Exceptions and counterexamples: Understanding Abel's comment on Cauchy's Theorem

AbstractIt may seem odd that Abel, a protagonist of Cauchy's new rigor, spoke of “exceptions” when he criticized Cauchy's theorem on the continuity of sums of continuous functions. However, when interpreted contextually, exceptions appear as both valid and viable entities in the early 19th century. First, Abel's use of the term “exception” and the role of the exception in his binomial paper is documented and analyzed. Second, it is suggested how Abel may have acquainted himself with the exception and his use of it in a process denoted critical revision is discussed. Finally, an interpretation of Abel's exception is given that identifies it as a representative example of a more general transition in the understanding of mathematical objects that took place during the period. With this interpretation, exceptions find their place in a fundamental transition during the early 19th century from a formal approach to analysis toward a more conceptual one

Maximal partial Latin cubes

We prove that each maximal partial Latin cube must have more than 29.289% of its cells filled and show by construction that this is a nearly tight bound. We also prove upper and lower bounds on the number of cells containing a fixed symbol in maximal partial Latin cubes and hypercubes, and we use these bounds to determine for small orders n the numbers k for which there exists a maximal partial Latin cube of order n with exactly k entries. Finally, we prove that maximal partial Latin cubes of order n exist of each size from approximately half-full (n3/2 for even n ≥ 10 and (n3 + n)/2 for odd n ≥21) to completely full, except for when either precisely 1 or 2 cells are empty

Stenomusen runder de 60 numre

I anledning af de 60 udgivelser fortæller matematikhistorikeren Henrik Kragh Sørensen, Aarhus Universitet, her om tallet 60

70 – et fuldt liv eller fuld af liv?

I anledning af, at Stenomusen nu runder 70 numre, fortæller professor mso Henrik Kragh Sørensen, Institut for Naturfagenes Didaktik, Københavns Universitet, om dette tal

Observationer, eksperimenter og iagttagelser i videnskab og undervisning

Kommentar til Morten Rask Petersen, Helle Kruse Krossá: Udvikling af elevernes kemiske observationskompetencer, MONA 2019‑

Stenomusen runder et blødt hjørne

Med dette nummer er Stenomusen udkommet i 80 udgaver. I den anledning fortæller en litteraturhistoriker og en matematikhistoriker om tallet 80, spejlsymmetri og matematiske finurligheder

Adapting practice-based philosophy of science to teaching of science students

The “practice turn” in philosophy of science has strengthened the connections between philosophy and scientific practice. Apart from reinvigorating philosophy of science, this also increases the relevance of philosophical research for science, society, and science education. In this paper, we reflect on our extensive experience with teaching mandatory philosophy of science courses to science students from a range of programs at University of Copenhagen. We highlight some of the lessons we have learned in making philosophy of science “fit for teaching” outside of philosophy circles by taking selected cases from the students’ own field as the starting point. We argue for adapting philosophy of science teaching to particular audiences of science students, and discuss the benefits of drawing on research within science education to inform curriculum and course design. This involves reconsidering teaching resources, assumptions about students, intended learning outcomes, and teaching formats. We also argue that to make philosophy of science relevant and engaging to science students, it is important to consider their potential career trajectories. By anticipating future contexts and situations in which methodological, conceptual, and ethical questions could be relevant, philosophy of science can demonstrate its value in the education of science students