历史与综述
The substantial gender gap in the science, technology, engineering, and mathematics (STEM) workforce can be traced back to the underrepresentation of women at various milestones in the career pathway. Calculus is a necessary step in this…
August M\"obius discovered his eponymous strip --- also found almost contemporaneously by Johann Listing --- in 1858, so a pre-1858 M\"obius band would be an interesting object. It turns out there were lots of them.
The close relationship among the polynomial functions and Fibonacci numerical sequences is shown in this paper. These numerical sequences are defined by the recurrence equation $x_{k + n} = \displaystyle\sum_{j = 0}^{n-1}\alpha_j x_{k +…
Abraham Robinson's framework for modern infinitesimals was developed half a century ago. It enables a re-evaluation of the procedures of the pioneers of mathematical analysis. Their procedures have been often viewed through the lens of the…
The present text is a collection of notes about differential geometry prepared to some extent as part of tutorials about topics and applications related to tensor calculus. They can be regarded as continuation to the previous notes on…
Some little step forward is made in the analysis of the mathematical structure of Tonal Harmony, a task begun by Galilei, Euler and the Lagrange of the first two volumes of Miscellania Taurinensia
In this paper, we propose that 'embodied mathematics' should be studied not only by reduction to the present individual bodily experience but in an historical context as well, as far as the origins of mathematics are concerned. Some early…
In this paper we briefly review and analyze three published proofs of Chaitin's theorem, the celebrated information-theoretic version of G\"odel's incompleteness theorem. Then, we discuss our main perplexity concerning a key step common to…
The "quantum-event / prime ideal in a category/ noncommutative-point" alternative to "classical-event / commutative prime ideal/ point" is suggested. Ideals in additive categories, prime spectra and representation of quivers are considered…
This is a review of the 5-volumes of Ramanujan's Notebooks, as worked over by Bruce C. Berndt over the last quarter of the XX-th Century. To illustrate how useful Ramanujan's insights could be for anyone who indulges in the wild pleasure of…
We describe some motivations lurking behind the making of a Math exhibition. In particular, we refer to MadeInMath and its two set-ups in Triennale di Milano and Museo della Scienza in Trento (MUSE), where the life and works of Italian…
This note is a preface to various responses [math.HO/9404229,math.HO/9404236] to an opinion piece by Jaffe and Quinn [math.HO/9307227] on the relationship between mathematics and theoretical physics.
Is speculative mathematics dangerous? Recent interactions between physics and mathematics pose the question with some force: traditional mathematical norms discourage speculation, but it is the fabric of theoretical physics. In practice…
This article revisits an integral of radical trigonometric functions. It presents several methods of integration where the integrand takes the form $\sqrt{1 \pm \sin x}$ or $\sqrt{1 \pm \cos x}$. The integral has applications in Calculus…
A translation of "Verallgemeinerung des Sylow'schen Satzes" by F. G. Frobenius, Sitzungsberichte K. Preuss. Akad. Wiss. Berlin, 1895 (II).
A group of friends organize their tennis games by submitting each their availability over the weekdays. They want to obtain an assignment such that: each game must be a double tennis match, i.e. requires four people, and nobody plays in a…
A friend of 12 is a positive integer different from 12 with the same abundancy index. By enlarging the supply of methods of Ward [1], it is shown that (i) if n is an odd friend of 12, then n=m^2, where m has at least 5 distinct prime…
The purpose of this paper is to show that the mathematical treatment of three dimensional rotations can be simplified, and its geometrical understanding improved, by using the Rodrigues' vector representation. We present a novel geometrical…
We attempt to grasp the mathematics behind the planetary theories of the Syrian astronomer Ibn al-Shatir (1304-1375) in his treatise Nihayat al-Sul. Following the Maragha school of astronomers, by composing circular movements with constant…
We show how Cartesian method can be used in the proof of fundamental planimetric topics of the school course, such as introduction of trigonometric functions, equation of a line and similarity of triangles. This work also can be considered…