On music production in mathematics teacher education as an aesthetic experience

ZDM – Mathematics Education - This paper addresses the integrated use of the arts and digital technology in mathematics education—specifically involving aspects of preservice...     

Computing devices,mathematics education and mathematics: Sexton’s omnimetre in its time

Material objects can tell us much about mathematical practice. In 1899, Albert Sexton, a Philadelphia mechanical engineer, received the John Scott Medal of the Franklin Institute for his invention of the omnimetre. This inexpensive circular slide rule was one of a host of computing devices that became common in the United States around 1900. It is inscribed “NUMERI MUNDUM REGUNT”. In part because of instruments such as the omnimetre, numbers increasingly ruled the practical world of the late 19th and early 20th century. This changed not only engineering, but mathematics education and mathematical work.     

The mathematics of war

During the Desert Storm, the Gulf war, it was possible to read in the newspapers words such as: “Inmathematical terms, was is becoming more and more electronically controlled and, as a result, it is moving away from the battlefield. Then, when war comes down to earth, it becomes bloody, it loses its mathematical asceticism” Reading the newspapers in those days, one had the impression that modern warfare is based on mathematics, as if it were not men but computers that decided where to carry out “surgical operations”. By contrast, the volume published a few years before the Gulf war conceived as a didactic unit to be used in schools with a guide for the teacher with the titleLa matematica della guerra (The Mathematics of War) published by Gruppo Abele in Turin begins with the words “Mathematics, like any other discipline, lends itself to building several paths towards education for peace”. The volume, written by a group of teachers belonging to an anti-violence organisation forming part of the “education for peace” project, highlights the power or ambiguitiy of mathematical models used to simulate war or conflict situations and demonstrates that in some cases the use of mathematics leads to a better understanding of the situation, but in other cases, the mathematical model itself can lead to conclusions which are either wrong or morally unacceptable.     

The emergence of nonlinear programming: interactions between practical mathematics and mathematics proper

Conclusion  It was the duality theorem for linear programming-that is, a purely theoretical result-that sparked the interest of Kuhn and Tucker. It was the duality theory they wanted to extend to the general (quadratic) nonlinear case. It is in this respect that I find the development of the duality theorem in linear programming so crucial for the emergence of nonlinear programming.     

The mathematics of eigenvalue optimization

 Optimization problems involving the eigenvalues of symmetric and nonsymmetric matrices present a fascinating mathematical challenge. Such problems arise often in theory and practice, particularly in engineering design, and are amenable to a rich blend of classical mathematical techniques and contemporary optimization theory. This essay presents a personal choice of some central mathematical ideas, outlined for the broad optimization community. I discuss the convex analysis of spectral functions and invariant matrix norms, touching briefly on semidefinite representability, and then outlining two broader algebraic viewpoints based on hyperbolic polynomials and Lie algebra. Analogous nonconvex notions lead into eigenvalue perturbation theory. The last third of the article concerns stability, for polynomials, matrices, and associated dynamical systems, ending with a section on robustness. The powerful and elegant language of nonsmooth analysis appears throughout, as a unifying narrative thread. Received: December 4, 2002 / Accepted: April 22, 2003 Published online: May 28, 2003 Key Words.  eigenvalue optimization – convexity – nonsmooth analysis – duality – semidefinite program – subdifferential – Clarke regular – chain rule – sensitivity – eigenvalue perturbation – partly smooth – spectral function – unitarily invariant norm – hyperbolic polynomial – stability – robust control – pseudospectrum – H _∞ norm Mathematics Subject Classification (2000): 90C30, 15A42, 65F15, 49K40     

The mathematics of Bruce Rothschild

A review is given of some of the mathematical research of Bruce Rothschild, emphasizing his results in combinatorial theory, especially that part known as Ramsey Theory. Special emphasis is given to the Graham-Rothschild Parameter Sets Theorem, its consequences, and some extensions.