历史与综述

The concept of a symplectic structure first appeared in the works of Lagrange on the so-called "method of variation of the constants". These works are presented, together with those of Poisson, who first defined the composition law called…

It is well known that Al-Khay\^am, for the first time in history, formulated a complete theory to solve third degree equations using the intersection of geometric curves and moreover solved the fourteen types of equations using this method.…

The analytical aspects of the "Trait\'e des \'equations" of Sharaf al-D\^in al-T\^us\^i (2nd half of the XIIth century) have been underlined by R. Rashed (1974, 1986). In the present paper, we consider again some of those aspects, when…

Irving John ("Jack") Good (9 December 1916 - 5 April 2009) was one of my greatest heroes and influencers. On Oct. 25, 2009, I gave a twenty-three minute talk with the present title, and this article is an extended transcript of that talk.…

Democracy functions of wavelet admissible bases are computed for weighted Orlicz Spaces in terms of its fundamental function. In particular, we prove that these bases are greedy if and only if the Orlicz space is a Lebesgue space. Also,…

Folklore tells us that there are no uninteresting natural numbers. But some natural numbers are more interesting then others. In this article we will explain why 3435 is one of the more interesting natural numbers around. We will show that…

In the mid-1960s A. Pfister discovered extraordinary, strongly multiplicative forms which are now called Pfister forms. From that time on, these forms played a dominant role in the theory of quadratic forms. One of the key properties of a…

We give an overview of issues surrounding computer-verified theorem proving in the standard pure-mathematical context. This is based on my talk at the PQR conference (Brussels, June 2003).

In this short note, we provide an elementary complex analytic method for converting known real integrals into numerous strange and interesting looking real integrals.

This paper has been withdrawn due to an error, and no further revisions will be made.

In order to prove irrationality of \sqrt{2} by using only decimal expansions (and not fractions), we develop in detail a model of real numbers based on infinite decimals and arithmetic operations with them.

We propose to address the problem of how to know students' knowledge in an entirely new approach called ?epistemography? which is, roughly, an attempt to describe the structure of this knowledge. We claim that what is to be known is made of…

An interpretation of selected parts of Newton's Principia, with modern notation and methods. Keplers Laws are derived from an inverse square law using Newton's methods.

The topic of this paper is, on the one hand to introduce algebraic analysis results of \'Etienne B\'ezout (1730- 1783) not as we know them today but as he found them in his time, and on the other hand to emphasize his innovating viewpoints.…

This note describes a way of obtaining e that differs from the standard one. It could be used as an alternate way of showing how the value of e is obtained. No attempt is made to show the existence of the limit in the definition of e that…

We derive some, seemingly new, curious additive relations in the Pascal triangle. They arise in summing up the numbers in the triangle along some vertical line up to some place.

This paper provides an introduction to trace diagrams at a level suitable for advanced undergraduates. Trace diagrams are a non-traditional notation for linear algebra. Vectors are represented by edges in a diagram, and matrices by markings…

We study the problem of construction of a triangle from the feet of its internal angle bisectors. It is proved that in general case ruler-and-compass solution of this problem is impossible.

We give a simple proof of a characterization of euclidean space due to Aronszajn and derive a well-known characterization due to Jordan & von Neumann as a corollary.

When people mention the number theoretical achievements in Ancient China, the famous Chinese Remainder Theorem always springs to mind. But, two more of them--the concept of primes and the algorithm for counting the greatest common divisor,…