Time and Place: Sustaining the American Mathematical Community

2015 ◽  
pp. 177-190
Author(s):  
Della Dumbaugh
Keyword(s):  
Mathematical Community

scholarly journals On known and less known relations of Leonhard Euler with Poland

2016 ◽  
Vol 15 ◽  
pp. 75-110
Author(s):  
Roman Sznajder ◽  
Keyword(s):  
Graph Theory ◽  
18Th Century ◽  
Mathematical Community ◽  
Geometric Interpretation ◽  
European Countries ◽  
Complex Numbers ◽  
And Topology ◽  
Bridge Problem ◽  
Leonhard Euler ◽  
The City

In this work we focus on research contacts of Leonhard Euler with Polish scientists of his era, mainly with those from the city of Gdańsk (then Gedanum, Danzig). L. Euler was the most prolific mathematician of all times, the most outstanding mathematician of the 18th century, and one of the best ever. The complete edition of his manuscripts is still in process (Kleinert 2015; Kleinert, Mattmüller 2007). Euler’s contacts with French, German, Russian, and Swiss scientists have been widely known, while relations with Poland, then one of the largest European countries, are still in oblivion. Euler visited Poland only once, in June of 1766, on his way back from Berlin to St. Petersburg. He was hosted for ten days in Warsaw by Stanisław II August Poniatowski, the last king of Poland. Many Polish scientists were introduced to Euler, not only from mathematical circles, but also astronomers and geographers. The correspondence of Euler with Gdańsk scientists and officials, including Carl L. Ehler, Heinrich Kühn and Nathanael M. von Wolf, originated already in the mid-1730s. We highlight the relations of L. Euler with H. Kühn, a professor of mathematics at the Danzig Academic Gymnasium and arguably the best Polish mathematician of his era. It was H. Kühn from whom Euler learned about the Königsberg Bridge Problem; hence one can argue that the beginning of the graph theory and topology of the plane originated in Gdańsk. In addition, H. Kühn was the first mathematician who proposed a geometric interpretation of complex numbers, the theme very much appreciated by Euler. Findings included in this paper are either unknown or little known to a general mathematical community.

Sometimes Less is More

2013 ◽  
pp. 12-36
Author(s):  
Karen Keene ◽  
Chris Rasmussen
Keyword(s):  
Differential Equations ◽  
Communities Of Practice ◽  
Mathematics Classroom ◽  
Tangent Vector ◽  
Classroom Community ◽  
Mathematical Community ◽  
Boundary Objects ◽  
Boundary Object ◽  
Mathematical Activity ◽  
First Semester

As described in the communities of practice literature (Lave & Wenger, 1991; Wenger, 1998), boundary objects are material things that interface two or more communities of practice. Extending this, Hoyles, Noss, Kent, and Bakker (2010) defined technology-enhanced boundary objects as, “software tools that adapt or extend symbolic artefacts identified from existing work practice, that are intended to act as boundary objects, for the purposes of employees’ learning and enhancing workplace communication” (p. 17). The authors adapt this idea to the undergraduate mathematics classroom and use the phrase “classroom technology-enhanced boundary object” to refer to a piece of software that acts as a boundary object between the classroom community and the mathematical community. They provide three extended examples of these objects as used in a first semester differential equations classroom to illustrate how students’ mathematical activity may advance as they interact with the software. These examples show how the applets operate to provide a way for the classroom community to implicitly encounter the mathematical community through the authentic practices of mathematics (Rasmussen, Zandieh, King, & Teppo, 2005). The first example centers on students beginning experience with a tangent vector field applet. The second example develops as the students learn more about solutions to differential equations and leads to a statement of the uniqueness theorem. In the third example, students use a specially designed applet that creates a numerical approximation and its associated image in 3-space relating to a non-technological visualization task that introduces solutions to systems of differential equations.

scholarly journals Non Smooth Contact Dynamics Approach for Mechanical Systems Subjected to Friction-Induced Vibration

Lubricants ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 59 ◽  
Author(s):  
Jean-Jacques Sinou ◽  
Olivier Chiello ◽  
Lucien Charroyer
Keyword(s):  
Mechanical Systems ◽  
Mathematical Community ◽  
Contact Dynamics ◽  
Strong Impact ◽  
Brake Squeal ◽  
Excited Vibration ◽  
Smooth Contact ◽  
Frictional Interface ◽  
The Stability ◽  
Friction Induced Vibration

The modeling of contact is one of the main features of contact dynamics in the context of friction-induced vibrations. It can have a strong impact on the numerical results and consequently on the design choices during the optimization or specification of industrial mechanical systems. This is particularly the case for scientific studies interested in brake squeal. The objective of the paper is to recall and to promote developments concerning the use of non smooth contact dynamics approach for numerical simulations based on finite element method. The specific problem of the prediction of self-excited vibration in the context of brake squeal is discussed. In order to illustrate the potential benefit for the mechanical community of using formulations and theoretical developments from the mathematical community, the stability analysis and the estimation of nonlinear vibrations of a brake system with multiple frictional interface is investigated.

scholarly journals Social science students’ concept images and concept definitions of anti-derivatives

Pythagoras ◽  
2019 ◽  
Vol 40 (1) ◽  
Author(s):  
Eunice K. Moru ◽  
Makomosela Qhobela
Keyword(s):  
Social Science ◽  
Mathematical Community ◽  
Concept Image ◽  
Science Students ◽  
Mathematical Concepts ◽  
Concept Definition ◽  
Concept Images ◽  
The Social ◽  
Mathematics Educators ◽  
Reported Study

The purpose of the reported study was to investigate the social science students’ concept images and concept definitions of anti-derivatives. Data were collected through asking students to answer 10 questions related to anti-derivatives and also by interviewing them. The theory of concept image and concept definition was used for data analysis. The results of the study show that the students’ definitions of anti-derivatives were personal reconstructions of the formal definition. Their concept images were coherent only to a certain extent as there were some conceptions of some ideas that were at variance with those of the mathematical community. These were more evident when students solved problems in the algebraic representation. Some students did not know which integration or differentiation methods they should apply in solving the problems. The significance of such findings is to enable the mathematics educators to pay attention not only to the use of signs and symbols representing mathematical concepts but also to their semantics.

School-College Relationships

1968 ◽  
Vol 15 (5) ◽  
pp. 447-449
Author(s):  
David M. Clarkson
Keyword(s):  
Elementary School Teachers ◽  
Elementary Mathematics ◽  
Mathematical Community ◽  
School Mathematics ◽  
Focused Attention ◽  
Schools Of Education ◽  
School Teachers ◽  
Teachers Colleges ◽  
Course Content ◽  
The Past

During the past decade the mathematical community has been prolific in offering advice to teachers colleges and schools of education concerning the preservice and in-service education of elementary mathematics teachers. Their recommendations, most notably those of the CUPM (Prepararion in Mathematics for Elementary School Teachers [rev. ed.; MAA, 1966]) and the Cambridge Conference on School Mathematics (Goals for School Mathematics [Houghton Mifflin, 1967]), have focused attention on the course content in mathematics currently offered new and senior teachers. It is, perhaps, unfortunate that these committees of mathematicians have not looked more deeply into the rather complex business of teaching mathematical ideas to young children, particularly since the effect of their recommendations so far has been less than overwhelmingly satisfactory.

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