Mathematical Circles Research Articles

Community detection on elite mathematicians’ collaboration network

Abstract Purpose This study focuses on understanding the collaboration relationships among mathematicians, particularly those esteemed as elites, to reveal the structures of their communities and evaluate their impact on the field of mathematics. Design/methodology/approach Two community detection algorithms, namely Greedy Modularity Maximization and Infomap, are utilized to examine collaboration patterns among mathematicians. We conduct a comparative analysis of mathematicians’ centrality, emphasizing the influence of award-winning individuals in connecting network roles such as Betweenness, Closeness, and Harmonic centrality. Additionally, we investigate the distribution of elite mathematicians across communities and their relationships within different mathematical sub-fields. Findings The study identifies the substantial influence exerted by award-winning mathematicians in connecting network roles. The elite distribution across the network is uneven, with a concentration within specific communities rather than being evenly dispersed. Secondly, the research identifies a positive correlation between distinct mathematical sub-fields and the communities, indicating collaborative tendencies among scientists engaged in related domains. Lastly, the study suggests that reduced research diversity within a community might lead to a higher concentration of elite scientists within that specific community. Research limitations The study’s limitations include its narrow focus on mathematicians, which may limit the applicability of the findings to broader scientific fields. Issues with manually collected data affect the reliability of conclusions about collaborative networks. Practical implications This study offers valuable insights into how elite mathematicians collaborate and how knowledge is disseminated within mathematical circles. Understanding these collaborative behaviors could aid in fostering better collaboration strategies among mathematicians and institutions, potentially enhancing scientific progress in mathematics. Originality/value The study adds value to understanding collaborative dynamics within the realm of mathematics, offering a unique angle for further exploration and research.

The Kelly Criterion: Optimizing Decision-Making in Risk Management

The Kelly capital growth investment criterion, or Kelly criterion, defines the fraction of wealth to invest in a favorable investment opportunity such that the exponential growth rate is maximized. Maximizing the exponential growth rate is equivalent to maximizing logarithmic utility.[1] It all began in the mid-20th century when John L. Kelly Jr., a researcher at Bell Labs, developed the criterion as a solution to a problem related to the efficient transmission of information in telecommunications. Kelly introduced the concept of the Kelly Criterion within his paper “A New Interpretation of Information Rate,” which he published in his early years. However, he did not refer to the Kelly Criterion by its now- known name. The Kelly Criterion initially gained recognition in academic and mathematical circles, primarily for its applications in information theory. Then, professional gamblers and investors started using the Kelly Criterion to manage their bankrolls and make more informed betting decisions. The financial industry also embraced the Kelly Criterion as an alternative approach to portfolio management and investment strategies. The Kelly Criterion gained further attention in investment circles, particularly in hedge funds and wealth management.

Научное творчество Н.Д.Введенской, связанное с работой в ИПМ им. М.В. Келдыша

The work is dedicated to Nikita Dmitrievna Vvedenskaya, a mathematician, a well-known person in the mathematical circles of Moscow, who lived a long and productive life. The part of Vvedenskaya's contribution to science related to her work at the Keldysh Institute of Applied Mathematics (KIAM) is described. Vvedenskaya proposed in the 60s computational algorithms for solving problems of the theory of the laminar boundary layer. The results obtained have become widely cited classics. Her work with co-authors from KIAM on the problem of flowing around bodies with a viscous incompressible fluid and along currents modeling atmospheric processes is the basis for further research and is world famous.

A Truncated Manuscript

In the mid-1980s, an enigmatic document began circulating in French mathematical circles. Entitled Récoltes et Semailles, it was a lengthy, philosophical and deeply personal tract from the elusive mathematician Alexander Grothendieck, by then living in self-imposed seclusion. Now published officially for the first time, Pierre Schapira casts a critical eye over the book and some notable omissions.

Senescent cells and cancer cells as apoptosis suppressors: Causes and effects

The death of some senescent cells (KS), as well as neoplastic cells (KN), can be paradoxically inhibited at the stage of apoptosis. Thus, the KS become inhibitors of oncogenesis at the beginning of the phenomenon. The influence of KS and KN on the inhibition of apoptosis is multidirectional, which is presented graphically in the form of Euler’s mathematical circles (Fig. 2). Senescence, like apoptosis, may to some extent inhibit oncogenesis. The neoplastic process is also associated with non-apoptotic death, i.e. entosis, as well as autophagy, i.e. autophagocytosis with the participation of lysosomes. The process of autophagy may also involve the cell proteolytic system via the ubiquitin-proteasome system (UPS), in which polyubiquitination of suppressor proteins, e.g. p53 protein, leads to oncogenesis. Therefore, both of the above-mentioned processes of autophagy favour oncogenesis. The paper also presents the role of human endogenous retroviruses (HERs) in oncogenesis, with particular emphasis on the syncytin gene and its participation in the induction of placental cancer (choriocarcinoma, chorioepithelioma).

An Analysis of Zeno’s Paradox and Non-measurable Sets Based on Dialectical Infinity

The Problem of Continuity and Discreteness is the basic problem of philosophy and mathematics. For a long time, there is no clear understanding of this problem, which leads to the stagnation of the problem, because the essence of the problem is a problem of finity and infinity. The essence of the philosophical thought on which the mathematical definition of “line segment is composed of dots” is the idea of actual infinity, and geometric dot is equivalent to algebraic zero in terms of measure properties. In view of the above contradictions, this paper presents two solutions satisfying both the philosophical and mathematical circles based on the view of dialectical infinity, and the authors make a deep analysis of Zeno’s paradox and the non-measurable set based on both solutions.

Influence of Practical Lesson on Some Morphological Characteristics of Female Students of Sports Education Department

Through observation of first-year students, the current study found that a group of students does not engage in any physical activity before being admitted to college, whether in clubs or sports teams. Physical lessons have become a new affair for them, and they need good fitness to perform the required duties. The current study aims to know the effect of the practical lesson on some of the morphological characteristics of female students in the Department of Sports Education. The experimental method has been applied for the study (N= 18). Random selection is employed to select study participants from the first-year female students of the Department of Sports Education, Soran University (mean age = 19.5 +-2). Results have shown no statistically significant moral effect between tribal and remote tests of practical lessons in the development of variables, all of which are met by female students. There are differences in mathematical circles in favour of remote but non-moral tests. Practical lessons for the first stage of the Department of Sports Education students are not enough to develop and develop functional variables.

When practice needs more research: the nature and nurture of mathematical giftedness.

The educational literature often includes debate over the nature and nurture of mathematical giftedness. The varied schools of thought reflect discrepancies between views, which are to a large extent functions of philosophical, political, and economic considerations. To address this debate, in the context of the current ZDM Special Issue, I attempt to analyze research and practices linked to mathematical giftedness in the Soviet Union in 1960–1980. I also look at the continuation of these Soviet-era practices, and to their influence on practices internationally. Particular attention is paid to the literature devoted to reaching a deeper understanding of the phenomenon of mathematical giftedness and of ways of nurturing this giftedness. The analysis starts with the discussion of domain-specific and domain-general characteristics of mathematical giftedness that have to be taken into account in educational environments for the mathematically gifted. It continues with a review of practices in special mathematical schools and classes in the Soviet Union, and a comparison to similar settings around the world in the twenty-first century. There is also an overview of enrichment mathematical activities, with a focus on mathematical circles, mathematical competitions and Olympiads, accompanied by a description of specificities of the mathematical content employed for the promotion of mathematical giftedness. Finally, the paper focuses on the question of what characterizes an excellent teacher of mathematically gifted students and on new educational technologies that are changing the education of these students worldwide. Following this analysis, I suggest some open questions for future research on the education of mathematically gifted students.

Comments on Vladimir Voevodsky's biologically motivated works

Vladimir Voevodsky's contribution to Algebraic K-Theory is well known and was recognised by awarding him the Fields Medal. He became widely known in mathematical circles for his daring project of reforming the Foundations of Mathematics, a project he pursued until his untimely death. His ideas on the so-called “univalent” foundations of mathematics were taken up by a broad community of mathematicians and continue to be developed today. Less well known is that he devoted several years of his life to a biologically motivated project aimed at developing a mathematical theory of population dynamics. He never published anything about it. The aim of the article is to summarise his ideas on this project and to draw them to the attention of the scientific community.

"EFFICIENT" ALGORITHMS IN THE PROCESS TASKS

The paper analyzes one of the tasks for processes. We consider the problem that was proposed at the International Internet Olympiad in 2019. Solutions of this problem for the general case are considered. This option allows solving the problem in a more efficient way. The result can be useful for both those who work in mathematical circles, students participating in Olympiads, and those who are interested in difficult tasks, and beautiful solutions.

Развитие беглости и оригинальности мышления старшеклассников при решении задач, связанных с числами Фибоначчи

On the basis of the requirements of modern reality with its economic, cultural and social problems, the basic concepts of modern education are changing significantly. School in modern society must focus on the personality of the student, on their holistic development. Various and complex processes that take place in modern society, require to teach, educate and develop people who will be able to solve problems in a non-standard way, i.e. will have inventive, or, as now more often said, creative thinking, the main parameters of which are fluency, originality and flexibility of thinking. To develop fluency and originality of thinking, it is necessary to broaden horizons, off erring the integration of academic subjects with the various aspects of reality around us. These days the tasks of the USE in Mathematics contain problems in probability calculus and combinatorics. Therefore, it is necessary to train high school students to solve such problems. The problems associated with Fibonacci numbers contain many popular publications in mathematics, they are analysed in the classroom of school mathematical circles, they are included in the set of tasks for mathematical Olympiads.

Cristóbal de Rojas: nuevos datos sobre su biografía y primeras obras

La biografía del ingeniero militar Cristóbal de Rojas era poco conocida hasta el momento. Este artículo pretende ofrecer nuevos datos sobre la misma, tanto en sus orígenes, como en su posible formación y aparición en Sevilla. Posteriormente se aborda la realización de lo que sería su primera obra documentada: la portada del hastial de la parroquia de Cañete de las Torres (Córdoba). Además, se plantea delimitar su participación en la obra de El Escorial a un contacto con los círculos matemáticos de Juan de Herrera, como parte de su capacitación como ingeniero con Tiburcio Spanocchi. Finalmente se ofrecen algunas novedades sobre sus distintos matrimonios.

On known and less known relations of Leonhard Euler with Poland

In this work we focus on research contacts of Leonhard Euler with Polish scientists of his era, mainly with those from the city of Gdańsk (then Gedanum, Danzig). L. Euler was the most prolific mathematician of all times, the most outstanding mathematician of the 18th century, and one of the best ever. The complete edition of his manuscripts is still in process (Kleinert 2015; Kleinert, Mattmüller 2007). Euler’s contacts with French, German, Russian, and Swiss scientists have been widely known, while relations with Poland, then one of the largest European countries, are still in oblivion. Euler visited Poland only once, in June of 1766, on his way back from Berlin to St. Petersburg. He was hosted for ten days in Warsaw by Stanisław II August Poniatowski, the last king of Poland. Many Polish scientists were introduced to Euler, not only from mathematical circles, but also astronomers and geographers. The correspondence of Euler with Gdańsk scientists and officials, including Carl L. Ehler, Heinrich Kühn and Nathanael M. von Wolf, originated already in the mid-1730s. We highlight the relations of L. Euler with H. Kühn, a professor of mathematics at the Danzig Academic Gymnasium and arguably the best Polish mathematician of his era. It was H. Kühn from whom Euler learned about the Königsberg Bridge Problem; hence one can argue that the beginning of the graph theory and topology of the plane originated in Gdańsk. In addition, H. Kühn was the first mathematician who proposed a geometric interpretation of complex numbers, the theme very much appreciated by Euler. Findings included in this paper are either unknown or little known to a general mathematical community.

Applicability of effective medium description to photonic crystals in higher bands: Theory and numerical analysis

We consider conditions under which photonic crystals (PCs) can be homogenized in the higher photonic bands and, in particular, near the $\Gamma$-point. By homogenization we mean introducing some effective local parameters $\epsilon_{\rm eff}$ and $\mu_{\rm eff}$ that describe reflection, refraction and propagation of electromagnetic waves in the PC adequately. The parameters $\epsilon_{\rm eff}$ and $\mu_{\rm eff}$ can be associated with a hypothetical homogeneous effective medium. In particular, if the PC is homogenizable, the dispersion relations and isofrequency lines in the effective medium and in the PC should coincide to some level of approximation. We can view this requirement as a necessary condition of homogenizability. In the vicinity of a $\Gamma$-point, real isofrequency lines of two-dimensional PCs can be close to mathematical circles, just like in the case of isotropic homogeneous materials. Thus, one may be tempted to conclude that introduction of an effective medium is possible and, at least, the necessary condition of homogenizability holds in this case. We, however, show that this conclusion is incorrect: complex dispersion points must be included into consideration even in the case of strictly non-absorbing materials. By analyzing the complex dispersion relations and the corresponding isofrequency lines, we have found that two-dimensional PCs with $C_4$ and $C_6$ symmetries are not homogenizable in the higher photonic bands. We also draw a distinction between spurious $\Gamma$-point frequencies that are due to Brillouin-zone folding of Bloch bands and "true" $\Gamma$-point frequencies that are due to multiple scattering. Understanding of the physically different phenomena that lead to the appearance of spurious and "true" $\Gamma$-point frequencies is important for the theory of homogenization.

Math Circles in North Bay – the Northern Experience

Identifying mathematically talented children and working with them in various forms to help them achieve their full potential has been a priority in many countries around the world in the last 50 years [1-3]. In the last 20 years, special attention has been paid to this in North America as well [4-6]. One of the most common forms is the so-called Mathematical Circles. In recent years, a large number of universities have taken leadership in organizing Mathematical Circles in their respective cities and communities. Many of these activities are related to mathematical Olympiads or other competitions [7,8]. They also help prepare children for the transition into college/university at an advanced level. There are several forums for people involved in this activity, including the Special Interest Group on Mathematical Circles of the Mathematical Association of America [9-11]. In this paper, we describe the experience of a group of faculty and students at Nipissing University in running the Math Circles in North Bay, Ontario. *Corresponding author: E-mail: tzvetalv@nipissingu.ca Huntington & Vassilev; BJESBS, 6(3), 189-195, 2015; Article no.BJESBS.2015.055

Extremely generalized planar Smith chart based on Möbius transformations

AbstractIn this article, extremely generalized planar Smith chart (EGPSC) is proposed based on Mőbius transformations (MTs). And the rigid mathematical circles equations of this proposed EGPSC are obtained. The EGPSC includes omnipotent Smith chart (OSC) and other different kinds of generalized Smith charts which have been reported recently. Finally, according to the rigid mathematical equations, the corresponding characteristics of EGPSC are comprehensively analyzed and illustrated through numerical simulations. © 2009 Wiley Periodicals, Inc. Microwave Opt Technol Lett 51: 1164–1167, 2009; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.24293

UNLEASHING THE VERMIN (VECTORED ROUTE-LENGTH MINIMIZATION)

We have posed a simple but interesting graph theoretic problem and posited a heuristic solution procedure, which we have christened as Vectored Route-lenght Minimization (VeRMin). Basically, it constitutes a re-casting of the classical "shortest route" problem in a strictly Euclidean space. We have presented only a heuristic solution process hoping that a formal proof will eventually emerge as the problem receives wider exposure within mathematical circles.

Mathematics Workshops for Parents: An Example of Non-fomal Adult Education

The world of adult mathematics education presents itself as a mosaic when it comes to all the different shapes it may take on. Some of these differences are related to the approach and the motivation for learning mathematics (FitzSimons, 2007). One of these variations is the length of the experience, from a once-in-a-lifetime event to a college degree in mathematics, which implies several years. Another variation is that of the purpose for the course, may it be as part of a GED program, as part of a vocational training, or to learn about home finances, to mention a few. One could be required to take a course in mathematics to advance in one's career, as in a training program at work, one may attend a talk in mathematics for the fun of it, or to understand what your children learn in school these days. Safford-Ramus (2008) presents a list of different instructional settings of adult mathematics education, such as basic education, secondary, undergraduate, prison, military, workplace, and more. Within all these variations, we place initiatives for adults learning mathematics on a scale from informal to formal models. In the one extreme, we have those sporadic events that may occur as part of a science fair at one's child's school, such as a short presentation on the concept of zero according to the Mayans. This experience is not structured with a follow up on number systems series of lessons or anything else, you are not forced to attend, and your job is not in jeopardy for not going to this talk. On the other extreme, you have the regular school courses that you are expected to attend a few days per week, a few weeks a semester; do homework and take tests; receive grades; and eventually will lead to a degree that has social or professional recognition. Between these two extremes, we have a model of adult education in non formal settings. In the context of adult education on agricultural issues, Etllng (1993) defines the term nonformal, citing Kleis (1973, p. 6), as any intentional and systematic educational enterprise (usually outside of traditional schooling) in which content is adapted to the unique needs of the students (or unique situations) (p. 73). Kalantzis (n.d.) defines semi formal learning as follows: Semi-formal learning involves partially institutionalized settings focused on particular life or workplace learning. It generally does not involve accreditation but aligns with learner's aspirations. Indeed the idea of self-directed learning became an important feature of adult education, particularly in relation to workplace and community learning (p. 2). In the context of the mathematics workshops around which our work takes place, what we refer to as nonformal education is the type of education that is systematic, not for accreditation or promotion, adapted to the unique situation of the participants, of voluntary attendance, and relatively flexible structure (Menendez & Civil, 2009). In this article, we share our experiences facilitating a series of mathematics for parents' workshops (MFP) throughout two and a half years and address the structure, history and development of these workshops. We then analyze how this experiment fits the concept of nonformal adult education and conclude with our assessment of the pros and cons of our implementation, as well as recommendations for future initiatives. Mathematics Workshops Our work with parents is modeled after our prior experiences with Latino/a parents and mathematics and, in particular, we structured these workshops as Tertulias Matematicas (Mathematical Circles) (Bratton, Quintos, & Civil, 2004; Quintos, Bratton, & Civil, 2005). The word tertulia connotes the image of a group of people who gets together regularly to talk about different topics (e.g., discussing a book). This is the flavor that we seek to develop in our workshops. Description and Evolution of the Workshop In the fall semester of 2006, we started to facilitate MFP workshops at a middle school in a predominantly Latino neighborhood in a borderland city of the Southwestern United States. …

Stories and Numbers: How a Romantic Tale of Geographical Exploration Transformed Mathematics

January 2004 · Historically Speaking 13 Stories and Numbers: How a Romantic Tale of Geographical Exploration Transformed Mathematics Amir Alexander Evariste Galois was a young mathematical genius, who was beginning to make a name for himselfin European mathematical circles in die early 19th century . He was also a political radical, and an enthusiastic participantin French revolutionary politics. At the young age oftwenty-two he was challenged to a duel over his radical political beliefs. Knowing that he may not survive the morning, he spent the night before the encounterwriting down his latest mathematical insights. Tragically, he was indeed killed in the duel. His hastily jotted notes, however, bequeathed to mathematics an entire new field ofinquiry: the Theory of Groups. I cannot vouch for the accuracy of this story, which I heard repeatedly from mymathematics professors , but then, it was not told for its historicalveracity. Itwas told as a morality tale: the young Galois, we are left to surmise, would have presented the world with many more mathematical wonders if he had not been lured awayfrom his true vocation by politics and violence. The passions and turmoil ofhuman history appear as nothing more than senseless strife when viewed against the beauty and coherence ofeternal mathematics. One may argue—and most historians would—with the value judgments ofhistory and mathematics implicitin this tale. Butthe story does bring out the fundamental problem ofa history ofmathematics: mathematics deals with unchanging Platonic universale ; history deals with unexpected earthly contingencies. How, then, can one write a meaningful contingent history ofuniversal mathematics? The problem is shared, to a degree, with other areas of the history of science, where historians have had to deal with such stubbornlyahistorical factors as universal gravitation and the laws ofthermodynamics. Nevertheless , over the past thrity years historians ofscience have been remarkably successful in providinginsightful and culturallyrich historical accounts of crucial episodes in the development ofscience. Not so historians of mathematics, who have remained surprisingly unperturbed by the intellectual tempests raging in adjacent fields. Many historians of mathematics, though by no means all, remain thoroughly satisfied with the "Galois" model of history and are contentto contrasthistoryand madiematics rather than connecting them. In their viewhistorymight be the "theater" ofmathematics —since different mathematicians live in different historical times and places and Traditional mathematics sought to determine the nature ofthe world through rigorous deduction; Cavalieri andhis colleagues sought to learn ofit by exploring the secrets hidden within existing objects. I make no effort here to argue for this method in the abstract; rather, I will simply demonstrate how it is done. This, then, is the story ofhow a romantic tale of exploration and discoverychanged the face ofmathematics and opened thewayto the development of the calculus. • · · In 1539 GeorgJoachim Rheticus, professor of mathematics atthe UniversityofWittenberg, set out for the Prussian town ofFrauenburg to visit the reclusive astronomer Nicholas Copernicus. Rheticus had heard rumors of Copernicus's heliocentric system, and he was determined to investigate the truth and validity ofthis radical cosmology at first hand. Under the old canon's tutelage, Rheticus quickly became an ardent Copernican. He ended up stayinginFrauenburgfortwo years, often impressing upon his host the significance ofhis discoveries, and the importance of making them available to a wider audience. A few months after his arrival he composed a short treatise, summarizing the main points ofthe Copernican theory. It each gets a glimpse ofa part ofthe realm of was published in 1540 and became known as mathematics. History is not, however, the the Narratio Prima, the first published dimension of mathematics, since in these accounts mathematics trulyresides in its own insular Platonic sphere. What, then, can be done? How can a historical account be given of a field as insular and self-contained as mathematics? My suggestion here is to lookfor the narratives that structure mathematical systems, the underlyingstories thatguide mathematicians' work and help them construct their intricate systems . Most important for historians, these narratives are historically specific: different stories at different times can and do produce different types ofmathematical practices. account ofCopernicus's views. At the end of the treatise, Rheticus reflected upon the hospitality offered him by narrating the adventures ofthe philosopherAristippus ofCyrene: The story is frequently told of the shipwrecked Aristippus, which they say occurred...

Ventura Reyes Prósper (1863-1922) y la introducción de la nueva lógica en España

With a view to an unnoticed paper by Reyes Prósper (1891), «La lógica simbólica», I examine the first and unsuccessful introduction of modern logic in mathematical circles in Spain, in the end of the 19th century and beginnings of 20th. Such reception failures are usually attributed to external and/or general circumstances, ranging from personal vicissitudes to institutional and cultural conditions of Spanish learning. But here we should also pay attention at the very working of the so-called «sowers», i.e. introducing people. Some consequences concerning the study of reception are incidentally suggested.