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  • 1.
    Bengmark, Samuel
    et al.
    Matematiska vetenskaper, Chalmers och Göteborgs universitet..
    Thunberg, Hans
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Winberg, Mikael
    Institutionen för naturvetenskapernas och matematikens didaktik, Umeå universitet.
    Success-factors in transition to university mathematics2017In: International journal of mathematical education in science and technology, ISSN 0020-739X, E-ISSN 1464-5211Article in journal (Refereed)
    Abstract [en]

    This study examines different factors' relative importance for students' performance in the transition to university mathematics. Students' characteristics (motivation, actions and beliefs) were measured when entering the university and at the end of the first year. Principal component analysis revealed four important constructs: Self-efficacy, Motivation type, Study habits and Views of mathematics. Subsequently, orthogonal partial least squares (OPLS) analysis was used for measuring the constructs' ability to predict students' university mathematics grades. No individual constructs measured at the time of entrance predicted more than 5% of the variation. On the other hand, jointly they predicted 14%, which is almost in pair with upper secondary grades predicting 17%. Constructs measured at the end of the first year were stronger predictors, jointly predicting 37% of the variation in university grades, with Self-efficacy (21%) and Motivation (12%) being the two strongest individual predictors. In general, Study habits were not important for predicting university achievement. However, for students with low upper secondary grades, the textbook and interaction with peers, rather than internet-based resources, contributed positively to achievement. The association between Views of mathematics and performance was weak for all groups and non-existing for students with low grades.

  • 2. Lindstrom, Torsten
    et al.
    Thunberg, Hans
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    An elementary approach to dynamics and bifurcations of skew tent maps2008In: Journal of difference equations and applications (Print), ISSN 1023-6198, E-ISSN 1563-5120, Vol. 14, no 8, p. 819-833Article in journal (Refereed)
    Abstract [en]

    In this paper, the dynamics of skew tent maps are classified in terms of two bifurcation parameters. In time series analysis such maps are usually referred to as continuous threshold autoregressive models (TAR(1)-models) after Tong (Non-Linear Time Series, Clarendon Press, Oxford, UK, 1990). This study contains results simplifying the use of TAR(1)-models considerably, e.g. if a periodic attractor exists it is unique. On the other hand, we also claim that care must be exercised when TAR models are used. In fact, they possess a very special type of dynamical pattern with respect to the bifurcation parameters and their transition to chaos is far from standard.

  • 3.
    Thunberg, Hans
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    A recycled characterization of kneading sequences1999In: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, ISSN 0218-1274, Vol. 9, no 9, p. 1883-1887Article in journal (Refereed)
    Abstract [en]

    For any infinite sequence E on two symbols one can define two sequences of positive integers S(E) (the splitting times) and T(E) (the cosplitting times), which each describe the self-replicative structure of E. If E is the kneading sequence of a unimodal map, it is known that S(E) and T(E) carry a lot of information on the dynamics, and that they are disjoint. We show the reverse implication: A nonperiodic sequence E is the kneading sequence of some unimodal map if the sequences S(E) and T(E) are disjoint.

  • 4.
    Thunberg, Hans
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Absolutely continuous invariant measures and superstable periodic orbits: weak*-convergence of natural measures1993Report (Other academic)
  • 5.
    Thunberg, Hans
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Abundance of chaos in one-dimensional population dynamics1999In: International Conference on Differential Equations, Berlin 1999 / [ed] Fiedler B., Gröger K. & Sprekels J., World Scientific, 1999, Vol. 2Conference paper (Refereed)
    Abstract [en]

    We show that strongly chaotic maps appera with poitive frequency in parameter space within both the Ricker family and the Hassel family.

  • 6.
    Thunberg, Hans
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Feigenbaum Numbers for Certain Flat-Top Families1994In: Experimental Mathematics, ISSN 1058-6458, E-ISSN 1944-950X, Vol. 3, no 1, p. 51-57Article in journal (Refereed)
  • 7.
    Thunberg, Hans
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Matematiska perspektiv på musik - tankar kring "Formalized Music"1999In: Nutida Musik, ISSN 1652-6082, Vol. 40, no 3, p. 8-17Article in journal (Other (popular science, discussion, etc.))
    Abstract [sv]

    Om matematiken i tonsättaren Iannsi Xenakis arbete.

  • 8.
    Thunberg, Hans
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    On Approach-Rate Conditions in Unimodal DynamicsManuscript (preprint) (Other academic)
  • 9.
    Thunberg, Hans
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Periodicity versus chaos in certain population models2000In: Stochastic and Chaotic Dynamics in the Lakes: Stochaos / [ed] D. S. Broomhead, E. A. Luchinskaya, P. V. E. McClintock & T. Mullin, American Institute of Physics (AIP), 2000Conference paper (Refereed)
  • 10. Thunberg, Hans
    Periodicity versus chaos in one-dimensional dynamics2001In: SIAM Review, ISSN 0036-1445, E-ISSN 1095-7200, Vol. 43, no 1, p. 3-30Article in journal (Refereed)
    Abstract [en]

    We survey recent results in one-dimensional dynamics and, as an application, we derive rigorous basic dynamical facts for two standard models in population dynamics, the Ricker and the Hassell families. We also informally discuss the concept of chaos in the context of one-dimensional discrete time models. First we use the model case of the quadratic family for an informal exposition. We then review precise generic results before turning to the population models. Our focus is on typical asymptotic behavior, seen for most initial conditions and for large sets of maps. Parameter sets corresponding to different types of attractors are described. In particular it is shown that maps with strong chaotic properties appear with positive frequency in parameter space in our population models. Natural measures (asymptotic distributions) and their stability properties are considered.

  • 11.
    Thunberg, Hans
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Positive exponent in families with flat critical point1999In: Ergodic Theory and Dynamical Systems, ISSN 0143-3857, E-ISSN 1469-4417, Vol. 19, no 3, p. 767-807Article in journal (Refereed)
    Abstract [en]

    It is known that in generic, full unimodal families with a critical point of finite order, there exists a set of positive measure in parameter space such that the corresponding maps have chaotic behaviour. In this paper we prove the corresponding statement for certain families of unimodal maps with flat critical point. One of the key-points is a large deviation argument for sums of ‘almost’ independent random variables with only finitely many moments.

  • 12.
    Thunberg, Hans
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Recurrence of the critical point1993Report (Other academic)
  • 13.
    Thunberg, Hans
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Some Problems in Unimodal Dynamics1996Doctoral thesis, comprehensive summary (Other academic)
  • 14.
    Thunberg, Hans
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Student Teacher-Training in Science and Mathematics: Experiences from a Combined Teacher-Training and Engineering Programme2010In: Teachers of Mathematics: Recruitment and Retention, Professional Identity and Development / [ed] G. Anthony, & B. Grevholm, Svensk förening för MatematikDidaktisk Forskning , 2010Chapter in book (Other academic)
    Abstract [en]

    This paper reports on experiences from a new combined engineering and teacher-training programme, run by The Royal Institute of Technology (KTH) and The Stockholm Institute of Education (LHS) in cooperation. We give a brief description of the structure of the programme, where integration of subject matter, didactics and engineering skills is a key concept. We describe the profile and the expectations of the student group; it seems that this programme to a very large extent has attracted students that do have a wish to work as teachers in science and mathematics, but would have gone for a traditional engineering education in the absence of this new opportunity

  • 15.
    Thunberg, Hans
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Tonsättaren Per Nörgårds ''oändlighetsserie"2013In: Normat, ISSN 0801-3500, Vol. 61, no 1, p. 33-47Article in journal (Refereed)
    Abstract [en]

    This article presents a mathematical description, in terms of recursively defined number sequences, of the algorithms devised by the Danish composer Nørgård. The ambition of the latter was to generate from a very short sequence of tones melodies rich in symmetries and selfsimilarities, melodies which could be aperiodic and hence infinite in length. Given the mathematical presentation a variety of results can be formulated and proved. Note that the well-known Thue-Morse sequence is essentially a special case.

  • 16. Thunberg, Hans
    Unfolding of chaotic unimodal maps and the parameter dependence of natural measures2001In: Nonlinearity, ISSN 0951-7715, E-ISSN 1361-6544, Vol. 14, no 2, p. 323-337Article in journal (Refereed)
    Abstract [en]

    We consider one-parameter families f(a) of interval maps, and discuss the structure in parameter space and the (dis)continuity properties of the natural measure as a function of the parameter near certain strongly chaotic maps (post-critically finite Misiurewicz maps and Benedicks-Carleson maps). In particular, it is shown that the mapping a bar right arrow mu (a) (the natural measure of f(a)) is severely discontinuous at these strongly cli8dtii: maps and is not continuous on any full measure set of parameters in full, generic families. Going in the other direction, it is also shown that if such a chaotic map has a measure for which the critical point is generic, then this measure can be,approximated with measures supported on periodic attractors of nearby maps. The main idea is to construct cascades of post-critically finite Misiurewicz map and cascades of maps with periodic attractors, whose critical oibits reproduce various invariant sets of the unperturbed map. In the special case of the quadratic family, generalizations can be made to any non-renormalizable maps.

  • 17.
    Thunberg, Hans
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Brandell, Gerd
    Lund University.
    Hemmi, Kirsti
    Stockholm University.
    The Widening Gap — A Swedish Perspective2008In: Mathematics Education Research Journal, ISSN 1033-2170, E-ISSN 2211-050X, Vol. 20, no 2, p. 38-56Article in journal (Refereed)
    Abstract [en]

    Transition problems from secondary to tertiary level in mathematics have been arecurrent issue in Sweden. This paper summarises the development during the lastdecades. Results from two recent research studies that illuminate the transitionproblem are presented. The first one, based on empirical data from a major Swedishtechnical university, characterises the widening gap, in content and in approach,between secondary school and first year university courses. The second study dealswith students’ encounters with mathematical proof and is based on a largeinvestigation at another main Swedish university. We discuss the influence on thecurrent transition problems of school reforms and of the great expansion of highereducation in Sweden during the last 10 – 15 years in view of the results from theresearch studies.

  • 18.
    Thunberg, Hans
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Filipsson, Lars
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Aims versus Expectations – a Swedish study of problems related to the transition from secondary to tertiary education in mathematics2008Conference paper (Refereed)
    Abstract [en]

    For a number of years now there has been reports that beginning science and engineering students at Swedish universities are having difficulties in passing their mathematics courses. Several studies involving diagnostic tests given to such students report a decline in student knowledge in areas generally considered to be important prerequisites of university mathematics. In order to describe, understand and explain the situation, we have performed a study involving not only the university perspective but also the perspective of students and secondary school teachers. We pinpoint areas of mathematics that constitute a gap of content, i.e. areas that are not covered in secondary school but nevertheless at university are treated as if they had already been covered. We also find a clash of cultures, i.e. a discrepancy in views of what constitutes important mathematical knowledge. Our method using questionnaires as well as course materials and official documents allows for a detailed description of how the goals of secondary school mathematics education are implemented in classroom practice, and how they compare with the expectations on newcomers in the classroom practice at the university.

  • 19.
    Thunberg, Hans
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Filipsson, Lars
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Cronhjort, Mikael
    KTH, School of Education and Communication in Engineering Science (ECE), Learning.
    Gymnasiets mål och högskolans förväntningar2006In: Nämnaren : tidskrift för matematikundervisning, ISSN 0348-2723, Vol. 33, no 2, p. 10-15Article in journal (Other (popular science, discussion, etc.))
  • 20.
    Thunberg, Hans
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Lingefjärd, Thomas
    Öppet brev till Skolverket: Avancerade räknare - hjälper eller stjälper?,2006In: Nämnaren : tidskrift för matematikundervisning, ISSN 0348-2723, Vol. 33, no 4, p. 10-13Article in journal (Other (popular science, discussion, etc.))
  • 21.
    Thunberg, Hans
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Stadler, Erika
    Bengmark, Samuel
    Winberg, Mikael
    Approaches to Learning Mathematics - Differences Between Beginning and Experienced University Students2013Conference paper (Refereed)
  • 22.
    Thunberg, Hans
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Stadler, Erika
    Linnaeus University.
    Bengmark, Samuel
    Chalmers University of Technology/University of Gothenburg.
    Winberg, Mikael
    Umeå University.
    Novice mathematics students at the university: Experiences, orientations and expectations2012In: Evaluation and comparison of mathematical achievement: Dimensions and perspectives: Proceedings of MADIF8 / [ed] Bergsten, C., Jablonka, E., & Raman, M., Linköping: Svensk förening för MatematikDidaktisk Forskning - SMDF, 2012Conference paper (Refereed)
    Abstract [en]

    In this paper, we report an on-going study of novice university students in mathematics and the secondary-tertiary transition. A total of 146 novice mathematics students from three Swedish universities were given a questionnaire in the beginning of their first semester. The aim was to characterize them as learners of mathematics. The results were summarized with descriptive statistics, and Principal Component Analysis (PCA) was used to look for correlations. The results show that the teacher and the textbook play a crucial role in their learning of mathematics. Furthermore, the students can be characterized as either individual or interactive learners, which relates to students’ grades.

1 - 22 of 22
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