| 1. |
- Levenson, Esther, et al.
(författare)
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Young children's aesthetic development in the context of mathematical explanation
- 2017
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Ingår i: Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education (CERME10). - Dublin : Dublin City University. - 9781873769737 ; , s. 1861-1868
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Konferensbidrag (refereegranskat)abstract
- Mathematicians routinely report that beauty is both a reward and a motivation for the work they do. However, how and to what extent children can appreciate mathematical beauty is an open question. This exploratory study looks at young children (ages 6-12, with a focus on the younger years) as they evaluate different explanations of claims about even numbers and triangular numbers. While our results are fairly speculative, we provide case studies which illustrate possible kinds of aesthetic reactions, and some of the factors which might impact on those reactions.
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| 2. |
- Raman-Sundström, Manya, 1971-
(författare)
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A pedagogical history of compactness
- 2015
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Ingår i: The American mathematical monthly. - : Informa UK Limited. - 0002-9890 .- 1930-0972. ; 122:7, s. 619-635
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Tidskriftsartikel (refereegranskat)abstract
- Compactness is a central notion in advanced mathematics, but we often teach the concept without much historical motivation. This paper fills in many of the gaps left by the standard textbook treatment, including what motivated the definition, how did the definition evolve, and how can compactness be expressed in terms of nets and filters.
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| 3. |
- Raman Sundström, Manya, 1971-
(författare)
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An Exercise on Limits
- 2016
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Ingår i: Journal of Humanistic Mathematics. - : Claremont Colleges Library. - 2159-8118. ; 6:2
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Tidskriftsartikel (populärvet., debatt m.m.)abstract
- A poem about different kinds of limits, not all mathematical.
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| 4. |
- Raman Sundström, Manya, 1971-, et al.
(författare)
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Mathematical fit : A first approximation
- 2015
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Ingår i: Proceedings of the ninth conference of the Euorpean Society for research in Mathermatics education (CERME9). - Prague : Charles University. - 9788072908448 ; , s. 185-191
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Konferensbidrag (refereegranskat)abstract
- We discuss here the notion of mathematical fit, a concept that might relate to mathematical explanation and mathematical beauty. We specify two kinds of fit a proof can have, intrinsic and extrinsic, and provide characteristics that help distinguish different proofs of the same theorem.
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| 5. |
- Raman-Sundström, Manya, 1971-, et al.
(författare)
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Mathematical fit : a case study
- 2018
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Ingår i: Philosophia mathematica. - Cary : Oxford University Press. - 0031-8019 .- 1744-6406. ; 26:2, s. 184-210
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Tidskriftsartikel (refereegranskat)abstract
- Mathematicians routinely pass judgments on mathematical proofs. A proof might be elegant, cumbersome, beautiful, or awkward. Perhaps the highest praise is that a proof is right, that is that the proof fits the theoremin an optimal way. It is also common to judge that a proof fits better than another, or that a proof does not fit a theorem at all. This paper attempts to clarify the notion of mathematical fit. We suggest six criteria that distinguish proofs as being more or less fitting, and provide examples from several different mathematical fields.
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| 6. |
- Raman-Sundström, Manya, 1971-, et al.
(författare)
-
The Nature and Experience of Mathematical Beauty
- 2016. - 1
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Ingår i: Journal of Humanistic Mathematics. - Claremont, CA, USA : Claremont Colleges Library. - 2159-8118. ; 6:1, s. 3-7
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Tidskriftsartikel (refereegranskat)
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| 7. |
- Raman Sundström, Manya, 1971-
(författare)
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The Notion of Fit as a Mathematical Value
- 2016
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Ingår i: Mathematical Cultures. - Basel : Birkhäuser Verlag. - 9783319285825 ; , s. 271-285
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Bokkapitel (refereegranskat)abstract
- Fit, or the lack of it, might occur in a large number of different settings, from visual art, to music, to relationships between people, and so on. This paper explores the metaphor of beauty as fit as it occurs in mathematics. The central claim is that, be it instantiated in the relationship of a type of tree to its natural shape or of a particular proof to a theorem, fit is what brings about the feeling that that tree or that theorem is beautiful. The greater the degree of fit, the greater our sense of beauty (given that we have the requisite understanding to appreciate the fit.) This claim will not be fully defended, but we will set up some ground work for doing so. In particular, the paper will illustrate two distinct types of fit in mathematics via contrasting examples of proofs typically held to be beautiful or not beautiful.
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| 8. |
- Raman-Sundström, Manya
(författare)
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The Notion of Fit as a Mathematical Value
- 2016
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Ingår i: MATHEMATICAL CULTURES. - Cham : BIRKHAUSER VERLAG AG. - 9783319285825 - 9783319285801 ; , s. 271-285
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Konferensbidrag (refereegranskat)
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| 9. |
- Sundstrom, Manya Raman
(författare)
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Seduced by the beauty of mathematics
- 2015
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Ingår i: New scientist (1971). - 0262-4079. ; 225:3006, s. 26-27
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)
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