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  • 1.
    Barza, Sorina
    et al.
    Karlstad University, Faculty of Technology and Science, Department of Mathematics.
    Niculescu, N. C.
    Strong and weak weighted norm inequalities for the geometric fractional maximal operator2012In: Bulletin of the Australian Mathematical Society, ISSN 0004-9727, E-ISSN 1755-1633, Vol. 86, no 2, p. 205-215Article in journal (Refereed)
  • 2.
    Gashkov, S. B.
    et al.
    Moscow State University, Russia.
    Gashkov, Igor
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Fast Algorithm of Square Rooting in Some Finite Fields of Odd Characteristic2018In: Moscow University Mathematics Bulletin, ISSN 0027-1322, Vol. 73, no 5, p. 176-181Article in journal (Refereed)
    Abstract [en]

    It was proved that the complexity of square root computation in the Galois field GF(3 (s) ), s = 2 (k) r, is equal to O(M(2 (k) )M(r)k + M(r) log(2) r) + 2 (k) kr (1+o(1)), where M (n) is the complexity of multiplication of polynomials of degree n over fields of characteristics 3. The complexity of multiplication and division in the field GF(3 (s) ) is equal to O(M(2 (k) )M(r)) and O(M(2 (k) )M(r)) + r (1+o(1)), respectively. If the basis in the field GF(3 (r) ) is determined by an irreducible binomial over GF(3) or is an optimal normal basis, then the summands 2 (k) kr (1+o(1)) and r (1+o(1)) can be omitted. For M(n) one may take n log(2) n psi(n) where psi(n) grows slower than any iteration of the logarithm. If k grow and r is fixed, than all the estimates presented here have the form O (r) (M (s) log (2) s) = s (log (2) s)(2) psi(s).

  • 3.
    Jannborg Flyg, Johan
    Karlstad University, Faculty of Arts and Social Sciences (starting 2013).
    Geometri: Varierad undervisning i kreativ anda2015Independent thesis Advanced level (professional degree), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    The purpose of this study is to observe which method that is used when it comes to teaching geometry. The study aims to take a closer look at four different ways of teaching: illustrations, using practical objects, brainstorming and verbal communication. The method used to get the results is observation. With the result, we can deduce primarily that the educators make use of the four didactic methods to varying degrees. There are similarities between most of the teachers but also differences between them. What we can learn from the study is that communication between teacher and student is aimed at ultimate weight and especially the verbal communication. The pattern found is that all the educators are using verbal communication as their primary tool when teaching math.

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