 305a-
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Konferensbidrag (populärvet., debatt m.m.)abstract
- Flera års forsknings- och utvecklingsarbete har resulterat i en handfull lärandeaktiviteter för elever i årskurs 4-9, som i undersökande aktiviteter använder ny teknik i form av datorer, projektorer, interaktiva skrivtavlor,webbkameror och mobiltelefoner. Tekniken kan låta oss möta meningsfull matematik på nya sätt i nyasammanhang och kan göra det möjligt att sammanfläta undersökande utomhusaktiviteter i små grupper medinomhusaktiviteter i helklass. Vi ger flera konkreta exempel på hur tekniken kan stimulera och stödjakommunikation och representation av ett matematiskt innehåll.
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| 9. |
- Sollervall, Håkan
(författare)
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From Euclid to GPS : designing an innovative spatial coordination activity with mobile technologies
- 2012
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Ingår i: Proceedings of th 36th Conference of the International Group for the Psychology of Mathematics Education. - Prague : The International Group For Psychology of Mathematics Education. ; , s. 4:107-4:114
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Konferensbidrag (refereegranskat)abstract
- Guided by the notion of design research we develop a learning activity for 12 year old students, who are asked to coordinate themselves physically in terms of distances with respect to two given points in an outdoor setting. The outdoor activity, as well as its continuation into the mathematics classroom, involves mobile software applica-tions specifically developed to support this activity. In this paper, we argue that the design of innovative learning activities is enhanced by the coordination of expertise and knowledge from several research domains, whose collaboration is facilitated by using affordances for representation and communication as design instruments. We present a case where ancient Greek mathematics, modern psychology and techno-logical affordances guide the design of an innovative spatial coordination activity.
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| 10. |
- Sollervall, Håkan, 1962-, et al.
(författare)
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Instruments for improving teachers' use of artefacts for the learning of mathematics
- 2012
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Ingår i: ICME-12 Pre-proceedings. - Seoul : International Commission on Mathematical Instruction (ICMI). ; , s. 4885-4890
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Konferensbidrag (refereegranskat)abstract
- Mathematical tasks have always been and still are a major object of concern in the mathematics classroom. Teachers’ daily work includes planning, implementing, and evaluating the mathematical tasks that student engage in during class by making use of material and immaterial artefacts. We argue that teachers’ mathematical knowledge has to include instruments for controlling how these artefacts become involved when students engage in solving mathematical tasks. We propose to meet this demand by coordinating the matching notions of affordances (for planning) and objects of activity (for evaluation). We briefly illustrate how these notions can be used as analytical instruments in a fashion that connects to what teachers already do in their daily work.
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