历史与综述
A counter-intuitive result of Gauss (formulae (1.6), (1.7) below) is made less mysterious by virtue of being generalized through the introduction of an additional parameter.
This text tries to give an elementary introduction to the mathematical properties of infinite sets. The aim is to keep the approach as simple as possible. Advanced knowledge of mathematics is not necessary for a proper understanding, and…
We solve the difference equation with linear coefficients by the Momentenansatz to obtain explicit formulas for orthogonal polynomials.
We give another proof for \[ \sum_{n=1}^{\infty}\frac{1}{n^2}=\frac{\pi^2}{6} \] that basically follows from the theory of difference equations.
Boggle logic puzzles are based on the popular word game Boggle, where you are given list of words, and your goal is to recreate a Boggle board. In this paper we give an overview of known results and then propose a number of problems related…
In Early Transcendentals (The American Mathematical Monthly, Vol. 104, No 7) Steven Weintraub presents a rigorous justifcation of the "early transcendental" calculus textbook approach to the exponential and logarithmic functions. However,…
We make some observations regarding the competition between Universidad de la Ca\~nada (Unca) and other universities, using the Lotka-Volterra model, for the Informatics major, applying ideas introduced by McPherson in 1983. As a…
We present a comprehensive survey of constructions of the real numbers (from either the rationals or the integers) in a unified fashion, thus providing an overview of most (if not all) known constructions ranging from the earliest attempts…
In the article we give an appreciation of Edward Nelson's multifaceted contribution to mathematics, and particularly to foundational theories of infinitesimals.
Adolf Hurwitz is rather famous for his celebrated contributions to Riemann surfaces, modular forms, diophantine equations and approximation as well as to certain aspects of algebra. His early work on an important generalization of…
This is a typeset version of Alan Turing's declassified Second World War paper \textit{Paper on Statistics of Repetitions}. See the companion paper, \textit{The Applications of Probability to Cryptography}, also available from arXiv at…
This is a typeset version of Alan Turing's Second World War research paper \textit{The Applications of Probability to Cryptography}. A companion paper \textit{Paper on Statistics of Repetitions} is also available in typeset form from arXiv…
We explain the link between the so-called "three gap theorem" and the construction of musical scales. Nous expliquons le lien entre un th\'eor\`eme classique d'approximation diophantienne (le th\'eor\`eme des trois distances), et la…
A fractal can be simply understood as a set or pattern in which there are far more small things than large ones, e.g., far more small geographic features than large ones on the earth surface, or far more large-scale maps than small-scale…
In this note, we shall give a brief survey of the results that are found in Ramanujan's Lost Notebook related to cranks. Recent work by B. C. Berndt, H. H. Chan, S. H. Chan and W. -C. Liaw have shown conclusively that cranks was the last…
Here we present the transcription of the handwritten notes, carefully taken by an anonymous student, of the last lecture course taught by Guido Castelnuovo in 1922-23. The title of the course is "Curve algebriche piane e sghembe" ("Plane…
The use of algorithmic information theory (Kolmogorov complexity theory) to explain the relation between mathematical probability theory and `real world' is discussed.
We sketch the outlines of Gian Carlo Rota's interaction with the ideas that Hermann Grassmann developed in his Ausdehnungslehre of 1844 and 1862, as adapted and explained by Giuseppe Peano in 1888. This leads us past what Rota variously…
Poly-infix operators and operator families are introduced as an alternative for working modulo associativity and the corresponding bracket deletion convention. Poly-infix operators represent the basic intuition of repetitively connecting an…
The first 2x2x2 twisty cube was created as a demonstration tool by Erno Rubik in 1974 to help his students understand the complexity of space and the movements in 3D. He fabricated a novel 3x3x3 mechanism where the 26 cubies were turning,…