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"Real Normed Algebras Revisited," the last paper of the late Gadi Moran, attempts to reconstruct the discovery of the complex numbers, the quaternions, and the octonions, as well as proofs of their properties, using only what was known to 19th-century mathematicians. In his research, Gadi had discovered simple and elegant proofs of the above-mentioned classical results using only basic properties of the geometry of Euclidean spaces and tools from high school geometry. His reconstructions underline an interesting connection between Euclidean geometry and these algebras, and avoid the advanced machinery used in previous derivations of these results. The goal of this article is to present Gadi's derivations in a way that is accessible to a wide audience of readers. [ABSTRACT FROM AUTHOR]

On 5 May 1957, Leopold Löwenheim passed away in a Berlin hospital following a short but severe illness, unnoticed by the community of mathematical logicians who believed that he had perished in a Nazi concentration camp in or shortly after 1940 (the year of publication in the Journal of Symbolic Logic of his last paper before the end of World War II). The 50th anniversary of his death seems an appropriate date for the posthumous publication of a paper that was supposed to appear in Fundamenta Mathematicae in 1939, the galley proofs of which Löwenheim had already seen and corrected when German troops invaded Poland on 1 September 1939. Löwenheim managed to save the proofs through the War, despite the loss of most of his possessions during the bombing of Berlin in 1943 and 1944. By another lucky chance, a copy of the proofs survived in the present author's possession, when the originals were lost during a flat clearing in Berlin as part of the estate of Johannes Teichert (1904-1994), Löwenheim's step-son, when his widow moved into a nursing-home in May 1999. Later, I will expand these short remarks slightly but seize the present opportunity to resume (and in some places add to) the extant data on Löwenheim's life and writings. [ABSTRACT FROM AUTHOR]

In the Handbook of Mathematical Logic, the Paris-Harrington variant of Ramsey's theorem is celebrated as the first result of a long 'search' for a purely mathematical incompleteness result in first-order Peano arithmetic. This paper questions the existence of any such search and the status of the Paris-Harrington result as the first mathematical incompleteness result. In fact, I argue that Gentzen gave the first such result, and that it was restated by Goodstein in a number-theoretic form. [ABSTRACT FROM AUTHOR]

In this paper we examine two mathematicians who published manuscripts on geometry and origami in the same year, 1893: Hermann Wiener and Sundara Row. The main question that concerns us is to situate these works in the correct historical and mathematical background. We suggest that Wiener and Row offer us, via folding a piece of paper, a new conception of geometry that is very different to the common conception at the time. [ABSTRACT FROM PUBLISHER]

In the paper by Daniel Tisdale, published in this journal, a ‘previously unpublished note’ by Jitsuro Nagura is reproduced and discussed. Actually, in 1956, this article was published in a bulletin of the Department of General Education, Rikkyo University. [ABSTRACT FROM PUBLISHER]

The paper argues for three points. The first purpose of the paper is to show that Carl Menger would have rejected Ludwig von Mises' methodological apriorism. Second, I argue that Carl Menger was a pluralist about the methods of theoretical economics and that Mises was rather less of a pluralist, if not altogether a monist, about the legitimate method(s) of economic theorising. Finally, I try to establish the broad consistency of Menger's pluralism with the tolerant methodological attitude of his son, the mathematician, logician, and philosopher of science, Karl Menger. [ABSTRACT FROM AUTHOR]

This paper aims to investigate the reasons some female mathematicians give to justify their choice to not work in academia after finishing their doctoral studies. Nine female mathematicians who finished a PhD in Sweden answered a written questionnaire. Through collective narrative analysis, two main tracks were identified. One narrative described the struggle with self-identity in a gendered structure which included implicit power, while the other was more positive about exposure to discrimination, and highlighted the desire to work with applied mathematics. Through deductive thematic analysis, the results show that the main obstacle raised was the difficulty of getting a job in academia after their doctoral studies, especially permanent positions, without support. Compared to previous research, the lack of family-oriented political policies was not considered a main problem. Instead, the reasons provided by the respondents are structural problems, such as access to post-doc positions, and the stress of having to get research grants, as well as cultural aspects within the structure, including implicit and explicit use of power. [ABSTRACT FROM AUTHOR]

Lutsky in 2008 and 2009, where they investigated the invertibility of parabolic pseudo-differential operators with rapidly growing symbols and obtained estimates of exponential behaviour of solutions of pseudo-differential operators with growing and discontinuous symbols. During several years which followed the defense of the PhD thesis there appeared Vladimir's publications presenting interesting results for quasi-elliptic pseudodifferential operators and on solvability of Cauchy and Goursat problems for parabolic pseudodifferential equations (1971-1979 and later on), on solvability difference-differential equations (1978-1985 and later on), on Fredholmness of elliptic pseudodifferential operators and associated boundary value problems on noncompact manifolds (papers of 1971-1979). In 1993 he defended his doctoral thesis "The method of limit operators in solvability of pseudo-differential equations and convolution equations". [Extracted from the article]

The article discusses on an article by David R. Bellhouse published within "Historia Mathematica" in its May 2007 issue. The article by Bellhouse discusses on the work of Philip Stanhope, the second earl of Stanhope, on probability theory and his correspondence with Bishop Berkeley's criticism on Isaac Newton's calculus. Bellhouse writes that Stanhope was strongly influenced by Abraham de Moivre's work on a method of calculating the probability of events in play and by Pierre Rémond's essay. Bellhouse adds that one of Stanhope's contribution to mathematics was his work on determining the probability of a run of at least r sucesses in n trials which was posed by de Moivre. Stanhope also worked on the duration of play in the gambler's ruin problem.

Mathematicians in academic institutions utilize a variety of resources and strategies to seek, find, and use scholarly information and news. Using a sample of mathematicians, researchers surveyed 112 students and faculty at four Canadian university institutions to explore self-perceived success rates, resources consulted, databases used, use of social media, and citation management systems. Further, 12 follow-up interviews were completed with mathematicians to better interpret survey results, resulting information-seeking behaviors, choices, strategies, and feelings on keeping up to date with information needs. According to survey results, a minority of mathematicians (12.5 percent) acknowledged that they were successfully keeping up to date. However, a significant number of mathematicians (28.6 percent) indicated that they were unsuccessful and could do better in remaining current with information needs. Co-investigators, using qualitative analyses, identified four emergent themes related to remaining current: (1) The "slower pace of math" pervades all aspects of this discipline;" (2) There are "too many papers – and not enough time" to effectively search, evaluate, and read scholarly papers of interest; (3) Mathematicians collectively acknowledge that they are open to strategies and technologies where they "could do better" keeping up to date; and (4) Mathematicians have divided loyalties using databases when searching for information by means of "MathSciNet in a Google world." Additional insights document how mathematicians are guided by mathematical peculiarities and discipline-specific practices. This study helps to shed light on opportunities for academic librarians to identify and meet mathematicians' evolving information needs. [ABSTRACT FROM AUTHOR]

In this work, we discuss the development of descriptive actions that facilitators take in semester-long online professional development geared at supporting instructional change at the undergraduate level. Current work in undergraduate mathematics education includes various large-scale projects aimed to support individuals or departments in reforming their instruction to align with recommendations from professional organizations and existing mathematics education research standards. One research area that has recently grown is the use of online synchronous environments to form collaborations to support the inclusion of student-centered instruction in mathematics. This paper discusses the actions that facilitators take in these collaborative environments and highlights how these actions supported the overall goal of the semester-long online faculty development. [ABSTRACT FROM AUTHOR]

The first proof of the transcendence of π by Ferdinand Lindemann in 1882 prompted the publication of a wave of further proofs, all attempting to elucidate, simplify, or generalize this epoch-making result. Modifications by the likes of Weierstrass, Gordan, and Hilbert all entered the literature. But one such proof sank without a trace and was almost completely ignored. This is surprising as, not only did it appear in a major journal with a large international readership, but it was also written by one of the most famous mathematicians of the time—James Joseph Sylvester. This paper tells its story. [ABSTRACT FROM AUTHOR]

Mathematics is becoming increasingly specialized, divided into a vast and growing number of subfields. While this division of cognitive labor has important benefits, it also has a significant drawback: it can sometimes impede mathematical progress by making it difficult for mathematicians to make connections to subfields other than their own. Mathematicians can address this by making their own subfield more accessible to researchers working in other areas. One way they can do this is by engaging in exposition, as I illustrate with the User's Guide Project in algebraic topology. However, the current reward structure of mathematics does not appropriately credit mathematicians who make their subfields more accessible via exposition. I thus conclude that the reward structure of mathematics should be changed to more highly value such work, with changes being adopted at the level of departments, professional societies and funding agencies. [ABSTRACT FROM AUTHOR]

This paper attempts a new interpretation of Euclid's Elements Book X. This study of irrational lines has long been viewed as an anomaly within the Euclidean corpus: it includes a tedious and seemingly pointless classification of lines, known as 'the cross of mathematicians'. Following Ken Saito's toolbox conception, we do not try to reconstruct the book's mathematical process of discovery, but, instead, the kind of applications for which it serves as a toolbox. Our claim is that the book provides tools for solving questions about proportional lines inspired by results in music theory and a context of Pythagorean-Platonic interest in proportions. We show that the entire content of Book X can indeed be accounted for as a set of tools for these questions, augmented by the general editorial norms that govern the Elements. We conclude by explaining why the purpose of Book X as reconstructed here has disappeared from mathematical memory. [ABSTRACT FROM AUTHOR]

In this paper, I explore an intriguing view of definable numbers proposed by a Cambridge mathematician Ernest Hobson, and his solution to the paradoxes of definability. Reflecting on König's paradox and Richard's paradox, Hobson argues that an unacceptable consequence of the paradoxes of definability is that there are numbers that are inherently incapable of finite definition. Contrast to other interpreters, Hobson analyses the problem of the paradoxes of definability lies in a dichotomy between finitely definable numbers and not finitely definable numbers. To bypass this predicament, Hobson proposes a language dependent analysis of definable numbers, where the diagonal argument is employed as a means to generate more and more definable numbers. This paper examines Hobson's work in its historical context, and articulates his argument in detail. It concludes with a remark on Hobson's analysis of definability and Alan Turing's analysis of computability. [ABSTRACT FROM AUTHOR]

This two-part paper investigates the discovery of an intriguing and fundamental connection between the famous but apparently unrelated mathematical work of two late third-century mathematicians, a link that went unnoticed for well over 1500 years. In this, the first installment of the paper, we examine the initial chain of mathematical events that would ultimately lead to the discovery of this remarkable link between two seemingly distinct areas of mathematics, encompassing contributions by a variety of mathematicians, from the most distinguished to the relatively unknown. [ABSTRACT FROM PUBLISHER]

We contribute to the zoo of dubious identities established by J.M. and P.B. Borwein in their 1992 paper, "Strange Series and High Precision Fraud" with five new entries, each of a different variety than the last. Some of these identities are again a high precision fraud and picking out the true from the bogus can be a challenging task with many unexpected twists along the way. This work is dedicated to the Borwein family, mathematicians extraordinaire with a propensity for the implausible. [ABSTRACT FROM AUTHOR]

Ballistics is an area of flight, and fewer subjects were of greater importance to nation states in the eighteenth century. William Mountaine who published on the topic in 1747 and 1781, wrote: 'It is not possible in the nature of things for any one kingdom to continue long in a state of peace and tranquility', and 'the art of gunnery has from time to time engaged the attention of the most eminent mathematicians'. This paper describes the slow up-take of ideas, first put forward explicitly by Benjamin Robins in 1742, which challenged the belief that air resistance could be neglected in the flight of cannon balls, and asks why it could be, that for a topic so pressing, a clearly wrong mathematical theory was upheld for so long. While considering a number of factors, it argues the attraction of beautiful and simple geometry can be beguiling. [ABSTRACT FROM AUTHOR]

In recent years, congruence properties for the coefficients of mock theta functions have been studied by mathematicians. Recently, Silva and Sellers proved some congruences modulo 3 and 9 for the coefficients of the third order mock theta function ξ(q) given by Gordon and McIntosh. Motivated by their work, we prove new congruences modulo 9 for the coefficients of ξ(q) based on the formula for the number of representations of an integer as sums of seven squares in this paper. Those congruences involve in_nitely many primes. [ABSTRACT FROM AUTHOR]

For the past three decades, peer review practices have received much attention in the literature. But although this literature covers many research fields, only one previous systematic study has been devoted to the practice of peer review in mathematics, namely a study by Geist, Löwe, and Van Kerkhove from 2010. This lack of attention may be due to a view that peer review in mathematics is more reliable, and therefore less interesting as an object of study, than peer review in other fields. In fact, Geist, Löwe, and Van Kerkhove argue that peer review in mathematicsisrelatively reliable. At the same time, peer review in mathematics differs from peer review in most, if not all, other fields in that papers submitted to mathematical journals are usually only reviewed by a single referee. Furthermore, recent empirical studies indicate that the referees do not check the papers line by line. I argue that, in spite of this, mathematical practice in general and refereeing practices in particular are such that the common practice of mathematical journals of using just one referee is justified from the point of view of proof validity assessment. The argument is based on interviews I conducted with seven mathematicians. [ABSTRACT FROM PUBLISHER]

The celebrated number theorist Louis Joel Mordell spent around two and a half decades working in Manchester and for most of the rest of his career he was based in St John's College, Cambridge. There was, however, a brief period when he was based in London. The standard biographies of Mordell's life by and largely tend to overlook this period almost to the point of being deceptive about it. In this paper we will address this imbalance by discussing this chapter in Mordell's life in more detail. [ABSTRACT FROM AUTHOR]

In this paper, we investigate how a research mathematician conjectures and proves when conducting her research. To be precise, the aim of this study is to achieve a comprehensive understanding of the way this research mathematician develops these mathematical practices and thus gain insight to improve the teaching and learning of these two practices in an educational context. For this purpose, we consider Rasmussen, Zandieh, King and Teppo's ([2005]. Advancing mathematical activity: A practice-oriented view of advanced mathematical thinking. Mathematical Thinking and Learning, 7(1), 51–73) theoretical constructs of horizontal and vertical mathematizing. In particular, we have adopted a case study methodological approach with a single research mathematician. Analysis of the data lead to the identification of eleven categories of activities. Each category is linked either to the practice of conjecturing or to the practice of proving, and also to the horizontal or vertical dimension of such practice. Finally, we compare and contrast our results with other related studies and give some educational suggestions that may derive from our work. [ABSTRACT FROM AUTHOR]

Piers Bohl (1865–1921) was an outstanding Latvian mathematician whose name is particularly connected with several crucial achievements that were ahead of their time. Unfortunately, the contemporary mathematical community did not recognize their significance. This paper discusses one of Bohl's results from 1908 that remained nearly unnoticed, even up until the present. It concerns a general complex trinomial and answers the problem of the distribution of its roots with respect to a given modulus. During the last few decades, this and other related problems have been extensively studied in numerous particular cases, without knowledge of this existing answer. This paper recalls the aforementioned Bohl's result and illustrates how easily it can imply conclusions of recent as well as older works regarding this topic. [ABSTRACT FROM AUTHOR]

In this paper we follow a hypothetical mathematician who is working on a problem that is eventually solved. We treat this problem as if it were difficult for the mathematician. In following the mathematician's work, we note both what she does and what she doesn't do in the process. By the latter, we consider the times when progress is not being made and how this lack of progress is resolved. The purpose here is to give some idea of how a research mathematician might approach a research level problem. We also propose that the problem under discussion is one of many problems that tertiary students can valuably tackle using a discovery-based approach as a means of using their mathematical content knowledge as well as learning to be creative. [ABSTRACT FROM AUTHOR]

What is the "right way" to define dimension? Mathematicians working in the early and middle 20th-century formalized three intuitive definitions of dimension that all turned out to be equivalent on separable metric spaces. But were these definitions the "right" ones? What would it mean to have the "right" definition of dimension? In this paper we attempt to inspire thought about these questions by introducing Abbott dimension, a geometrically intuitive definition of dimension based on Edwin Abbott's 1884 novella Flatland. We show that while Abbott dimension has intuitive appeal, it does not always agree with the classical definitions of dimension on separable metric spaces. [ABSTRACT FROM AUTHOR]

In this paper the author looks at the letters of two renowned women mathematicians and scientists of the Victorian period, Mary Somerville and Ada Lovelace, while also considering the imperceptibility of Sophie Germain, an important French mathematician and philosopher in their epistolary exchanges and philosophical writings. Drawing on the importance of mathematical correspondences and epistolary education in the creation, circulation and dissemination of knowledge, as well as in processes of formal and informal learning, the author argues that Lovelace’s and Somerville’s letters leave traces of a remarkable genealogical line of women’s mentorship and personal relations in the nineteenth century world of British mathematics in the backdrop of contradictory discourses around gender, mathematics, and science education. [ABSTRACT FROM AUTHOR]

Differential calculus was introduced into eighteenth-century Spain through the teaching of several authors in different scientific institutions. One of the more noteworthy of these Spanish authors was the Jesuit Tomàs Cerdà (1715–1791), who taught mathematics at the College of Cordelles in Barcelona and at the Imperial College in Madrid. This mathematician introduced differential calculus through the manuscript entitled 'Tratado de Fluxiones' (1757–1759), which had as a main source The Doctrine and Application of Fluxions (1750) by Thomas Simpson (1710–1761). Our aim in this paper is to analyse Cerdà's special contribution to the introduction into Spain of the Newtonian theory of fluxions based on Simpson's definition of a fluxion. Specifically, the paper shows that Cerdà deduced the fluxion of the product of two variables and the area under a curve by previously establishing the fluxion of a curvilinear surface, a particular and different approach to that employed by other contemporaneous mathematicians in Spain. [ABSTRACT FROM AUTHOR]

In 1932, the mathematician Hans Hahn delivered a lecture titled 'The crisis of intuition', held within a lecture series called 'Crisis and Reconstruction in the Exact Sciences', organized by Karl Menger. In order to account for the various crises, Hahn and his colleagues employed various metaphors. That being said, the dominant metaphor was architectural. Why was this particular metaphor used? And were there other metaphors that were equally important? In this paper, I aim not only to answer these questions, taking into account the image of mathematics and of the mathematician which was conveyed by those metaphors, but also to examine how the various crises were considered via these metaphorical reactions. [ABSTRACT FROM AUTHOR]

'The mathematisation of time has limits,' writes Derrida in 'Ousia and Gramme.' Taking this quote in all possible senses, this paper considers Derrida's definition of limit as gramme, trace, and aporia, and develops the 'mathematisation' of all three. I will consider the structure of mathematical limit in Fregean arithmetics, calculus, and topology. I argue that a topological approach to the concept of gramme creates a new 'limit' that illustrates the map of our 'commute' to the unknown, and therefore avoids the aporetic act of crossing the impassible limit between life and death. This new 'limit,' often referred to by mathematicians as a 'cone,' is a shapeless shape that offers us knowledge about time and space that we otherwise cannot gain. By redefining the 'limit' of time through three mathematical systems – arithmetic, calculus, and topology – this paper offers new perspectives to couple mathematics with philosophy. [ABSTRACT FROM AUTHOR]

Information about several papers of Working Group 12 (WG12) discussed at the Seventh Congress of the European Society for Research in Mathematics Education (CERME 7) held February 9-13, 2011 at Rzeszów in Poland is presented. Topics include the influence of other related fields when searching for theoretical constructs and the development of a questionnaire for determining pre-service teachers. Another paper focuses on the identity of Portuguese mathematics educators from 1981-1990.

It is generally accepted that teachers' beliefs impact their instructional choices, but characterizations of that relationship are limited in college settings. Furthermore, examinations of instructor beliefs, instruction, and student beliefs together in one setting are rarely described. Based on interviews with two Abstract Algebra instructors, classroom video from three units of instruction, and survey and interview data from students in the classes, this paper examines instructors' stated beliefs, ways these beliefs manifested in their teaching, and students' beliefs across the course. Both instructors made curricular choices clearly aligned with their stated views of the nature of mathematics, learning, and teaching. Day-to-day instructional choices reflected these stated beliefs as well, but the difficulty of material and tensions with other beliefs like the importance of interactivity manifested. Characterizations of the interactivity of classes and placement of the mathematical authority in class are provided through descriptive and quantitative measures. These characterizations of instruction provide nuanced portrayals of classroom norms and changes in those norms throughout the semester. Furthermore, subtle shifts in student beliefs about teaching and learning are noticeable, suggesting students' beliefs about teaching and learning mathematics can be influenced even by modest changes in instructional practice. [ABSTRACT FROM AUTHOR]

In his Formal Logic, Arthur N. Prior (1914–1969) declared that Jan Łukasiewicz's logical notation is 'unquestionably the best logical symbolism for most purposes'. Whether he had a substantive, and not only practical, reason for this notational preference is unclear. Through an investigation of his philosophical outlook towards the nature of logic and representation in general, and the nature of logical 'operators' in particular, this paper suggests that there might be a substantive argument for this declaration. This argument is premised on Prior's own metaphysical view that an adequate notation must represent the functional nature of these operators. [ABSTRACT FROM AUTHOR]

In the 1760s, the international debate on the solution to determining longitude at sea is at its acme. Two solutions emerge, the mechanical and the astronomical ones. The Portuguese mathematician and astronomer José Monteiro da Rocha (1734–1819) is well aware of that debate. For him, Harrison's No. 4 marine timekeeper cannot be seen as a solution. The desirable solution could only be astronomical. In a manuscript from c. 1765, which unfortunately he fails to publish, Monteiro da Rocha is very critical of Lacaille's lunar-distance method (1759) and proposes another one. In this paper, we intend to analyse Monteiro da Rocha's criticisms and proposals, trying to understand how this manuscript fits into the international longitude debate and the Portuguese scientific scenario at the time. Concurrently, we will re-examine the classical historiography around the English vs. French priority proposal of the lunar-distance method, purging it from its mythologies to shift it towards a more open, less linear history. [ABSTRACT FROM AUTHOR]

This paper describes a case study of two pure mathematicians who flipped their lecture to teach matrix determinants in two large mathematics service courses (one at Stage I and the other at Stage II). The purpose of the study was to transform the passive lecture into an active learning opportunity and to introduce valuable mathematical skills, such as debate, argument and disagreement. The students were told in advance to use the online material to prepare, which had a short handout on matrix determinants posted, as the lesson would be interactive and would rely on them having studied this. At the beginning of the lesson, the two mathematicians worked together to model the skill of professional disagreement, one arguing for the cofactor expansion method and the other for the row reduction method. After voting for their preferred method, the students worked in small groups on examples to defend their choice. Each group elected a spokesperson and a political style debate followed as the students argued the pros and cons of each technique. Although one lecture does not establish whether the flipped lecture model is preferable for student instruction, the paper presents a case study for pursuing this approach and for further research on incorporating this style of teaching in Science, Technology, Engineering and Mathematics subjects. [ABSTRACT FROM PUBLISHER]

This essay, which won the 2018 BSHM undergraduate essay prize, investigates the collaborative mathematical practice of Paul Erdős. It draws on new unpublished primary sources and oral history in both English and Hungarian. It raises the question of whether communal mathematics, or mathematics as a social activity, can lead to individual success. [ABSTRACT FROM AUTHOR]

In this paper I discuss different approaches to past mathematical texts. The question I address is: should we stress the continuity of past mathematics with the mathematics practiced today, or should we emphasize its difference, namely what makes it a product of a distant mathematical culture? [ABSTRACT FROM AUTHOR]

This paper will consider the range of British participation in mathematics internationally during the nineteenth century through an analysis of British mathematical contributions to scientific journals outside of Britain. Viewing scientific papers contained in journals as significant indicators of research, we consider scientists who authored or read and responded in print to papers in a given area within a given group of journals to constitute a publication community. The extent of publication by British mathematicians in these journals can help characterize the role of foreign publication in nineteenth-century British mathematics. Moreover, the isolation of educational, societal, and personal circumstances which motivated British mathematicians to present their work to foreign journals highlights limited but concentrated groups of mathematicians committed to developing and strengthening international mathematical ties with Britain. [ABSTRACT FROM AUTHOR]

The two main British exponents of the theory of invariants, Arthur Cayley and James Joseph Sylvester, first encountered the idea of an “invariant” in an 1841 paper by George Boole. In the 1850s, Cayley, Sylvester, and the Irish mathematician, George Salmon, formulated the basic concepts, developed the key techniques, and set the research agenda for the field. As Cayley and Sylvester continued to extend the theory off and on through the 1880s, first Salmon in 1859 and later Edwin Bailey Elliott in 1895 codified it in high-level textbooks. This paper sketches the development of nineteenth-century invariant theory in British hands against a backdrop of personal, nationalistic, and internationalistic mathematical goals. [ABSTRACT FROM AUTHOR]

In this article, the author offers gratitude to Professor Jean Cunge for his comments on the research paper on river hydraulics. Topics discussed include information related to fluid flow behavior and mechanisms, strengthening the links between mathematicians, hydrodynamic scientists and numerical analysts, and details related to the fundamentals of fluid flow behavior, turbulence and boundary layers.

This paper is a short essay about Sergei L'vovich Sobolev (1908–1989), an outstanding mathematician of the 20th century, who made fundamental contributions to the development of the modern theory of partial differential equations, equations of mathematical physics, functional analysis, function theory, and computational mathematics. [ABSTRACT FROM AUTHOR]

A convergence rate of Mann iteration has been studied by many mathematicians. Recently, its rate was improved in a Hilbert space. In this paper, we consider a convergence rate in a geodesic space and generalize the known result. [ABSTRACT FROM AUTHOR]

Over the last two decades, special matrix functions have become a major area of study for mathematicians and physicists. The famous four Appell hypergeometric matrix functions have received considerable attention by many authors from different points of view. The present paper is devoted to provide further investigations on the two variables second Appell hypergeometric matrix functions. Precisely, we derive certain mathematical properties such as limit formulae of Humbert hypergeometric matrix functions, recursion formulae using contiguous matrix relations, some differentiation and summation formulae. We also find general differential operators which induce some differential equations. This enriches the theory of special matrix functions. The obtained results are believed to be newly presented. [ABSTRACT FROM AUTHOR]

This paper describes a collaboration between a mathematician and a compositionist who developed a sequence of collaborative writing assignments for calculus. This sequence of developmentally appropriate assignments presents peer review as a collaborative process that promotes reflection, deepens understanding, and improves exposition. First, we distinguish writing-to-learn from writing-in-the-disciplines. Then, we review collaborative writing pedagogies and explain best practices for teaching peer review. Finally, we present an implementation plan and examples of student work that illustrate improved understanding of content and improved exposition. [ABSTRACT FROM PUBLISHER]

In this paper, we provide an alternative approach to establish the solution existence and uniqueness for elliptic variational-hemivariational inequalities. The new approach is based on elementary results from functional analysis, and thus removes the need of the notion of pseudomonotonicity and the dependence on surjectivity results for pseudomonotone operators. This makes the theory of elliptic variational-hemivariational inequalities more accessible to applied mathematicians and engineers. In addition, equivalent minimization principles are further explored for particular elliptic variational-hemivariational inequalities. Representative examples from contact mechanics are discussed to illustrate application of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we explore the role that examples play as mathematicians formulate conjectures, and we describe and exemplify one particular example-related activity that we observed in interviews with thirteen mathematicians. During our interviews, mathematicians productively used examples as they formulated conjectures, particularly by creating systematic lists of examples that they examined for patterns, an activity that we call “Comprehensive Example Generation”. We elaborate this construct, and we discuss ways in which it afforded productive conjecturing activity. The results suggest further research and pedagogical implications for explicitly targeting examples in conjecturing, and the study contributes to a body of literature that points to the benefits of exploring, identifying, and leveraging examples in proof-related activity. [ABSTRACT FROM AUTHOR]

This paper makes both a critical analysis of some popular cultural texts about mathematics and mathematicians, and explores the ways in which young people deploy the discourses produced in these texts. We argue that there are particular (and sometimes contradictory) meanings and discourses about mathematics that circulate in popular culture, that young people use these as resources in identity making as (non-)mathematicians, negotiating their meaning in ways that are not always predictable, and that their influence on young people is diffuse and nevertheless important. The paper discusses the discourses that prevail in some of the popular cultural images of mathematics and mathematicians that came up in our research. We show how mathematics is represented as a secret language, while mathematicians are often mad, mostly male and almost invariably white. We then explore how young people negotiate these discourses, positioning themselves in relation to mathematics. Here we draw attention to the fact that both those who continue with mathematics after it ceases to be compulsory and those who do not, deploy similar images of mathematics and mathematicians. What is different is how they respond to and negotiate these images. [ABSTRACT FROM AUTHOR]

The meeting of the British Society for Research into Learning Mathematics held at the University of Southampton on 21st June 2008 was dedicated to the memory of Brian Griffiths, who had died earlier that month. At the meeting it was suggested that I write a paper tracing the development of research in mathematics education in the UK up to the writing of Mathematics: Society and Curricula, a book that Brian and I co-authored, published in 1974. This paper is dedicated to Brian's memory: I hope that it will be considered a fitting tribute to a great friend and colleague, and to an outstanding mathematician and mathematics educator. [ABSTRACT FROM AUTHOR]

In our modern world, we are inundated and grapple with data daily. As mathematicians, we are often more comfortable discussing the behavior of functions presented analytically, in contrast with the data-driven or tabular presentations of functions ubiquitous in our culture. This paper introduces an entry-level course, Mathematical Modeling and Applied Calculus, for students who will most likely take only one calculus-level course in college and who often have a weak algebraic background that suggests they would most likely not be successful in a traditional calculus course. During the first half of the course, students review precalculus ideas while learning techniques for identifying elementary functional models whose graphs correspond to the underlying shapes of data sets, refining their models in response to new data, and using the method of least squares to find "best possible" models of a given type. During the second half of the course, these functional models are analyzed using the tools of calculus. Mathematical Modeling and Applied Calculus focuses on real-life contexts and data sets, uses RStudio to study large data sets, and explores big picture conceptual understandings in order to develop the insights and skills needed to describe, model, and analyze many aspects of our world. [ABSTRACT FROM AUTHOR]