历史与综述
We present the problems and solutions to the 61st Annual International Mathematical Olympiad
This review paper highlights research findings from the authors' participation in the SUMMIT-P project, which studied how to build and sustain multi-institutional interdisciplinary partnerships to design and implement curricular change in…
Between the poker hands of straight, flush, and full house, which hand is more common? In standard 5-card poker, the order from most common to least common is straight, flush, full house. The same order is true for 7-card poker such as…
As is now well known, the generalization of the square of opposition to a hexagon was discovered independently by three philosophers in the early 1950s: Paul Jacoby, Augustin Sesmat, and Robert Blanch\'{e} . Much less well known is the…
The literature dealing with G\"{o}del's legacy is largely preoccupied with challenging his philosophical views, regarding them as outdated. We believe that such an approach prevents us from seeing G\"{o}del's views in the right light and…
This book concentrates on functional analysis. The text is written so that it can be followed on the basis of high school mathematics. The book introduces the set theoretical foundations of mathematics, the basic theories of linear algebra…
In this note we present a survey on some classical and modern approaches on Pythagorean triples. Some questions are also posed in direction of some materials under review. In particular some non commutative and operator theoretical…
We give the definition, main properties and integral expressions of the auxiliary function of Riemann $\mathop{\mathcal R }(s)$. For example we prove $$\pi^{-s/2}\Gamma(s/2)\mathop{\mathcal R }(s)=-\frac{e^{-\pi i s/4}}{…
This is a point of view of the work of Herbert Busemann (1905-1994), seen as a return to the geometry of Ancient Greece. The importance of this work, its recognition and its relation with other works are discussed. The final version of this…
Fitch Cheney's 5-card trick was introduced in 1950. In 2013, Mulcahy invented a 4-card trick in which the cards are allowed to be displayed face down. We suggest our own invention: a 3-card trick in which the cards can be face down and also…
We provide an example of the application of quantitative techniques, tools, and topics from mathematics and data science to analyze the mathematics community itself in order to quantify and document inequity in our discipline. This work is…
We humbly and briefly offer corrections and supplements to Mathematical Constants (2003) and Mathematical Constants II (2019), both published by Cambridge University Press. Comments are always welcome.
Roger Carter (1934--2022) was a very well known mathematician working in algebra, representation theory and Lie theory. He spent most of his mathematical career in Warwick. Roger was a great communicator of mathematics: the clarity,…
Through a series of elementary exercises, we explain the fractal structure of Pascal's triangle when written modulo $p$ using an 1852 theorem due to Kummer: A prime $p$ divides $\dfrac {n!}{i!j!} $ if and only if there is a carry in the…
The paper deals with the resolution of third and fourth degree equations by means of radicals. It is a survey of some historical details about this fundamental problem. Moreover, it explains practical methods for the resolution of third and…
In 2013, Conway and Ryba wrote a fascinating paper called Fibonometry. The paper, as one might guess, is about the connection between Fibonacci numbers and trigonometry. We were fascinated by this paper and looked at how we could generalize…
This paper examines what computational procedures \'Sankara Varman (1774-1839) and Sangamagrama M\=adhava (c. 1340 - 1425), astronomer-mathematicians of the Kerala school, might have used to arrive at their respective values for the…
This paper is intended to serve two purposes: one, to present an account of the life of Sangamagr\=ama M\=adhava, the founder of the Kerala school of astronomy and mathematics which flourished during the 15th - 18th centuries, based on…
The primary sourcebook for developments based on the data of the world components "Theory of Intellectualities and Mathematical Statistics" (TIMS) collections of the Department of Mathematics, Physics and Astronomy of Odessky National…
``Calabi-Yau Manifolds: a Bestiary for Physicists'' by Tristan Hubsch in 1992 was a classic that served to introduce algebraic geometry to physicists when the first string theory revolution of 1984 - 94 brought, inter alia, the subject of…