The purpose of this talk is to present an (apparently) new way to look at the intersection complex of a singular variety over a finite field, or, more generally, at the intermediate extension functor on pure perverse sheaves, and an application of this to the cohomology of noncompact Shimura varieties.

pdf/proceedings-of-the-international-congress-of-mathematicians-32epad3tqi.pdf

Proceedings of the International Congress of Mathematicians

This review of the introductory instructional substance of functions and graphs analyzes research on the interpretation and construction tasks associated with functions and some of their representations: algebraic, tabular, and graphical. The review also analyzes the nature of learning in terms of intuitions and misconceptions, and the plausible approaches to teaching through sequences, explanations, and examples. The topic is significant because of (a) the increased recognition of the organizing power of the concept of functions from middle school mathematics through more advanced topics in high school and college, and (b) the symbolic connections that represent potentials for increased understanding between graphical and algebraic worlds. This is a review of a specific part of the mathematics subject mailer and how it is learned and may be taught; this specificity reflects the issues raised by recent theoretical research concerning how specific context and content contribute to learning and meaning.

https://www.math.ksu.edu/~bennett/onlinehw/qcenter/lzs.pdf

Functions, Graphs, and Graphing: Tasks, Learning, and Teaching

Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education

This article explores the rich heritage of the boundary element method (BEM) by examining its mathematical foundation from the potential theory, boundary value problems, Green's functions, Green's identities, to Fredholm integral equations. The 18th to 20th century mathematicians, whose contributions were key to the theoretical development, are honored with short biographies. The origin of the numerical implementation of boundary integral equations can be traced to the 1960s, when the electronic computers had become available. The full emergence of the numerical technique known as the boundary element method occurred in the late 1970s. This article reviews the early history of the boundary element method up to the late 1970s.

https://www.olemiss.edu/sciencenet/benet/05eabeb.pdf

Heritage and early history of the boundary element method

The logical structure of the world

(1974). Is Mathematical Truth Time-Dependent? The American Mathematical Monthly: Vol. 81, No. 4, pp. 354-365.

/pdf/is-mathematical-truth-time-dependent-4td07uw6m9.pdf

Is Mathematical Truth Time-Dependent?

Great moments in mathematics (after 1650)

First the derivative was used, then discovered, explored and developed, and only then, defined.

/pdf/the-changing-concept-of-change-the-derivative-from-fermat-to-ugnyflharu.pdf

The Changing Concept of Change: The Derivative from Fermat to Weierstrass

1. INTRODUCTION. Eighteenth-century Scotland was an internationally-recog- nized center of knowledge, "a modern Athens in the eyes of an enlightened world." (74, p. 40) (81) The importance of science, of the city of Edinburgh, and of the universities in the Scottish Enlightenment has often been recounted. Yet a key figure, Colin Maclaurin (1698-1746), has not been highly rated. It has become a commonplace not only that Maclaurin did little to advance the calculus, but that he did much to retard mathematics in Britain although he had (fortunately) no influence on the Continent. Standard histories have viewed Maclaurin's major mathematical work, the two-volume Treatise of Fluxions of 1742, as an unread monument to ancient geometry and as a roadblock to progress in analysis. Nowadays, few people read the Treatise of Fluxions. Much of the literature on the history of the calculus in the eighteenth and nineteenth centuries implies that few people read it in 1742 either, and that it marked the end the dead end of the We will show that Maclaurin's Treatise of Fluxions did develop important ideas and techniques and that it did influence the mainstream of mathematics. The Newtonian tradition in calculus did not come to an end in Maclaurin's Britain. Instead, Maclaurin's Treatise served to transmit Newtonian ideas in calculus, improved and expanded, to the Continent. We will look at what these ideas were, what Maclaurin did with them, and what happened to this work aftetwards. Then, we will ask what by then should be an interesting question: why has Maclaurin's role been so consistently underrated? These questions will involve general matters of history and histortcal writing as well as the development of mathematics, and will illustrate the inseparability of the external and internal approaches in under- standing the history of science. 2. THE STANDARI) PICTURE. Let us begin by reviewing the standard story about Maclaurin and his Treatise of Fluxions. The calculus was invented indepen- dently by Newton and Leibniz in the late seventeenth century. Newton and Leibniz developed general concepts-differential and integral for Leibniz, fluxion and fluent for Newton and devised notation that made it easy to use these concepts. Also, they found and proved what we now call the Fundamental Theorem of Calculus, which related the two main concepts. Last but not least, they successfully applied their ideas and techniques to a wide range of important problems.

/pdf/was-newton-s-calculus-a-dead-end-the-continental-influence-3ex1z530ih.pdf

Was Newton’s Calculus a Dead End? The Continental Influence of Maclaurin’s Treatise of Fluxions

The calculus as algebra : J.-L. Lagrange, 1736-1813

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