Judith R. Goodstein: Einstein’s Italian Mathematicians – Ricci,Levi-Civita,and the Birth of General Relativity

Mathematische Semesterberichte -     

Aims and Objectives in the Teaching of Mathematics to non‐Mathematicians∗

After a discussion on what is a non‐mathematician and what is an applied mathematician, aims that have been variously suggested are presented and discussed. Attention is drawn to the importance of an understanding of model building and of mathematics as the language of science, and this leads to a plea for co‐operation between the mathematician and the non‐mathematician. Reference is made to the relevance of the ‘New Mathematics’ and to the demand for mathematical rigour, and the paper closes with a brief discussion of the importance of detailed objectives.

     

Viribus unitis! shall be our watchword: the first International Congress of Mathematicians,held 9–11 August 1897 in Zurich

Georg Cantor voiced the need for opportunities facilitating international mathematical cooperation as early as in 1888. A decade and efforts by a number of mathematicians later, the first International Congress of Mathematicians marked the beginning of an era where personal relations between mathematicians were considered to be of great importance. Furthermore, it set the standards for future congresses. As well as giving an overview of the pre-history and the organization of the congress, I look at a wider historic context, conjecture on the reasons why it was held in Zurich and why such a great emphasis was placed on the social aspect. This paper is a slightly modified version of the talk given at the BSHM Research in Progress Meeting held 3 March 2012 in Oxford.     

Gol’dberg’s constants

We study two extremal problems of geometric function theory introduced by A. A. Gol’dberg in 1973. For one problem we find the exact solution, and for the second one we obtain partial results. In the process, we study the lengths of hyperbolic geodesics in the twice punctured plane, prove several results about them, and make a conjecture. Gol’dberg’s problems have important applications to control theory.     

A link between Wilson’s and d’Alembert’s functional equations

If \({f, g : G \to \mathbb{C}}\), f ≠ 0, is a solution of Wilson’s functional equation on a group G, then g is a d’Alembert function.     

Reich’s problem concerning Halpern’s convergence

We discuss Halpern’s convergence for nonexpansive mappings in Hilbert spaces. We prove that one of the conditions in [R. Wittmann, Approximation of fixed points of nonexpansive mappings, Arch. Math. (Basel), 58 (1992), 486–491] is the weakest sufficient condition among the conditions known to us. We also improve a necessary condition, which is close to Wittmann’s. This is one step to solve the problem raised by Reich in 1974 and 1983. Received: 15 July 2008     

On an alternative d’Alembert’s equation

Aequationes mathematicae - Roger Cuculière [Problem 11998, The American Mathematical Monthly 124 no. 7 (2017)] has posed the following problem: Find all continuous functions $$f: mathbb R...     

L’Extension Abelienne D’une Categorie semi-abelienne

We show that if (K,L) is a semi-abelian category, there exists an abelian categoryK ^x with the followings properties: