By David K. Haley (auth.)
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Extra resources for Equational Compactness in Rings: With Applications to the Theory of Topological Rings
Example text
For the purposes of this paper, I include scientists and engineers within this community, although it is clear that there are important distinctions between these groups. The mathematical research community discourse is structured according to a “logic of discovery” (cf. Popper [ 1959]) stressing the actions of making conjectures and refutations. The characteristic that distinguishes mathematicians from other research communities is their subtle reliance on notions regarding the nature of proof.
Kuhn [1963], p. 358) The “particular way of viewing the world” is the main product of a graduate education. This is in sharp contrast to the particular way of viewing the world that is engendered by the school mathematics curriculum. The process of graduate education brings the student into a particular research community with its own methodology and research program, and its own discourse. There is a continuous process of acculturation that gradually introduces the student to the creative processes of the community.
Kuhn [1963], p. 358) The “particular way of viewing the world” is the main product of a graduate education. This is in sharp contrast to the particular way of viewing the world that is engendered by the school mathematics curriculum. The process of graduate education brings the student into a particular research community with its own methodology and research program, and its own discourse. There is a continuous process of acculturation that gradually introduces the student to the creative processes of the community.