Search

Structuralists typically appeal to some variant of the widely popular 'mapping' account of mathematical representation to suggest that mathematics is applied in modern science to represent the world's physical structure. However, in this paper, I argue that this realist interpretation of the 'mapping' account presupposes that physical systems possess an 'assumed structure' that is at odds with modern physical theory. Through two detailed case studies concerning the use of the differential and variational calculus in modern dynamics, I show that the formal structure that we need to assume in order to apply the mapping account is inconsistent with the way in which mathematics is applied in modern physics. The problem is that a realist interpretation of the 'mapping' account imposes too severe of a constraint on the conformity that must exist between mathematics and nature in order for mathematics to represent the structure of a physical system. • This paper presents a critique of the 'mapping' account of mathematical representation. • The 'mapping' account requires that physical systems possess an assumed structure. • This structure is at odds with modern physical theory. • I argue that a realist interpretation of the account imposes a severe constraint on the conformity between math and nature. • The argument is defended through two case studies concerning the differential and variational calculus. [ABSTRACT FROM AUTHOR]

Abstract In this paper we introduce a notion of sensitivity for topological dynamical systems and show some of its basic features and relation to dynamical properties such as transitivity and weak mixing. Finally, we will restrict our attention to the related class of weakly positively expansive dynamical systems. [ABSTRACT FROM AUTHOR]

Padé approximants are rational functions, with a denominator which does not vanish at zero, and whose series expansion match a given series as far as possible. These approximants are usually written under a rational form. In this paper, we will show how to write them also under two different barycentric forms, and under a partial fraction form, depending on free parameters. According to the choice of these parameters, Padé-type approximants can be obtained under a barycentric or a partial fraction form. [ABSTRACT FROM AUTHOR]

• Mathematical Knowledge for Teaching for secondary mathematics teachers. • Design of tasks for pre-service mathematics teachers. • Mathematics as a human activity. This paper describes theoretical design principles emerging from the development of tasks for standard undergraduate mathematics courses that address applications to teaching secondary mathematics. While researchers recognize that mathematical knowledge for teaching is a form of applied mathematics, applications to teaching remain largely absent from curriculum resources for courses for mathematics majors. We developed various materials that contain applications to teaching that have been integrated into four standard undergraduate mathematics courses. Three primary principles influenced the design of the tasks that prepare future teachers to learn and apply mathematics in a manner central to their future work. Additionally, this paper provides guidance for instructors desiring to develop or implement similar applications. The process of developing these tasks underscores the importance of key features regarding the roles of human beings in the tasks, the intentional focus on advanced content connected to school mathematics, and the integration of active engagement strategies. [ABSTRACT FROM AUTHOR]

The authors found a minor incorrect citation (Lemma 3.3) in their above titled paper which should be corrected in this Corrigendum. [ABSTRACT FROM AUTHOR]