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  • 301. Bestill onlineKjøp publikasjonen >>
    Bergman Ärlebäck, Jonas
    Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Mathematical modelling in upper secondary mathematics education in Sweden2010Doktoravhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    The aim of this thesis is to investigate and enhance our understanding of the notions of mathematical models and modelling at the Swedish upper secondary school level. Focus is on how mathematical models and modelling are viewed by the different actors in the school system, and what characterises the collaborative process of a didactician and a group of teachers engaged in designing and developing, implementing and evaluating teaching modules (so called modelling modules) exposing students to mathematical modelling in line with the present mathematics curriculum. The thesis consists of five papers and reports, along with a summary introduction, addressing both theoretical and empirical aspects of mathematical modelling.

    The thesis uses both qualitative and quantitative methods and draws partly on design-based research methodology and cultural-historical activity theory (CHAT). The results of the thesis are presented using the structure of the three curriculum levels of the intended, potentially implemented, and attained curriculum respectively.

    The results show that since 1965 and to the present day, gradually more and more explicit emphasis has been put on mathematical models and modelling in the syllabuses at this school level. However, no explicit definitions of these notions are provided but described only implicitly, opening up for a diversity of interpretations.

    From the collaborative work case study it is concluded that the participating teachers could not express a clear conception of the notions mathematical models or modelling, that the designing process often was restrained by constraints originating from the local school context, and that working with modelling highlights many systemic tensions in the established school practice. In addition, meta-results in form of suggestions of how to resolve different kinds of tensions in order to improve the study design are reported.

    In a questionnaire study with 381 participating students it is concluded that only one out of four students stated that they had heard about or used mathematical models or modelling in their education before, and the expressed overall attitudes towards working with mathematical modelling as represented in the test items were negative. Students’ modelling proficiency was positively affected by the students’ grade, last taken mathematics course, and if they thought the problems in the tests were easy or interesting. In addition empirical findings indicate that so-called realistic Fermi problems given to students working in groups inherently evoke modelling activities.

    Delarbeid
    1. Towards understanding teachers’ beliefs and affects about mathematical modelling
    Åpne denne publikasjonen i ny fane eller vindu >>Towards understanding teachers’ beliefs and affects about mathematical modelling
    2009 (engelsk)Konferansepaper, Publicerat paper (Annet vitenskapelig)
    Abstract [en]

    Work in progress on a framework aiming at capturing teachers’ beliefs about mathematical models and modelling is presented. It is suggested that the belief structure of mathematical models and modelling as perceived by teachers fruitfully might be explored as partly constituted of the teachers’ beliefs about the real world, the nature of mathematics, school mathematics, and applying and applications of mathematics. Some aspects of the suggested framework are explored using two case study interviews. It is found that the two teachers do not have any well formed beliefs about mathematical models and modelling, and that the interpreted beliefs structure of the teachers contain inconsistencies which are made explicit within the framework. The empiric findings also suggest some modifications of the framework.

    HSV kategori
    Identifikatorer
    urn:nbn:se:liu:diva-54316 (URN)
    Konferanse
    CERME 6 - Sixth Conference of European Research in Mathematics Education Lyon, France, January 28 - February1
    Tilgjengelig fra: 2010-03-09 Laget: 2010-03-09 Sist oppdatert: 2018-09-01
    2. On the use of realistic Fermi problems for introducingmathematical modelling in school
    Åpne denne publikasjonen i ny fane eller vindu >>On the use of realistic Fermi problems for introducingmathematical modelling in school
    2009 (engelsk)Inngår i: The Montana Mathematics Enthusiast, ISSN 1551-3440, E-ISSN 1551-3440, Vol. 6, nr 3, s. 331-364Artikkel i tidsskrift (Fagfellevurdert) Published
    Abstract [en]

    In this paper an analytical tool referred to as the MAD (Modelling Activity Diagram) framework adapted from Schoenfeld’s parsing protocol coding scheme is used to address the issues of how to introduce mathematical modelling to upper secondary students. The work of three groups of students engaged in solving so called realistic Fermi problems were analysed using this framework, and it was observed that the processes involved in a typical mathematical modelling cycle were richly represented in the groups’ solving processes. The importance of the social interactions within the groups was noted, as well as the extensive use of extra-mathematical knowledge used by the students during the problem solving session.

    sted, utgiver, år, opplag, sider
    Montana Council of Teachers of Mathematics & Information Age Publishing, 2009
    Emneord
    Fermi problems, Fermi estimates, Modelling cycles, Mathematical modelling, Modelling activity diagram
    HSV kategori
    Identifikatorer
    urn:nbn:se:liu:diva-54664 (URN)
    Tilgjengelig fra: 2010-03-30 Laget: 2010-03-30 Sist oppdatert: 2017-12-12
    3. First results from a study investigating Swedish upper secondary students’ mathematical modelling competencies
    Åpne denne publikasjonen i ny fane eller vindu >>First results from a study investigating Swedish upper secondary students’ mathematical modelling competencies
    2009 (engelsk)Konferansepaper, Publicerat paper (Annet vitenskapelig)
    Abstract [en]

    This paper reports on the first results from a study investigating Swedish upper secondary students’ (11th – 12th grade) mathematical modelling competency. Using non-parametric statistical methods the data from 381 students are analysed and the students’ modelling competency is described in terms of seven subcompetencies. Possible factors affecting the students’ mathematical competency such as attitudes toward modelling, previous experiences, last taken mathematics course, grade, class and gender were also investigated.

    HSV kategori
    Identifikatorer
    urn:nbn:se:liu:diva-54317 (URN)
    Konferanse
    14th International Conference on the Teaching of Mathematical Modelling and Applications (ICTMA 14), University of Hamburg, 27th to 31st July, Germany
    Tilgjengelig fra: 2010-03-09 Laget: 2010-03-09 Sist oppdatert: 2014-06-23bibliografisk kontrollert
    4. Matematisk modellering i svenska gymnasieskolans kursplaner i matematik 1965-2000
    Åpne denne publikasjonen i ny fane eller vindu >>Matematisk modellering i svenska gymnasieskolans kursplaner i matematik 1965-2000
    2009 (svensk)Rapport (Annet vitenskapelig)
    Abstract [en]

    Denna rapport studerar hur begreppen matematisk modell och matematisk modellering behandlats i kursplanerna i matematik för motsvarande svenska gymnasieskolans naturvetenskapliga program mellan åren 1965 och 2000. En översikt över sex kursplaners olika form och innehåll ges och tre olika analyser på tre olika nivåer genomförs; en innehållsanalys, en kvalitativ analys, och en analys som beaktar relationen mellan begreppen modellering, tillämpningar och problemlösning. Analysen visar att matematiska modeller och modellering förekommit implicit sedan kursplanen från 1965, men att begreppen främst i de två senaste kursplanerna lyfts fram explicit och fått en central position i kursplanerna. I den nuvarande kursplanen Gy2000 framgår att matematiska modeller kan tolkas både som ett undervisningsmål i sig och som ett didaktiskt hjälpmedel att lära matematik.

    sted, utgiver, år, opplag, sider
    Linköping University: Linköping Universtity Electronic Press, 2009. s. 93
    Serie
    LiTH-MAT-R, ISSN 0348-2960 ; 2009:8
    HSV kategori
    Identifikatorer
    urn:nbn:se:liu:diva-54267 (URN)LiTH-MAT-R-2009-8 (ISRN)
    Tilgjengelig fra: 2010-03-05 Laget: 2010-03-05 Sist oppdatert: 2014-06-23
    5. Designing, implementing and evaluating mathematical modelling modules at the upper secondary level
    Åpne denne publikasjonen i ny fane eller vindu >>Designing, implementing and evaluating mathematical modelling modules at the upper secondary level
    2009 (engelsk)Rapport (Annet vitenskapelig)
    Abstract [en]

    This study provides an account of how it is possible to work with mathematical models and modelling at the Swedish upper secondary level. It shows how a researcher and two teachers, departing from what is written in the mathematics curriculum document about mathematical models and modelling and the teachers’ mathematics teaching practices, collaborate to design and develop two so called modelling modules. These two modules designed for, and integrated in, the Mathematics C and Mathematics D course respectively, were implemented in the teachers’ classes and the whole process was evaluated. The students’ experiences of working with the modules were also investigated.

    The conceptual framework used to study this process of design, implementation, and evaluation is built up of design-based research methodology, cultural historical activity theory (CHAT), and co-learning agreement between the researcher and the participants.

    The teachers as well as the students expressed that they enjoyed working on the modules and found the experience positive and rewarding. However, some doubt concerning the learning outcome on behalf of the students were raised among the teachers, and the wish to incorporate more scheduled time into the modules was expressed by the students.

    It is concluded that the participating teachers could had difficulties in expressing a clear conception of the notions of mathematical models or modelling and no affirmative conclusions could be drawn that the participation of the teachers changed their attitudes towards mathematical models and modelling. The designing process was often was restrained by constraints originating from the local school context, and working with modelling highlights many systemic tensions in the established school practice. Also, meta-results in form of suggestions of how to resolve different kinds of tensions in order to improve the study design are reported.

    sted, utgiver, år, opplag, sider
    Linköping University: Linköping Universtiy Electronic Press, 2009. s. 219
    HSV kategori
    Identifikatorer
    urn:nbn:se:liu:diva-54269 (URN)LiTH-MAT-R-2009-9 (Lokal ID)LiTH-MAT-R-2009-9 (Arkivnummer)LiTH-MAT-R-2009-9 (OAI)
    Tilgjengelig fra: 2010-03-05 Laget: 2010-03-05 Sist oppdatert: 2014-06-23
    Fulltekst (pdf)
    Mathematical modelling in upper secondary mathematics education in Sweden
    Download (pdf)
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  • 302.
    Bergman Ärlebäck, Jonas
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    On the use of realistic Fermi problems for introducingmathematical modelling in school2009Inngår i: The Montana Mathematics Enthusiast, ISSN 1551-3440, E-ISSN 1551-3440, Vol. 6, nr 3, s. 331-364Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper an analytical tool referred to as the MAD (Modelling Activity Diagram) framework adapted from Schoenfeld’s parsing protocol coding scheme is used to address the issues of how to introduce mathematical modelling to upper secondary students. The work of three groups of students engaged in solving so called realistic Fermi problems were analysed using this framework, and it was observed that the processes involved in a typical mathematical modelling cycle were richly represented in the groups’ solving processes. The importance of the social interactions within the groups was noted, as well as the extensive use of extra-mathematical knowledge used by the students during the problem solving session.

  • 303.
    Bergman Ärlebäck, Jonas
    et al.
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Bergsten, Christer
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Utbildningsvetenskap.
    On the Use of Realistic Fermi Problems in Introducing Mathematical. Modelling in Upper Secondary Mathematics2010Inngår i: Modeling Students' Mathematical Modeling Competencies, ICTMA 13 / [ed] Richard Lesh, Peter L. Galbrait, Christopher R. Haines and Andrew Hurford, Springer US , 2010, s. 597-609Konferansepaper (Fagfellevurdert)
    Abstract [en]

    This paper reports on a study aiming to investigate the possible potential of using Fermi problems to introduce mathematical modelling to Swedish upper secondary school students. Three groups of students- work on realistic Fermi problems were analysed using an analytic tool, referred to as the -modelling activity diagram-, adapted and developed by the author. It was observed that the processes involved in a mathematical modelling cycle were richly represented in the problem solving processes of the groups. The students also frequently used their personal extra-mathematical knowledge in the solving process in three different ways; a creative, a verifying and a social way.

  • 304.
    Bergman Ärlebäck, Jonas
    et al.
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Claesson, Marcus
    Kungsgårdsgymnasiet Norrköping.
    Hällgren, Malin
    Birgittaskolan vuxenutbildning Linköping.
    Lindh, Sofia
    Hagagymnasiet Norrköping.
    Lundell, Mia
    Djäkneparksskolan Norrköping.
    Nordling, Mattias
    Anders Ljungstedts gymnasium Linköping.
    IPAs - ihopparningsaktiviteter: aktiviteter med låg tröskel som tränar elevers begrepps-, procedur-/ metod- och resonemangsförmåga2017Rapport (Annet vitenskapelig)
    Abstract [sv]

    Syftet med denna rapport är att på ett beskrivande sätt delge hur arbetet i projektet om IPAs som genomförts HT2014 – VT2015 gått till och vilka erfarenheter och slutsatser som arbetet resulterat i. Den tänkte läsaren är framför allt kommunernas matematiklärare, men vi tror även att andra lärare och skolpersonal kan finna innehållet intressant och användbart. Det är vår förhoppning att rapporten med tillhörande aktiviteter kan inspirera till reflektion och en mer varierad undervisning. När pronomen som vi och oss används i rapporten åsyftats alla som aktivt ingått i IPAprojektets forskande grupp, vilken har bestått av såväl deltagande lärare som forskare:

    Marcus Claesson (Kungsgårdsgymnasiet, Norrköping), Malin Hällgren (Birgittaskolans vuxenutbildning, Linköping), Sofia Lindh (Hagagymnasiet, Norrköping), Mia Lundell (Djäkneparksskolan, Norrköping), Mattias Nordling (Anders Ljungstedska gymnasiet, Linköping) och Jonas Bergman Ärlebäck (LiU). Huvudansvaret för författandet av rapporten har Jonas haft som medverkande forskare i projektet. De medforskande lärarna har bidragit med analyser, erfarenheter och exempel från sina klassrum, utvecklat, testat och formulerat aktiviteterna som utgjort navet i projektet, samt läst och kommenterat rapporten under dess framställning.

    Rapporten följer samma logik och uppbyggnad som de rapporter skrivna inom det övergripande samarbetsprojektet Matematikdidaktik för bättre matematikkunskaper av det arbete och den forskning som bedrivits av Lisa Björklund Boistrup (Björklund Boistrup et al. 2013a; 2013b; 2013c; 2014a; 2014b). Vissa delar av texten använder därför, eller bygger till viss del på, Lisas texter, och när så är fallet tydliggörs detta med fotnoter. Andra delar av texten, så som exempelvis beskrivningen av de teoretiska utgångspunkterna, är i stort identiskt i samtliga delprojektsrapporter för de projekt som Jonas medverkat i som forskare (Ärlebäck et. al. 2017a, 2017b, 2017c, 2017d). Rapporten är dock skriven för att kunna läsas helt fristående från de andra rapporterna författade i projektet och förutsätter med andra ord ingen tidigare kunskap eller kännedom om projektet och de perspektiv som används. De läsare som redan tagit del av arbetet inom samarbetsprojektet Matematikdidaktik för bättre matematikkunskaper på olika sätt kommer här och var att känna igen sig, men vi hoppas att de delar som är unikt specifika för just detta delprojekt ska vara intressant och inspirerande.

    Fulltekst (pdf)
    IPAs - ihopparningsaktiviteter: Aktiviteter med låg tröskel som tränar elevers begrepps-, procedur-/ metod- och resonemangsförmåga
    Download (jpg)
    presentationsbild
  • 305.
    Bergman Ärlebäck, Jonas
    et al.
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Doerr, Helen M.
    Syracuse University.
    At the core of modelling: Connecting, coordinating and integrating models2015Inngår i: Proceedings of the 9th Congress of European Research in Mathematics Education / [ed] K. Krainer & N. Vondrová, 2015, s. 802-808Konferansepaper (Fagfellevurdert)
    Abstract [en]

    This theoretical paper introduces the notions of connecting, coordinating and integrating models to analyse and reflect on how models are created and developed. We define, discuss and apply these constructs to some theoretical perspectives in the present modelling discourse. We draw on an example from a model application activity within a model development sequence to illustrate these constructs. Our hope is to spark a discussion that will enhance our understanding about the nature of mathematical modelling and the teaching and learning of, and through, modelling.

  • 306.
    Bergman Ärlebäck, Jonas
    et al.
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Edgar, Brian
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Herberthson, Magnus
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    The Bach tensor and other divergence-free tensors2005Inngår i: International Journal of Geometric Methods in Modern Physics (IJGMMP), ISSN 0219-8878, Vol. 2, nr 1, s. 13-21Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In four dimensions, we prove that the Bach tensor is the only symmetric divergence-free 2-tensor which is also quadratic in Riemann and has good conformal behavior. In n > 4 dimensions, we prove that there are no symmetric divergence-free 2-tensors which are also quadratic in Riemann and have good conformal behavior, nor are there any symmetric divergence-free 2-tensors which are concomitants of the metric tensor gab together with its first two derivatives, and have good conformal behavior.

  • 307.
    Bergqvist, Göran
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Causal tensors in Lorentzian geometry2003Inngår i: Publications of the Spanish mathematical society, Vol. 5, s. 73-83Artikkel i tidsskrift (Fagfellevurdert)
  • 308.
    Bergqvist, Göran
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Curves and envelopes that bound the spectrum of a matrix2018Inngår i: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 557Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A generalization of the method developed by Adam, Psarrakos and Tsatsomeros to find inequalities for the eigenvalues of a complex matrix A using knowledge of the largest eigenvalues of its Hermitian part H(A) is presented. The numerical range or field of values of A can be constructed as the intersection of half-planes determined by the largest eigenvalue of H(e(i theta) A.). Adam, Psarrakos and Tsatsomeros showed that using the two largest eigenvalues of H(A), the eigenvalues of A satisfy a cubic inequality and the envelope of such cubic curves defines a region in the complex plane smaller than the numerical range but still containing the spectrum of A. Here it is shown how using the three largest eigenvalues of H(A) or more, one obtains new inequalities for the eigenvalues of A and new envelope-type regions containing the spectrum of A. (C) 2018 Elsevier Inc. All rights reserved.

    Fulltekst tilgjengelig fra 2020-07-24 14:59
  • 309.
    Bergqvist, Göran
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Exact probabilities for typical ranks of 2 × 2 × 2 and 3 × 3 × 2 tensors2013Inngår i: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 438, nr 2, s. 663-667Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We show that the probability to be of rank 2 for a 2×2×2 tensor with elements from a standard normal distribution is π/4, and that the probability to be of rank 3 for a 3×3×2 tensor is 1/2. In the proof results on the expected number of real generalized eigenvalues of random matrices are applied. For n×n×2 tensors with n≥4 we also present some new aspects of their rank.

    Fulltekst (pdf)
    fulltext
  • 310.
    Bergqvist, Göran
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Monotone quantities for the Penrose inequality2003Inngår i: Penrose Inequalities,2003, 2003Konferansepaper (Annet vitenskapelig)
  • 311.
    Bergqvist, Göran
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Spinors and conformal curvature2005Inngår i: Publications of the Spanish mathematical societyArtikkel i tidsskrift (Fagfellevurdert)
  • 312.
    Bergqvist, Göran
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    The Penrose inequality and null hypersurfaces2003Inngår i: Joint meeting of the American Mathematical Society and the Spanish Mathematical Society,2003, 2003Konferansepaper (Annet vitenskapelig)
  • 313.
    Bergqvist, Göran
    et al.
    Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Eriksson, Ingemar
    Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    The Chevreton tensor and Einstein-Maxwell spacetimes conformal to Einstein spaces2007Inngår i: Classical and Quantum Gravity, ISSN 0264-9381, Vol. 24, nr 13, s. 3437-3455Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper, we characterize the source-free Einstein–Maxwell spacetimes which have a trace-free Chevreton tensor. We show that this is equivalent to the Chevreton tensor being of pure radiation type and that it restricts the spacetimes to Petrov type N or O. We prove that the trace of the Chevreton tensor is related to the Bach tensor and use this to find all Einstein–Maxwell spacetimes with a zero cosmological constant that have a vanishing Bach tensor. Among these spacetimes we then look for those which are conformal to Einstein spaces. We find that the electromagnetic field and the Weyl tensor must be aligned, and in the case that the electromagnetic field is null, the spacetime must be conformally Ricci-flat and all such solutions are known. In the non-null case, since the general solution is not known on a closed form, we settle by giving the integrability conditions in the general case, but we do give new explicit examples of Einstein–Maxwell spacetimes that are conformal to Einstein spaces, and we also find examples where the vanishing of the Bach tensor does not imply that the spacetime is conformal to a C-space. The non-aligned Einstein–Maxwell spacetimes with vanishing Bach tensor are conformally C-spaces, but none of them are conformal to Einstein spaces.

  • 314.
    Bergqvist, Göran
    et al.
    Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Eriksson, Ingemar
    Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Senovilla, J. M. M.
    Departamento de Física Teórica, Universidad del País Vasco, Bilbao, Spain.
    New electromagnetic conservation laws2003Inngår i: Classical and Quantum Gravity, ISSN 0264-9381, Vol. 20, nr 13, s. 2663-2668Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The Chevreton superenergy tensor was introduced in 1964 as a counterpart, for electromagnetic fields, of the well-known Bel–Robinson tensor of the gravitational field. We here prove the unnoticed facts that, in the absence of electromagnetic currents, Chevreton's tensor (i) is completely symmetric, and (ii) has a trace-free divergence if the Einstein–Maxwell equations hold. It follows that the trace of the Chevreton tensor is a rank-2, symmetric, trace-free, conserved tensor, which is different from the energy–momentum tensor, and nonetheless can be constructed for any test Maxwell field or any Einstein–Maxwell spacetime.

  • 315.
    Bergqvist, Göran
    et al.
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Eriksson, Ingemar
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Senovilla, José M M
    New conservation laws in Einstein-Maxwell spacetimes2004Inngår i: 17th International Conference on General Relativity and Gravitation,2004, 2004Konferansepaper (Annet vitenskapelig)
  • 316.
    Bergqvist, Göran
    et al.
    Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Forrester, Peter J.
    University of Melbourne, Victoria, Australia.
    Rank probabilities for real random NxNx2 tensors2011Inngår i: Electronic Communications in Probability, ISSN 1083-589X, E-ISSN 1083-589X, Vol. 16, s. 630-637Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We prove that the probability P_N for a real random Gaussian NxNx2 tensor to be of real rank N is P_N=(Gamma((N+1)/2))^N/G(N+1), where Gamma(x) and G(x) denote the gamma and the Barnes G-functions respectively. This is a rational number for N odd and a rational number multiplied by pi^{N/2} for N even. The probability to be of rank N+1 is 1-P_N. The proof makes use of recent results on the probability of having k real generalized eigenvalues for real random Gaussian N x N matrices. We also prove that log P_N= (N^2/4)log (e/4)+(log N-1)/12-zeta'(-1)+O(1/N) for large N, where zeta is the Riemann zeta function.

    Fulltekst (pdf)
    fulltext
  • 317.
    Bergqvist, Göran
    et al.
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Lankinen, Paul
    Algebraic and differential Rainich conditions for symmetric trace-free tensors of higher rank2005Inngår i: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences, ISSN 1364-5021, E-ISSN 1471-2946, Vol. 461, nr 2059, s. 2181-2195Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We present a study of Rainich-like conditions for symmetric and trace-free tensors T. For arbitrary even rank we find a necessary and sufficient differential condition for a tensor to satisfy the source-free field equation. For rank 4, in a generic case, we combine these conditions with previously obtained algebraic conditions to gain a complete set of algebraic and differential conditions on T for it to be a superenergy tensor of a Weyl candidate tensor, satisfying the Bianchi vacuum equations. By a result of Bell and Szekeres, this implies that in vacuum, generically, T must be the Bel-Robinson tensor of the spacetime. For the rank 3 case, we derive a complete set of necessary algebraic and differential conditions for T to be the superenergy tensor of a massless spin-3/2 field, satisfying the source-free field equation.

  • 318.
    Bergqvist, Göran
    et al.
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Lankinen, Paul
    Algebraic and differential Rainich conditions for the Bel-Robinson tensor and other higher rank tensors2004Inngår i: 17th International Conference on General Relativity and Gravitation,2004, 2004Konferansepaper (Annet vitenskapelig)
  • 319.
    Bergqvist, Göran
    et al.
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Lankinen, Paul
    Unique characterization of the Bel-Robinson tensor2004Inngår i: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 21, nr 14, s. 3499-3503Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We prove that a completely symmetric and trace-free rank-4 tensor is, up to sign, a Bel-Robinson-type tensor, i.e., the superenergy tensor of a tensor with the same algebraic symmetries as the Weyl tensor, if and only if it satisfies a certain quadratic identity. This may be seen as the first Rainich theory result for rank-4 tensors.

  • 320.
    Bergqvist, Göran
    et al.
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Senovilla, José M. M.
    Structure of conformal Lorentz transformations2003Inngår i: Current Trends in Relativistic Astrophysics: theoretical, numerical, observational / [ed] L. Férnadez-Jambrina, L.M. González-Romero, Springer , 2003, s. 245-251Kapittel i bok, del av antologi (Annet vitenskapelig)
    Abstract [en]

    The present volume contains the expanded lectures of a meeting on relativistic astrophysics, the goal of which was to provide a modern introduction to specific aspects of the field for young researchers, as well as for nonspecialists from related areas. Particular emphasis is placed on the theory of black holes and evolution, relativistic stars and jet hydrodynamics, as well as the production and detection of gravitational waves. The book is complemented by further contributions and animation supplied on the accompanying CD-ROM.

  • 321.
    Bergsten, Christer
    Linköpings universitet, Utbildningsvetenskap. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    A classification of algebraic tasks2003Inngår i: New trends in mathematics education research: an European perspective,2003, 2003Konferansepaper (Annet vitenskapelig)
  • 322.
    Bergsten, Christer
    Linköpings universitet, Utbildningsvetenskap. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Beyond the representation given - The parabola and historical metamorphoses of meaning2004Inngår i: PME - Interbational Group for the Psychology of Mathematics Education,2004, Bergen: Bergen Univeristy College , 2004, s. 1-264-1-264Konferansepaper (Annet vitenskapelig)
    Abstract [en]

      Tracking the history of a mathematical object reveals a double influence on its development - from inside and outside the pure mathematical realm. From a semiotic point of view, a chain of metamorphoses of meanings is created, which becomes critical as the mathematical object by the social process of didactic transposition is turned into a presented object of teaching and learning. As an example, by representing the mathematical object -parabola- by means of its historical progression within classical geometry, analytic geometry, and dynamic geometry software, it is seen, by using analytic tools from semiotics, anthropo¬logical theory of didactics, and embodied cognition, how and why students- concept images and problem solving techniques may become disconnected and instrumental.

  • 323.
    Bergsten, Christer
    Linköpings universitet, Utbildningsvetenskap. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Datoranvändning i högskolans matematikundervisning1999Inngår i: Datorstödd eller datorstörd matematikundervisning,1998, Stockholm: Högskoleverket , 1999, s. 21-Konferansepaper (Fagfellevurdert)
    Abstract [sv]

     För att få en översiktlig bild av datoranvändningen i den svenska högskolans matematikundervisning genomfördes under våren 1998 en enkätundersöknng. Kursansvariga (eller motsvarande) lärare för kurser i matematik och matemaisk statistik besvarade frågor om bl.a. typ och omfång av datorstöd och argument för eller emot anvädningen av datorer i undervisningen. Resultatet kan sammanfattas i bl.a. följande slutsatser: stadig ökning av datoranvändning under de senaste tre åren til ca 50% av kurserna i matematik och ca 80% av kurserna i matemaisk statistik; stor skillnad mellan olika högskolor; ingen större skillnad mellan utbildningr (lärarutbildningar speciell situation) eller kurser (utom "tillämpade"); formerna för datoranvändning varierar i allmänhet inte så mycket; argumenten för och emot datoranvändning i matematikundervisningen varierar men ryms inom fem till sex kategorier; stor skillnad mellan högskolor i miniräknarpolicy på skriftlig tentamen i matematik, där totalt ca 1/3 av kurserna tillåter miniräknare; argumenten mot miniräknare på skriftlig tentamen i matematik är många och "motståndet" är starkt på flera håll: det finns ett uttalat intresse hos många lärare att utveckla datorstödet i matematikundervisningen.   

  • 324.
    Bergsten, Christer
    Linköpings universitet, Utbildningsvetenskap. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Datrostödd eller datorstörd matematikundervisning?1999Collection/Antologi (Annet vitenskapelig)
  • 325.
    Bergsten, Christer
    Linköpings universitet, Utbildningsvetenskap. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    En kommentar till den matematiska problemlösningens didaktik2006Inngår i: Perspektiv på kunskapens och lärandets villkor / [ed] Lisen Häggblom, Lars Burman & Ann-Sofi Röj-Lindberg, Vasa: Åbo Akademi , 2006, s. 165-176Kapittel i bok, del av antologi (Annet vitenskapelig)
    Abstract [sv]

     Grundat på en klassificering av teoretiska perspektiv, aspekter av matematiska problem, kunskapsbildning och undervisning, presenteras en epistemologisk modell för problemslösningens roll i en matematisk praktik.

  • 326.
    Bergsten, Christer
    Linköpings universitet, Utbildningsvetenskap. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Exploiting the gap between intuitive and formal knowledge in mathematics2008Inngår i: The International Congress on Mathematical Education, ICME,2004, Copenhagen: Roskilde University , 2008Konferansepaper (Fagfellevurdert)
  • 327.
    Bergsten, Christer
    Linköpings universitet, Utbildningsvetenskap. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    How do theories influence the research on teaching and learning limits of functions?2007Inngår i: CERME,2007, Nicosia: University of Cyprus , 2007, s. 1638-Konferansepaper (Fagfellevurdert)
  • 328.
    Bergsten, Christer
    Linköpings universitet, Utbildningsvetenskap. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Investigating quality in undergraduate mathematics lectures2007Inngår i: Mathematics Education Research Journal, ISSN 1033-2170, E-ISSN 2211-050X, Vol. 19, nr 3, s. 48-72Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The notion of quality in undergraduate mathematics lectures is examined by using theoretical notions and research results from the literature and empirical data from a case study on lecturing on limits of functions. A systemic triangular model is found to catch critical quality aspects of a mathematics lecture, consisting of mathematical exposition, teacher immediacy, and general quality criteria for mathematics teaching. Mathematical exposition involves the dynamic interplay of mathematical content, mathematical process, and institutionalisation. The discussion is a contribution to an increased pedagogical awareness in undergraduate mathematics teaching.

  • 329.
    Bergsten, Christer
    Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Lecture notes - On lecturing in undergraduate mathematics2007Inngår i: MADIF-5, 2006, Linköping: SMDF , 2007, s. 31-Konferansepaper (Annet vitenskapelig)
    Abstract [en]

    Lectures is a common teaching format in undergraduate mathematics. This study sets up to investigate the notion of a quality lecture, based on a literature review and a case study in a beginning calculus course. Critical aspects discussed include information delivery, connections, rigour-intuition, algebraic-imagistic modes, gestures, socio-mathematical norms, a mathematical mind, inspiration, personalisation, and general quality criteria for mathematics teaching, al of which came into play in the lecture studied.

  • 330.
    Bergsten, Christer
    Linköpings universitet, Utbildningsvetenskap. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Magic circels in the arbelos2006Rapport (Annet vitenskapelig)
  • 331.
    Bergsten, Christer
    Linköpings universitet, Matematiska institutionen. Linköpings universitet, Tekniska högskolan.
    Magic circles in the arbelos2010Inngår i: The Montana Mathematics Enthusiast, ISSN 1551-3440, E-ISSN 1551-3440, Vol. 7, nr 2&3, s. 209-222Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In the arbelos three simple circles are constructed on which the tangency points for three circle chains, all with Archimedes’ circle as a common starting point, are situated. In relation to this setting, some algebraic formulae and remarks are presented. The development of the ideas and the relations that were “discovered” were strongly mediated by the use of dynamic geometry software.

  • 332.
    Bergsten, Christer
    Linköpings universitet, Utbildningsvetenskap. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Några aspekter av matematikens formelspråk2008Inngår i: Matematiska språk. Sju essäer om symbolspråkets roll i matematiken., Stockholm: Santérus Förlag , 2008, s. 127-143Kapittel i bok, del av antologi (Annet (populærvitenskap, debatt, mm))
    Abstract [sv]

       

  • 333.
    Bergsten, Christer
    Linköpings universitet, Utbildningsvetenskap. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    On the influence of theory on research in mathematics education: the case of teaching and learning limits of functions2008Inngår i: ZDM : the international journal on mathematics education, ISSN 1863-9690, Vol. 40, nr 2, s. 189-199Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

     After an introduction on approaches, researh frameworks and theories in mathematics education research, three didactical research studies on limits of functions with different research frameworks are analysed and compared with respect to their theoretical perspectives. It is shown how a chosen research framework defines the world in which the reearch lives, pointing to the difficult but necessary task to compare research results within a common field of study but conducted within different frameworks.

  • 334.
    Bergsten, Christer
    Linköpings universitet, Utbildningsvetenskap. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    The relationships of theory and practice in mathematics education2003Inngår i: CERME 3 Third Conference of the European Society for Research in Mathematics Education,2003, 2003Konferansepaper (Annet vitenskapelig)
  • 335.
    Bergsten, Christer
    Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Trying to reach the limit: The role of algebra in mathematical reasoning2006Inngår i: Proceedings of the 30th conference of the International group for the psychology of mathematics education, vol2 / [ed] J. Novotná, H. Moraová, M. Krátká and N. Stehlíková, Prag: The International Group for the Psychology of Mathematics Education , 2006, s. 153-160Konferansepaper (Annet vitenskapelig)
    Abstract [en]

    In this paper the role of algebra in students- mathematical reasoning about limits of functions in undergraduate mathematics is analysed, considering the students- edu¬cational setting. Data from a video study where six students worked in pairs to solve problems on limits of functions, and an analysis of their calculus lectures, indicate that algebra is at the same time a key and a lock to reach the limit in these problems. This double effect is related to the mathematical organisation taught, as well as the students- sense of authority as internal or external.

  • 336.
    Bergsten, Christer
    Linköpings universitet, Matematiska institutionen. Linköpings universitet, Tekniska högskolan.
    Tvillingcirklar2009Inngår i: Normat - Nordisk matematisk tidskrift, ISSN 0801-3500, Vol. 57, nr 1, s. 22-31Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    This ties with previous articles on the arbelos of Archimedes, but instead of starting with two tangent circles, enclosed in a common tangent circle, no conditions are imposed on the two. We then get two cases, whether the circles intersect or not, and a detailed study is made on the nesuing circles. Much of the motivation for this paper is how the problems can be used to illustrate the power of various dynamic geometry software available on the market since the 80's.

  • 337.
    Bergsten, Christer
    et al.
    Linköpings universitet, Utbildningsvetenskap. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Fransson, Torbjörn
    Växjö universitet.
    Students interacting with an artefact designed to visualise three-dimensional analytic geometry2006Inngår i: CERME - Conference of the European Society for Research in Mathematics Education,2005, Barcelona: Universitat Ramon Llull , 2006, s. 71-Konferansepaper (Fagfellevurdert)
    Abstract [en]

     To investigate students- ways of working with concrete materials in mathematics, a three-dimensional static artefact was constructed and made available to upper secondary students, with pre-knowledge only in two-dimensional coordinate geo¬metry, for solving problems about planes and straight lines in space. Artefact interactivity was generally high, even students also disregarded the model to work only numerically with the coordinates, building on know¬ledge about lines in two dimensions. The model was used when trying to convince other students in the group. 

  • 338.
    Bergsten, Christer
    et al.
    Linköpings universitet, Utbildningsvetenskap. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Grevholm, BarbroHøgskolen i Agder.
    Conceptions of mathematics: proceedings of norma 01 : the 3rd Nordic Conference on Mathematics Education, Kristianstad, June 8-12, 20012005Collection/Antologi (Annet vitenskapelig)
    Abstract [en]

     Proceedings of Norma01, Third Nordic Conference on Mathematics Education, Kristianstad 2001

  • 339.
    Bergsten, Christer
    et al.
    Linköpings universitet, Utbildningsvetenskap. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Grevholm, BarbroUniversitetet i Agder.
    Developing and researching quality in mathematics teaching and learning2007Collection/Antologi (Fagfellevurdert)
  • 340.
    Bergsten, Christer
    et al.
    Linköpings universitet, Utbildningsvetenskap. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Grevholm, Barbro
    Knowledgeable teacher educators and linking practices2008Inngår i: The International Handbook of mathematics Teacher Education, Volume 4: The Mathematics Teacher Educator as a Developing Professional / [ed] Barbara Jaworski and Terry Woods, Rotterdam: Sense Publishers , 2008, 1, s. 221-246Kapittel i bok, del av antologi (Annet vitenskapelig)
    Abstract [en]

    The Handbook of Mathematics Teacher Education, the first of its kind, addresses the learning of mathematics teachers at all levels of schooling to teach mathematics, and the provision of activity and programmes in which this learning can take place. It consists of four volumes. Volume 4 of this handbook has the title The Mathematics Teacher Educator as a Developing Professional. The volume seeks to complement the other three volumes by focusing on knowledge and roles of teacher educators working with teachers in teacher education processes and practices. In this respect it is unique. Chapter authors represent a community of teacher educators world wide who can speak from practical, professional and theoretical viewpoints about what it means to promote teacher education practice. The volume is in 3 main sections. In the first we focus on Challenges to and Theory in Mathematics Teacher Education. Here authors write from perspectives of theory and/or challenge and relate this to examples and insights from their practice. The second section, Reflection On Developing as a Mathematics Teacher Educator has four autobiographical chapters in which authors delineate their experiences as teacher educators and relate these to theoretical and/or moral standpoints. In Section 3, Working With Prospective and Practising Teachers: What We Learn; What We Come to Know, authors write from perspectives on practice - in many cases, the practices in which they themselves have engaged - and relate this to theoretical perspectives and rationales for teacher education programmes. The volume also has an introductory chapter in which the purpose and content of the volume is set out, and a final chapter that syntheses themes and issues from the chapters as a whole, offering an overview of the field and suggesting future directions. Bibliographical Information for the complete set: VOLUME 1: Knowledge and Beliefs in Mathematics Teaching and Teaching Development Peter Sullivan, Monash University, Clayton, Australia and Terry Wood, Purdue University, West Lafayette, USA (eds.) paperback: 978-90-8790-541-5, hardback: 978-90-8790-542-2, ebook: 978-90-8790-543-9 VOLUME 2: Tools and Processes in Mathematics Teacher Education Dina Tirosh, Tel Aviv University, Israel and Terry Wood, Purdue University, West Lafayette, USA (eds.) paperback: 978-90-8790-544-6, hardback: 978-90-8790-545-3, ebook: 978-90-8790-546-0 VOLUME 3: Participants in Mathematics Teacher Education: Individuals, Teams, Communities and Networks Konrad Krainer, University of Klagenfurt, Austria and Terry Wood, Purdue University, West Lafayette, USA (eds.) paperback: 978-90-8790-547-7, hardback: 978-90-8790-548-4, ebook: 978-90-8790-549-1 VOLUME 4: The Mathematics Teacher Educator as a Developing Professional Barbara Jaworski, Loughborough University, UK and Terry Wood, Purdue University, West Lafayette, USA (eds.) paperback: 978-90-8790-550-7, hardback: 978-90-8790-551-4, ebook: 978-90-8790-552-1

  • 341.
    Bergsten, Christer
    et al.
    Linköpings universitet, Utbildningsvetenskap. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Grevholm, BarbroHøgskolen i Agder.
    Mathematics and language: proceedings of MADIF 4 : the 4th Swedish Mathematics Education Research Seminar, Malmö, January 21-22, 20042004Collection/Antologi (Annet vitenskapelig)
    Abstract [en]

     Proceedings of the 4th Swedish Mathematics Education Research Seminar, Malmö 2004 

  • 342.
    Bergsten, Christer
    et al.
    Linköpings universitet, Utbildningsvetenskap. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Grevholm, Barbro
    Realfag Høgskolen i Agder.
    The didactic divide and the education of teachers of mathematics in Sweden2004Inngår i: Nordisk matematikkdidaktikk, ISSN 1104-2176, Vol. 9, nr 2, s. 123-144Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    On a background of tradition versus renewal, a discussion on recent teacher education reforms in Sweden is given. A balance of different aspects of content and a need for research are seen as critical for the formation of mathematics teacher education. A conception of a -didactic divide- between disciplinary and pedagogical knowledge is used as an analytic tool to describe the rationale behind the design of the reforms. Empirical data from student teachers enrolled in the new teacher education programme highlight how the structure and content of the programme contribute to overcoming the divide.

  • 343.
    Bergsten, Christer
    et al.
    Linköpings universitet, Utbildningsvetenskap. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Grevholm, Barbro
    Favilli, Franco
    Learning to teach mathematics: expanding the role of practicum as an integrated part of a teacher education programme2009Inngår i: The professional education and development of teachers of mathematics. The 15th ICMI Study, New York: Springer , 2009, 1, s. 57-70Kapittel i bok, del av antologi (Annet vitenskapelig)
    Abstract [en]

    The premise of the 15th ICMI Study is that teachers are key to students' opportunities to learn mathematics. What teachers of mathematics know, care about, and do is a product of their experiences and socialization, together with the impact of their professional education. The Professional Education and Development of Teachers of Mathematics assembles important new international work- development, research, theory and practice - concerning the professional education of teachers of mathematics. As it examines critical areas to reveal what is known and what significant questions and problems warrant collective attention, the volume also contributes to the strengthening of the international community of mathematics educators. The Professional Education and Development of Teachers of Mathematics is of interest to the mathematics education community as well as to other researchers, practitioners and policy makers concerned with the professional education of teachers.

  • 344.
    Bergsten, Christer
    et al.
    Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Grevholm, BarbroUniversitetet i Agder.Strömskag Måsöval, HeidiSör-Tröndelag University College.Rönning, FrodeSör-Tröndelag University College.
    Relating practice and reserch in mathematics education: Proceedings of the Fourth Nordic Conference on Mathematics Education2007Collection/Antologi (Annet vitenskapelig)
  • 345.
    Bergsten, Christer
    et al.
    Linköpings universitet, Utbildningsvetenskap. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Lennerstad, Håkan
    Matematiska språk. Sju essäer om symbolspråkets roll i matematiken2008Collection/Antologi (Annet vitenskapelig)
    Abstract [sv]

    Språk är ytterst centralt för oss människor i nästan allt vi gör. Hur är förhåller sig matematik till språk? Man kan med fog hävda att matematik är ett ämne med ett stort antal språkliga sidor. I denna bok tar sju personer från skilda områden upp matematikens språkligheter ur sina respektive perspektiv. Resultatet är ett brett och fascinerande landskap, där matematik som rent räknande är en smal och porlande rännil.Författarna som beskriver sin syn på matematikens språkliga kvaliteter är: Christer Kiselman, professor i matematik, Uppsala universitet; Håkan Lennerstad, docent i tillämpad matematik, Blekinge Tekniska högskola; Lars Mouwitz, matematiklärare och doktor i teknologi och yrkeskunnande, Nationellt Centrum för Matematikutbildning, Göteborg; Madeleine Löwing, doktor i matematikdidaktik, Göteborgs universitet; Bo Göranzon, professor i yrkeskunnande och teknologi, Kungliga Tekniska Högskolan, KTH i Stockholm; Östen Dahl, professor i lingvistik, Stockholms universitet; Christer Bergsten, docent i matematikdidaktik, Linköpings universitet

  • 346.
    Bergstrand, Frida
    et al.
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning.
    Nguyen, Ngan
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning.
    Bakgrundsvariablers påverkan på enkätsvaren i en telefonintervju: En studie om effekt av intervjuarens, respondentens och intervjuns egenskaper2017Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
    Abstract [en]

    Norstat recurrently performs a survey that contains questions about how much the respondent is watching different tv-channels, how different media-devices are used, the ownership of different devices and the usage of different tv-channel sites on the internet, social media, internet services, magazine services and streaming services. In this thesis, data from the survey performed during the autumn of 2016 was used. The aim of this thesis is to examine if there is a difference in answers based on different characteristics of the interviewers and respondents. 

    The 15 most important questions from the survey were chosen in this thesis, and to further reduce the number of response variables principal component analysis was used. The new scores that were produced by the analysis were the reduced response variables, which kept the most important information from the questions in the survey. Thereafter multilevel analyses and regression analyses were performed to examine the effects.  

    The results showed that there was an effect of different characteristics in different questions in the survey. The characteristics that showed effect were the age of the interviewer, the length of the employment, the age of the respondent, education, sex and native language. Some of the questions also showed effect based on whether the respondent lived in a metropolitan region or not.

    Fulltekst (pdf)
    fulltext
  • 347.
    Berntsson, Fredrik
    Linköpings universitet, Matematiska institutionen. Linköpings universitet, Tekniska högskolan.
    A spectral method for solving the sideways heat equation1999Inngår i: Inverse Problems, ISSN 0266-5611, E-ISSN 1361-6420, Vol. 15, nr 4, s. 891-906Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We consider an inverse heat conduction problem, the sideways heat equation, which is the model of a problem where one wants to determine the temperature on the surface of a body, using interior measurements. Mathematically it can be formulated as a Cauchy problem for the heat equation, where the data are given along the line x = 1, and a solution is sought in the interval 0 ≤ x < 1.

    The problem is ill-posed, in the sense that the solution does not depend continuously on the data. Continuous dependence of the data is restored by replacing the time derivative in the heat equation with a bounded spectral-based approximation. The cut-off level in the spectral approximation acts as a regularization parameter. Error estimates for the regularized solution are derived and a procedure for selecting an appropriate regularization parameter is given. The discretized problem is an initial value problem for an ordinary differential equation in the space variable, which can be solved using standard numerical methods, for example a Runge-Kutta method. As test problems we take equations with constant and variable coefficients.

  • 348.
    Berntsson, Fredrik
    Linköpings universitet, Matematiska institutionen, Beräkningsvetenskap. Linköpings universitet, Tekniska högskolan.
    A survey of methods for determinig surface temperatures using interior measurements2001Inngår i: Trends in Heat, Mass & Momentum Transfer, ISSN 0973-2446, Vol. 7, nr pp, s. 105-128Artikkel i tidsskrift (Fagfellevurdert)
  • 349.
    Berntsson, Fredrik
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska högskolan.
    An Inverse Heat Conduction Problem and Improving Shielded Thermocouple Accuracy2012Inngår i: Numerical Heat Transfer, Part A Applications, ISSN 1040-7782, E-ISSN 1521-0634, Vol. 61, nr 10, s. 754-763Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A shielded thermocouple is a measurement device used for monitoring the temperature in chemically, or mechanically, hostile environments. The sensitive parts of the thermocouple are protected by a shielding layer. In order to improve the accuracy of the measurement device, we study an inverse heat conduction problem where the temperature on the surface of the shielding layer is sought, given measured temperatures in the interior of the thermocouple. The procedure is well suited for real-time applications where newly collected data is continuously used to compute current estimates of the surface temperature. Mathematically we can formulate the problem as a Cauchy problem for the heat equation, in cylindrical coordinates, where data is given along the line r = r 1 and the solution is sought at r 1 < r ≤ r 2. The problem is ill-posed, in the sense that the solution (if it exists) does not depend continuously on the data. Thus, regularization techniques are needed. The ill–posedness of the problem is analyzed and a numerical method is proposed. Numerical experiments demonstrate that the proposed method works well.

  • 350.
    Berntsson, Fredrik
    Linköpings universitet, Matematiska institutionen, Beräkningsvetenskap. Linköpings universitet, Tekniska högskolan.
    Numerical Methods for an Inverse Heat Conduction Problem1998Konferansepaper (Annet vitenskapelig)
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