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  • 1.
    Heidtmann, Pia
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Mathematics and Science Education.
    Jaldemark, Jimmy
    Mid Sweden University, Faculty of Human Sciences, Department of Education.
    Diskret matematik på distans2018In: Digitalisering av högre utbildning / [ed] Stefan Hrastinski, Lund: Studentlitteratur AB, 2018, p. 215-219Chapter in book (Other academic)
    Abstract [sv]

    I detta kapitel beskrivs en nätbaserad matematikkurs med stödmaterial, såsom datorrättade quiz, diskussionsforum, inspelade föreläsningar och nätbaserade träffar samt nätbaserad examination. Det överordnade målet är att skapa en lärgemenskap. 

  • 2.
    Johansson, Helena
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Mathematics and Science Education.
    Österholm, Magnus
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Mathematics and Science Education.
    Flodén, Liselott
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Mathematics and Science Education.
    Heidtmann, Pia
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Mathematics and Science Education.
    Teachers’ and students’ perception of the gap between secondary and tertiary mathematics2018In: Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education / [ed] Bergqvist, E., Österholm, M., Granberg, C., & Sumpter, L., Umeå, Sweden: PME , 2018, Vol. 5, p. 77-77Conference paper (Refereed)
  • 3.
    Nilson, Tomas
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Science Education and Mathematics.
    Heidtmann, Pia
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Science Education and Mathematics.
    Inner balance of symmetric designs2014In: Designs, Codes and Cryptography, ISSN 0925-1022, E-ISSN 1573-7586, Vol. 71, no 2, p. 247-260Article in journal (Refereed)
    Abstract [en]

    A triple array is a row-column design which carries two balanced incomplete block designs (BIBDs) as substructures. McSorley et al. (Des Codes Cryptogr 35: 21–45, 2005), Section 8, gave one example of a triple array that also carries a third BIBD, formed by its row-column intersections. This triple array was said to be balanced for intersection, and they made a search for more such triple arrays among all potential parameter sets up to some limit. No more examples were found, but some candidates with suitable parameters were suggested. We define the notion of an inner design with respect to a block for a symmetric BIBD and present criteria for when this inner design can be balanced. As triple arrays in the canonical case correspond to SBIBDs, this in turn yields new existence criteria for triple arrays balanced for intersection. In particular, we prove that the residual design of the related SBIBD with respect to the defining block must be quasi-symmetric, and give necessary and sufficient conditions on the intersection numbers. This, together with our parameter bounds enable us to exclude the suggested triple array candidates in McSorley et al. (Des Codes Cryptogr 35: 21–45, 2005) and many others in a wide search. Further we investigate the existence of SBIBDs whose inner designs are balanced with respect to every block. We show as a key result that such SBIBDs must possess the quasi-3 property, and we answer the existence question for all known classes of these designs.

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