历史与综述
Peano defined 'differentiability' of functions and 'lower tangent cones' in 1887, and 'upper tangent cones' in 1903, but uses the latter concept already in 1887 without giving a formal definition. Both cones were defined for arbitrary sets,…
The degree of Doctor of Sciences, honoris causa, was conferred on Raoul Bott by McGill University in 1987. Much of the work to make this happen was done by Carl Herz. Some of the author's personal recollections of both professors are…
The long-term objective of our research is to develop the instrumental approach for teachers. A first step, presented in this paper, is to observe stable behaviours of teachers using internet resources in mathematics. We retain the…
This work is an attempt to 'reconstruct' logarithms in the hypothetical case that mankind has suffered a catastrophe through which all repositories of (mathematical as well as other) knowledge are lost, with the exception of simple…
At the end of 19th century Peano discerned vector spaces, differentiability, convex sets, limits of families of sets, tangent cones, and many other concepts, in a modern perfect form. He applied these notions to solve numerous problems. The…
In this paper a construction of affine exterior algebra of Grassmann, with a special attention to the revisitation of this subject operated by Peano and his School, is examined from a historical viewpoint. Even if the exterior algebra over…
By retracing research on coexistent magnitudes (grandeurs coexistantes) by Cauchy (1841), Peano in "Applicazioni geometriche del calcolo infinitesimale" (1887) defines the "density" (strict derivative) of a "mass" (a distributive set…
The popular view according to which Category theory provides a support for Mathematical Structuralism is erroneous. Category-theoretic foundations of mathematics require a different philosophy of mathematics. While structural mathematics…
In solving diffusion problems, it is common to consider the finite difference equation to be an approximation to the differential equation. Nevertheless, history shows that the finite difference equation is primitive and that the…
Although the same mathematical expression is used to describe physical diffusion and stochastic diffusion, there are intrinsic similarities and differences in their nature. A comparative study shows that characteristic terms of physical and…
Stochastic diffusion equation, which attained prominence with Einstein's work on Brownian motion at the beginning of the twentieth century, was first formulated by Laplace a century earlier as part of his work on Central Limit Theorem.…
A focused modernization of Sophus Lie's brilliant writings about the foundations of geometry that every contemporary geometer should have at least once a look at. Translated, updated, commented.
It is well known that the Taylor series expansion of $(1+ z)^{A}$ does not converge for $|z|>1$ where A is a real number which is not equal to zero or a positive integer. A limited series expansion of this expression is obtained in this…
A quite old problem has been recently revitalized by Leonard Mlodinow's book The Drunkard's Walk, where it is presented in a way that has definitely confused several people, that wonder why the prevalence of the name of one daughter among…
We motivate and then prove a generalized pythagorean theorem for parallelepipeds in Euclidean space.
Polya Enumeration Theorem is one of the most useful tools dealing with the enumeration of patterns that are symmetric in some ways. What follows is a procedure for obtaining the results of Polya Theorem directly, bypassing the usual…
This is an English translation of Edmund Landau's Doctoral Dissertation.
A positive integer n is said to be perfect if sigma(n)=2n, where sigma denotes the sum of the divisors of n. In this article, we show that if n is an even perfect number, then any integer m<=n is expressed as a sum of some of divisors of n.
This study use some philological and historical means in order to understand Fermat's way of thinking.
Georgy Theodosiyovych Voronoi (1868-1908) is famous for his seminal contributions to number theory,perhaps mostly those involving quadratic forms and Voronoi tessellations. He was born and grew up in the town of Zhuravka in the Ukraine, at…