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- Andrén, Lina J., 1980-
(författare)
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On Latin squares and avoidable arrays
- 2010
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis consists of the four papers listed below and a survey of the research area. I Lina J. Andrén: Avoiding (m, m, m)-arrays of order n = 2k II Lina J. Andrén: Avoidability of random arrays III Lina J. Andr´en: Avoidability by Latin squares of arrays with even order IV Lina J. Andrén, Carl Johan Casselgren and Lars-Daniel Öhman: Avoiding arrays of odd order by Latin squares Papers I, III and IV are all concerned with a conjecture by Häggkvist saying that there is a constant c such that for any positive integer n, if m ≤ cn, then for every n × n array A of subsets of {1, . . . , n} such that no cell contains a set of size greater than m, and none of the elements 1, . . . , n belongs to more than m of the sets in any row or any column of A, there is a Latin square L on the symbols 1, . . . , n such that there is no cell in L that contains a symbol that belongs to the set in the corresponding cell of A. Such a Latin square is said to avoid A. In Paper I, the conjecture is proved in the special case of order n = 2k . Paper III improves on the techniques of Paper I, expanding the proof to cover all arrays of even order. Finally, in Paper IV, similar methods are used together with a recoloring theorem to prove the conjecture for all orders. Paper II considers another aspect of the problem by asking to what extent way a deterministic result concerning the existence of Latin squares that avoid certain arrays can be used when the sets in the array are assigned randomly.
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| 2. |
- Bergwall, Andreas, 1972-
(författare)
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Proof-related reasoning in upper secondary mathematics textbooks : Characteristics, comparisons, and conceptualizations
- 2021
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Proofs and proving are difficult to learn and difficult to teach. A common problem is that many students use specific examples as evidence for general statements. Difficulties with proofs are also part of the transition problems that exist between secondary and tertiary schooling in mathematics. As mathematics teaching often follows a textbook, the design of textbooks has been pointed out as one possible cause of the problems, and international textbook research suggests that proofs often have only a marginal place in textbooks.This thesis focuses on proofs and proving in upper secondary mathematics textbooks. It also addresses theoretical and methodological questions about what marks an opportunity to develop proving competence, and which properties of such opportunities are relevant to investigate and characterize. The thesis is based on data from four Swedish and Finnish textbook series for upper secondary school, and focuses on sections on logarithms, primitive functions, definite integrals, and combinatorics. It examines how addressed mathematical principles are justified, and whether the textbooks’ exercises offer opportunities to develop proof-related skills such as formulating and investigating hypotheses, developing and evaluating arguments, identifying and correcting errors, and finding counterexamples.The results show that just over half of the mathematical principles addressed in the analyzed textbook material are justified, and that only half of the justifications are general proofs. Few exercises are proof-related (10%), and those that include reasoning about general cases even fewer. General proofs are more common in the Finnish books, but proof-related tasks are more common and of a more varied nature in the Swedish ones. The most common form of proofs are direct derivations of calculation formulas, while reasoning about existence and uniqueness is unusual, as are contrapositive proofs and proofs by contradiction.Based on the results, explicit suggestions are offered as to what teaching can pay more attention to. For the analysis and design of proof-related activities, a framework consisting of four main categories is proposed: develop a statement, investigate a statement, develop an argument, and investigate an argument. Several properties that such activities may have, regardless of which category they belong to, are discussed. Finally, three areas for future research are suggested: how worked examples can support students’ learning of proof, how textbooks can be designed to stimulate formulation as well as the formal proving of hypotheses, and mapping of differences regarding proof between upper secondary and university textbooks.
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| 3. |
- Ehn, Micael
(författare)
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Modeling Specialization and Division of Labor in Cultural Evolution
- 2011
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Division of labor and division of knowledge are so important and common in society today that it is difficult to imagine a functional society where everyone knows the same things and performs the same tasks. In such a society everyone grows, or gathers, and prepares their own food, makes their own tools, builds their own house, and so on. Cultural evolution is the field of research that studies the creation and diffusion of ideas and societies. It is very uncommon for these studies to take into account the effects of specialization. This thesis will show that specialization is of great importance to cultural evolution. The thesis is divided into two parts: The first is an introduction to studies of specialization and division of labor. The thesis begins with an interdisciplinary survey of the research on division of labor and specialization, including both theoretic and empirical studies. Next is an introduction to modeling specialization and division of labor. This includes a general framework and a number of basic models of different aspects of specialization and division of labor. Part two consists of four papers. The first paper studies the interaction between specialization and cultural cumulation. The second and third papers examine cultural cumulation, specifically the circumstances under which cultural knowledge increases and how cultural knowledge is distributed in the population. The last paper is a mathematical model of how specialization of knowledge (i.e. higher education) leads to social stratification.
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| 4. |
- Ehn, Micael, 1983-
(författare)
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On the causes and effects of specialization : A mathematical approach
- 2009
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Division of labor and division of knowledge are so important andcommon in society today that it is almost impossible to imagine asociety where everyone knows the same things and perform the sametasks. This would be a society where everyone grows, or gathers, andprepares their own food, makes their own tools, builds their ownhouse, and so on. Cultural evolution is the field of research that studies the creationand diffusion of ideas and societies. It is very uncommon for thesestudies to take into account the effects of specialization. Thisthesis will show that specialization is of great importance tocultural evolution. The thesis is divided into three parts: one introduction and two papers. The introduction covers the mathematical models used byeconomists to study the relation between the market and division oflabor. The first paper is an interdisciplinary survey of the researchon division of labor and specialization, including both theoretic andempirical studies. The second paper is a mathematical model of howspecialization of knowledge (i.e. higher education) leads to socialstratification. The model is tested against statistical data fromseveral countries and found to be a good predictor of the differencesin income between people of high and low education.
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| 5. |
- Eriksson, Kimmo, 1967-
(författare)
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Comment on “The Evolution of Cultural Complexity : Not by the Treadmill Alone” by Andersson & Read
- 2016
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Ingår i: Current Anthropology. - 0011-3204 .- 1537-5382. ; 57, s. 275-276
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- At the end of their thoughtful target article, Andersson and Read conclude that formal models of cultural evolution are “useful but must be kept in perspective.” As a mathematician with a great interest in social science, I have some experience of working with such models. Based on this experience, I very much agree with the “but” part of the above conclusion. I see a clear tendency in the cultural evolution literature to put too much trust in the value of formal models.
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| 7. |
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| 8. |
- Eriksson, Kimmo, 1967-, et al.
(författare)
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The available evidence suggests the percent measure should not be used to study inequality : Reply to Norton and Ariely
- 2013
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Ingår i: Judgment and Decision Making. - : Cambridge University Press (CUP). - 1930-2975. ; 8:3, s. 395-396
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- In this reply, we reiterate the main point of our 2012 paper, which was that the measure of inequality used by Norton and Ariely (2011) was too difficult for it to yield meaningful results. We describe additional evidence for this conclusion, and we also challenge the conclusion that political differences in perceived and desired inequality are small.
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| 9. |
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| 10. |
- Eriksson, Kimmo, et al.
(författare)
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Vad vet vi om hyresregleringens effekter?
- 2005
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Ingår i: Ekonomisk Debatt. - 0345-2646. ; :4, s. 31-44
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- Hyresreglering framställs ibland som ett säkert sätt att förstöra en bostadsmarknad och ibland som det som räddar oss från att centrala delar av storstäderna helt tas över av rika hushåll. I denna artikel sammanställs resultaten från ett antal empiriska studier om effekterna av den svenska hyresregleringen på t exbostadsbyggande och segregation. Slutsatsen är att många föreställningar om hyresregleringens negativa såväl som positiva effekter är överdrivna. Det största problemet är att regleringen skapar en svart marknad som blir en grogrund för kriminell verksamhet och som medför att illegala transaktioner uppfattas som mer legitima när de framstår som enda sättet att få tag i bostäder i vissa områden.
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