The elements of applied mathematics including kinetics, statics, and hydrostatics.

Mode of access: Internet.

Tables of applied mathematics in finance, insurance, statistics,

Mode of access: Internet.

Structuralism and the Applicability of Mathematics

In this paper I argue for the view that structuralism offers the best perspective for an acceptable account of the applicability of mathematics in the empirical sciences. Structuralism, as I understand it, is the view that mathematics is not the science of a particular type of objects, but of structural properties of arbitrary domains of entities, regardless of whether they are actually existing, merely presupposed or only intentionally intended.

Mathematics, nature and cryptography: Insights from philosophy of information

One influential image that is popular among scientists is the view that mathematics is the language of nature. The present article discusses another possible way to approach the relation between mathematics and nature, which is by using the idea of information and the conceptual vocabulary of cryptography. This approach allows us to understand the possibility that secrets of nature need not be written in mathematics and yet mathematics is necessary as a cryptographic key to unlock these secrets. Various advantages of such a view are described in this article.

Conjecture, proof, and sense in Wittgenstein's philosophy of mathematics

One of the key tenets in Wittgenstein’s philosophy of mathematics is that a mathematical proposition gets its meaning from its proof. This seems to have the paradoxical consequence that a mathematical conjecture has no meaning, or at least not the same meaning that it will have once a proof has been found. Hence, it would appear that a conjecture can never be proven true: for what is proven true must ipso facto be a different proposition from what was only conjectured. Moreover, it would appear impossible that the same mathematical proposition be proven in different ways. — I will consider some of Wittgenstein’s remarks on these issues, and attempt to reconstruct his position in a way that makes it appear less paradoxical.

Applied philosophy of language

This chapter explores the extent to which philosophy of language can be considered an applied discipline. I consider, first, ways in which sub-sections of philosophy of language may be considered as applied in terms of their subject matter and/or the kinds of questions being addressed (e.g. philosophy of language which deals with derogatory or inflammatory uses of language, or the role of philosophy of language within feminist philosophy). Then, in the second part of the chapter, I turn to consider a more general (and perhaps more controversial) conception of philosophy of language as applied, which arises from the methodology adopted and the relationship of the discipline to empirical data.

Pedagogical practices carried out during an in-service teachers education project: approaching history and philosophy of science to physics teaching

We report here part of a research project developed by the Science Education Research Group, titled: "Teachers’ Pedagogical Practices and formative processes in Science and Mathematics Education" which main goal is the development of coordinated research that can generate a set of subsidies for a reflection on the processes of teacher training in Sciences and Mathematics Education. One of the objectives was to develop continuing education activities with Physics teachers, using the History and Philosophy of Science as conductors of the discussions and focus of teaching experiences carried out by them in the classroom. From data collected through a survey among local Science, Physics, Chemistry, Biology and Mathematics teachers in Bauru, a São Paulo State city, we developed a continuing education proposal titled “The History and Philosophy of Science in the Physics teachers’ pedagogical practice”, lasting 40 hours of lessons. We followed the performance of five teachers who participated in activities during the 2008 first semester and were teaching Physics at High School level. They designed proposals for short courses, taking into consideration aspects of History and Philosophy of Science and students’ alternative conceptions. Short courses were applied in real classrooms situations and accompanied by reflection meetings. This is a qualitative research, and treatment of data collected was based on content analysis, according to Bardin [1].

Final report on a survey of training and research in applied mathematics in the United States,

Mode of access: Internet.

The Quarterly journal of pure and applied mathematics.

Published: Longman, Brown, Green, Longman, and Roberts, 1864; Longmans, Green, 1866-1927.

The philosophy of mathematics, with special reference to the elements of geometry and the infinitesimal method,

Mode of access: Internet.