历史与综述
We publish a letter from Lebesgue to Cartan and a letter from Montel to Cartan, dated 1933--1934, about Gaston Julia, Paul Montel, and an election at the Paris Academy of Sciences. We discuss the context and the mathematics. The two letters…
Galois theory is developed using elementary polynomial and group algebra. The method follows closely the original prescription of Galois, and has the benefit of making the theory accessible to a wide audience. The theory is illustrated by a…
Seven mathematicians and one political scientist met at the Cambridge Apportionment Meeting in January 2011. They agreed a unanimous recommendation to the European Parliament for its future apportionments between the EU Member States. This…
We discuss a general formula for the area of the surface that is generated by a graph $[t_0, t_1] \to \mathbb R^2$ sending $t \mapsto \bigl(x(t), y(t) \bigr)$ revolved around a general line $L: A x + B y = C$. As a corollary, we obtain a…
In this paper, we study some cards shuffles which are used by magicians. We focus ourselves on the possibility to hit eventually the initial state after several shuffles. This is a classical problem arising in discrete dynamical systems.…
We explore the technical details and historical evolution of Charles Peirce's articulation of a truth table in 1893, against the background of his investigation into the truth-functional analysis of propositions involving implication. In…
Computational science and engineering (CSE) has been misunderstood to advance with the construction of enormous computers. To the contrary, the historical record demonstrates that innovations in CSE come from improvements to the mathematics…
The Cambridge Compromise composition of the European Parliament allocates five base seats to each Member State's citizenry, and apportions the remaining seats proportionately to population figures using the divisor method with rounding…
I have recently proposed that an object, found in an Egyptian tomb and exposed at the Egyptian Museum of Torino, could be a protractor. The tomb was that of architect Kha, supervisor at Deir El-Medina during the 18th Dynasty, and his wife…
Sparsity, Structure, Scaling and Stability in Computational Linear Algebra - Textbook from the IX School of Computer Science, held on July 24-31 of 1994 at Recife, Brazil. Esparsidade, Estrutura, Escalamento e Estabilidade em Algebra Linear…
In the famous Three-Door-Game Monte cannot help to win all the time by signaling location of the prize, using only the freedom he allowed to use. No matter which strategies played, there is always at least one door where the prize will not…
The basic Monty Hall problem is explored to introduce into the fundamental concepts of the game theory and to give a complete Bayesian and a (noncooperative) game-theoretic analysis of the situation. Simple combinatorial arguments are used…
We emphasize the dominance in the Monty Hall problem, both in the classical scenario and its multi-door generalization. This is used to show optimality of the class of always-switching strategies for nonuniform allocation of the prize and…
This is an introduction (in German) to projective geometry by the late Heinz Lueneburg. Projective spaces are treated as lattices with particular properties, and finite geometries receive special attention. The final chapters deal with…
Research universities in the United States have larger mathematics faculties outside their mathematics departments than inside. Members of this "extensive" faculty conduct most mathematics research, their interests are the most heavily…
Consider a periodical (in two independent directions) tiling of the plane with polygons (faces). In this article we shall only give examples using squares, regular hexagons, equilateral triangles and parallelograms ("unions" of two…
This is a short tribute to Alexandr Alexandrov (1912--1999).
This is a brief overview of the life of Leonid Kantorovich (1912--1986) and his contribution to the fields of linear programming and ordered vector spaces.
This is a short obituary of Saunders Mac Lane (1909--2005).
In this lecture notes we present the equations and the physics involved in the dynamic of incompressible fluids. We present the mathematical techniques needed in order to prove the existence and uniqueness result for the case where we…