Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Publication Year
- Publication
- Publication Type
Articles 91 - 97 of 97
Full-Text Articles in Physical Sciences and Mathematics
The Centrality Of Mathematics In The History Of Western Thought, Judith V. Grabiner
The Centrality Of Mathematics In The History Of Western Thought, Judith V. Grabiner
Pitzer Faculty Publications and Research
This article explores the interplay of mathematics and philosophy in Western thought as well as applications to other fields.
The Changing Concept Of Change: The Derivative From Fermat To Weierstrass, Judith V. Grabiner
The Changing Concept Of Change: The Derivative From Fermat To Weierstrass, Judith V. Grabiner
Pitzer Faculty Publications and Research
Historically speaking, there were four steps in the development of today's concept of the derivative, which I list here in chronological order. The derivative was first used; it was then discovered; it was then explored and developed; and it was finally defined. That is, examples of what we now recognize as derivatives first were used on an ad hoc basis in solving particular problems; then the general concept lying behind them these uses was identified (as part of the invention of calculus); then many properties of the derivative were explained and developed in applications both to …
On Multiple Solutions Of Nonlinear Elliptic Equations With Odd Nonlinearities, Alfonso Castro, J. V. A. Gonçalves
On Multiple Solutions Of Nonlinear Elliptic Equations With Odd Nonlinearities, Alfonso Castro, J. V. A. Gonçalves
All HMC Faculty Publications and Research
In this paper we stablish results on multiplicity of solutions for the boundary value problem where a e IR and f: R - IR is an odd continuous function.
Mathematics In America: The First Hundred Years, Judith V. Grabiner
Mathematics In America: The First Hundred Years, Judith V. Grabiner
Pitzer Faculty Publications and Research
There are two main questions I shall discuss in this paper. First, why was American mathematics so weak from 1776 to 1876? Second, and much more important, how did what happened from 1776-1876 produce an American mathematics respectable by international standards by the end of the nineteenth century? We will see that the "weakness" -at least as measured by the paucity of great names- co-existed with the active building both of mathematics education and of a mathematical community which reached maturity in the 1890's.
Multiplicatively Periodic Rings, Ted Chinburg, Melvin Henriksen
Multiplicatively Periodic Rings, Ted Chinburg, Melvin Henriksen
All HMC Faculty Publications and Research
We prove a generalization of Luh's result without using Dirichlet's Theorem. We then use Theorem 1 to show that the J-subrings of a periodic ring form a lattice with respect to join and intersection (the join of two subrings is the smallest subring containing both of them). After noting that every J-ring has nonzero characteristic, we determine for which positive integers n and m there exist J-rings of period n and characteristic m. This generalizes a problem posed by G. Wene.
Is Mathematical Truth Time-Dependent?, Judith V. Grabiner
Is Mathematical Truth Time-Dependent?, Judith V. Grabiner
Pitzer Faculty Publications and Research
Another such mathematical revolution occurred between the eighteenth and nineteenth centuries, and was focused primarily on the calculus. This change was a rejection of the mathematics of powerful techniques and novel results in favor of the mathematics of clear definitions and rigorous proofs. Because this change, however important it may have been for mathematicians themselves, is not often discussed by historians and philosophers, its revolutionary character is not widely understood. In this paper, I shall first try to show that this major change did occur. Then, I shall investigate what brought it about. Once we have done this, we can …
Calculus And The Computer: A Conservative Approach, Melvin Henriksen
Calculus And The Computer: A Conservative Approach, Melvin Henriksen
All HMC Faculty Publications and Research
This paper describes a program for making the use of numerical methods an integral part of the freshman college course in single variable calculus.