“Cultures as Toolboxes”: An Introduction to the Special Issue Focused on STEM

The Journal of Multicultural Affairs welcomes Dr. Anita Bright as a guest editor to lead a special issue on Science, Engineering, Technology, and Mathematics (STEM). Dr. Bright centers this special issue around one particularly simple, yet complex question, Is the teaching of science, technology, engineering, and mathematics multicultural

When is .999... less than 1?

We examine alternative interpretations of the symbol described as nought, point, nine recurring. Is "an infinite number of 9s" merely a figure of speech? How are such alternative interpretations related to infinite cardinalities? How are they expressed in Lightstone's "semicolon" notation? Is it possible to choose a canonical alternative interpretation? Should unital evaluation of the symbol .999 . . . be inculcated in a pre-limit teaching environment? The problem of the unital evaluation is hereby examined from the pre-R, pre-lim viewpoint of the student.Comment: 28 page

On Constructive Axiomatic Method

In this last version of the paper one may find a critical overview of some recent philosophical literature on Axiomatic Method and Genetic Method.Comment: 25 pages, no figure

A non-standard analysis of a cultural icon: The case of Paul Halmos

We examine Paul Halmos' comments on category theory, Dedekind cuts, devil worship, logic, and Robinson's infinitesimals. Halmos' scepticism about category theory derives from his philosophical position of naive set-theoretic realism. In the words of an MAA biography, Halmos thought that mathematics is "certainty" and "architecture" yet 20th century logic teaches us is that mathematics is full of uncertainty or more precisely incompleteness. If the term architecture meant to imply that mathematics is one great solid castle, then modern logic tends to teach us the opposite lession, namely that the castle is floating in midair. Halmos' realism tends to color his judgment of purely scientific aspects of logic and the way it is practiced and applied. He often expressed distaste for nonstandard models, and made a sustained effort to eliminate first-order logic, the logicians' concept of interpretation, and the syntactic vs semantic distinction. He felt that these were vague, and sought to replace them all by his polyadic algebra. Halmos claimed that Robinson's framework is "unnecessary" but Henson and Keisler argue that Robinson's framework allows one to dig deeper into set-theoretic resources than is common in Archimedean mathematics. This can potentially prove theorems not accessible by standard methods, undermining Halmos' criticisms. Keywords: Archimedean axiom; bridge between discrete and continuous mathematics; hyperreals; incomparable quantities; indispensability; infinity; mathematical realism; Robinson.Comment: 15 pages, to appear in Logica Universali

The Texas Mathematics Teachers' Bulletin, Volume XI, No. 1, edited by C.D. Rice

CONTENTS: Foreword by Editor (p.5) -- Algebra by T. U. Taylor (p.7) -- The Transition from High School to College by C. D. Rice (p.9) -- Learning to Talk by J. W. Calhoun (p.12) -- To Prospective Secondary School Teachers From Brown University (p.14) -- The German Gymnasium by C.D. Rice (p.16