Mathematical Work Research Articles

HOMOGENEOUS COLLATERAL SUBORDINATION IN MATHEMATICAL DISCOURSE IN RUSSIAN AND ROMANCE AND GERMANIC LANGUAGES

1. The purpose of this article is to study the structural and semantic particularities of multicomponent complex sentences with homogeneous collateral subordination in mathematical discourse and to conduct comparative analysis in the Russian and the Romance and Germanic languages. The article deals only with the structures that include object and attributive components. The authors identify the common patterns of functioning of these structures in the style used in exact sciences, as well as the differences in each of the languages. 2. The following methods are used in the work: the fundamental method is the structural and semantic analysis, which is considered to have been created by N.S. Pospelov and L.Yu. Maksimov, as well as the basic principles of communicative grammar; the transformational and textological analysis to identify the implicit differences in structure and semantics of the complex sentences under investigation; linguistic description based on the principle of induction; the statistical method to process the material and identify the frequency of the structures under investigation. The method of continuous sampling is used to collect the material. 3. As a result of the study, the authors have identified the particularities of the functioning of the structures in the style of exact sciences: the presence of the same/different conjunctions/connective words, the syntactical relations between the main clause and the subordinate clause, the consistency/inconsistency between the number of conjunctions and the number of subordinate clauses. Mathematical discourse has a certain effect on the structural and semantic qualities of these structures in the studied languages: they have a clear structure and their components are compact and have a standard structure. The structures under investigation have wide expressive possibilities and clear semantic relations which makes it easier to process complicated material. 4. This study can be useful for specialists who deal with both linguistics and mathematics. The study can be used in comparative analysis of texts in other fields of the functioning of the Russian and the Romance and Germanic languages, when writing new mathematical works, when translating scientific works into foreign languages, when conducting textological studies in other languages and when teaching linguistic subjects. 5. The scientific novelty of the study consists in the fact that this is the first instance of detailed analysis of the structure, semantics and the particularities of the functioning of multicomponent complex sentences with homogeneous collateral subordination in the style of exact sciences in the Russian and the Roman and Germanic languages. The structural and semantic varieties of the studied structures have been identified. The data have been provided on the frequency of their usage in mathematical works, the productivity of various types of connection of the main and the subordinate clause and the ratio of tense-aspect forms of the predicate in the main and the subordinate clauses.

Brouwer\u2019s Weak Counterexamples and the Creative Subject: A Critical Survey

I survey Brouwer’s weak counterexamples to classical theorems, with a view to discovering (i) what useful mathematical work is done by weak counterexamples; (ii) whether they are rigorous mathematical proofs or just plausibility arguments; (iii) the role of Brouwer’s notion of the creative subject in them, and whether the creative subject is really necessary for them; (iv) what axioms for the creative subject are needed; (v) what relation there is between these arguments and Brouwer’s theory of choice sequences. I refute one of Brouwer’s claims with a weak counterexample of my own. I also examine Brouwer’s 1927 proof of the negative continuity theorem, which appears to be a weak counterexample reliant on both the creative subject and the concept of choice sequence; I argue that it provides a good justification for the weak continuity principle, but it is not a weak counterexample and it does not depend essentially on the creative subject.

Episodes of interferences of War and Math in the Life and Work of Werner Fenchel

No presente artigo, estudamos episódios da vida e obra do matemático alemão-dinamarquês Werner Fenchel na perspectiva da importância da Segunda Guerra Mundial. Por um lado, veremos como a sociedade matemática, em particular o matemático Harald Bohr, ajudou Fenchel a estabelecer uma vida acadêmica em Copenhague, na Dinamarca. Por outro lado, veremos como a organização da contribuição do cientista para o esforço de guerra nos EUA durante a guerra e o financiamento militar pós-guerra da pesquisa acadêmica no período pós-guerra interferiu em alguns dos trabalhos matemáticos de Fenchel, especialmente em sua contribuição para a teoria da dualidade na programação não linear. Como tal, o estudo apresentado neste artigo contribui para nossa compreensão de como a matemática e as condições de um determinado local e tempo interferem na história da matemática.

Correlation of risk factors for coronary heart disease in type-2 diabetes mellitus using the chi-square method

The male sex is taken into account a crucial risk issue for coronary heart disease (CHD) within the general population, however, studies on diabetic patients counsel that diabetic girls have a better risk of developing CHD. This study was to determine whether there is correlation between risk factors and the incidence of CHD in patients with type 2 DM. Furthermore, this work also investigates the mathematical model work in calculating the magnitude of the risk of variables against the tendency of CHD complications for patients with type 2 diabetes. This research utilizes current information on the setup of Dr. Soetomo Hospital’s medical records in 2015-2016. Samples were all patients with type 2 diabetes with CHD and without CHD reported in the inpatient medical records of Dr. Soetomo Hospital Surabaya. Data processing was carried out using the chi-square test technique. As a result, the system is proof to calculate the worth of the chi-square and confirm the results of conditions on every variable. There is a distinction in price between the calculations of the chi-square on the system with the calculation of the manual chi-square test. This is often caused by taking variety of digits behind completely different commas (,). The variables of gender, age, GDA, GDP, GD2PP, triglycerides, HDL, weight, smoking, and length failed to have a significant relationship on the incidence of CHD in patients with sort two DM. Sterol variables and lipoprotein levels have a highly vital relationship within the incidence of CHD for patients with sort two polygenic disease.

Mathematical Modeling to Address Challenges in Pancreatic Cancer.

Pancreatic Ductal Adenocarcinoma (PDAC) is regarded as one of the most lethal cancer types for its challenges associated with early diagnosis and resistance to standard chemotherapeutic agents, thereby leading to a poor five-year survival rate. The complexity of the disease calls for a multidisciplinary approach to better manage the disease and improve the status quo in PDAC diagnosis, prognosis, and treatment. To this end, the application of quantitative tools can help improve the understanding of disease mechanisms, develop biomarkers for early diagnosis, and design patient-specific treatment strategies to improve therapeutic outcomes. However, such approaches have only been minimally applied towards the investigation of PDAC, and we review the current status of mathematical modeling works in this field.

Analysis and applications: The mathematical work of Elias Stein

Analysis and applications: The mathematical work of Elias Stein

Practices of reasoning: persuasion and refutation in a seventeenth-century Chinese mathematical treatise of "linear algebra".

This article documents the reasoning in a mathematical work by Mei Wending, one of the most prolific mathematicians in seventeenth-century China. Based on an analysis of the mathematical content, we present Mei's systematic treatment of this particular genre of problems, fangcheng, and his efforts to refute the traditional practices in works that appeared earlier. His arguments were supported by the epistemological values he utilized to establish his system and refute the flaws in the traditional approaches. Moreover, in the context of the competition between the Chinese and Western approaches to mathematics, Mei was motivated to demonstrate that the genre of fangcheng problems was purely a "Chinese" achievement, not discussed by the Jesuits. Mei's motivations were mostly expressed primarily in the prefaces to his works, in his correspondence with other scholars, in synopses of his poems, and in biographical records of some of his contemporaries.

The development of V. V. Strygin’s ideas in numerical mathematics in the works of Samara mathematicians

The article reviews the most important results in the field of numerical mathematics obtained by Professor V. V. Strygin’s disciples and the disciples of his disciples in 2000–2019 in the city of Samara. We present the results on spline interpolation of functions with a boundary layer, methods and algorithms for a posteriori adaptation of computational grids for singularly perturbed boundary value problems and the results on applied wavelet analysis based on spline wavelets.

Teaching a Formalized Logical Calculus

Classical first-order logic is in many ways central to work in mathematics, linguistics, computer science and artificial intelligence, so it is worthwhile to define it in full detail. We present soundness and completeness proofs of a sequent calculus for first-order logic, formalized in the interactive proof assistant Isabelle/HOL. Our formalization is based on work by Stefan Berghofer, which we have since updated to use Isabelle's declarative proof style Isar (Archive of Formal Proofs, Entry FOL-Fitting, August 2007 / July 2018). We represent variables with de Bruijn indices; this makes substitution under quantifiers less intuitive for a human reader. However, the nature of natural numbers yields an elegant solution when compared to implementations of substitution using variables represented by strings. The sequent calculus considered has the special property of an always empty antecedent and a list of formulas in the succedent. We obtain the proofs of soundness and completeness for the sequent calculus as a derived result of the inverse duality of its tableau counterpart. We strive to not only present the results of the proofs of soundness and completeness, but also to provide a deep dive into a programming-like approach to the formalization of first-order logic syntax, semantics and the sequent calculus. We use the formalization in a bachelor course on logic for computer science and discuss our experiences.

САМОСТІЙНА РОБОТА З МАТЕМАТИКИ ДЛЯ МАЙБУТНІХ УЧИТЕЛІВ ПОЧАТКОВИХ КЛАСІВ ЯК УМОВА ЇХНЬОГО ПРОФЕСІЙНОГО ЗРОСТАННЯ

The article is devoted to the problem of organizing independent work in mathematics for future primary school teachers. This problem is actualized today – in the period of education reform and Ukraine’s accession to the Bologna Process. Among the priority areas of pedagogical search is the problem of organizing the students’ independent work on the basis of personally-oriented and activity-based approaches using innovative teaching technologies. The development of important job-related qualities of a future teacher is to update and creatively apply theoretical knowledge, to form independency as a trait of character, in the approximation of educational activity to the future profession. The optimum use of all types of independent work, compliance with the conditions of its implementation, the functional preparation of the teacher and the student are the necessary conditions for its organization. Independent work of students in mathematics is one of the most important types of formation of subject and key competences, formation of a professiogram of future primary school teachers. The effectiveness of this process depends on the teacher’s ability to organize it correctly and optimally (clearly formulated tasks for students, availability of appropriate methodological support, timely consultations, discussion of results, an analysis of completed work, etc.).Today, within the framework of independent work in mathematics for students of the specialty “Elementary education” it is important to draw up an individual plan of study of the student (syllabus), which is at the same time a means of informing the student about the necessary amount of independent mastering of discipline. This ensures the organization of systematic independent work of students in mathematics during the semester. The syllabus, in particular, states the purpose and objectives of the course – to acquaint students with the basic concepts and methods of mathematics necessary for a thorough mastering of the entire course of mathematics, and the methods of teaching mathematics for the successful learning and education of younger students; to prepare students for the practical application of the acquired knowledge in their practical activities and for independent study of those sections of mathematics that may be required additionally in the practical and research work of future teachers.

Une situation qui problématise les passages discret-dense-continu

This article presents an analysis of the discussion and written work produced during an experiment in which two students in teacher training were asked to solve a version of the fixed-point problem initially proposed by Pontille, Feurly-Reynaud and Tisseron. Our interest lies in how the problem can be broken down into five tasks (proposed by us), and specifically the effect of an intermediary phase involving the set of numbers that have a maximum of five decimal places. We are also interested in how the students reorient their mathematical work based on the hints and clues provided by the researchers. In our analysis, we discuss─as much from an epistemological perspective as from a cognitive perspective─the problem of how to conceptualize/coordinate the properties of density and completeness when it comes to extending the set of rational numbers to the set of real numbers. We are particularly interested in the property of density (intrinsic, with respect to order) in ordered sets D and Q and the role it can play in the learner's ability to separate the numerical-arithmetic structure of the theoretical “real axis” from its representation in the figural register, which, according to our analysis, is one of the key aspects in the conceptualization of R.

Old Problem, New Perspectives: Applying Anzaldúan Concepts to Underrepresentation in STEM

Women and members of many ethnic minority groups continue to be significantly underrepresented in science, technology, engineering, and mathematics (STEM) education and work settings. In this article, we propose that Gloria Anzaldúa’s concepts of nepantla and nepantleras/os can be used to enrich perspectives on underrepresentation among those studying, working, and persisting in STEM fields. We describe how diversity practices may fail to address and foster inclusion in STEM education and workplaces and link inclusion and belonging to engagement and retention in STEM. Recommendations are offered for combining top-down and bottom-up strategies providing information, awareness, and skills training in STEM environments, including recognizing and engaging the insights and experiences of nepantleras/os.

The Jackson Heart Study: Preparing African American High School Students for Health Careers and Research.

In 1999, Tougaloo College (TC), located in Jackson, Mississippi, was charged, as a part of its role in the Jackson Heart Study (JHS), with creating a pool of well-trained high school students who, upon entering college, could successfully complete undergraduate and graduate or professional degrees in the health professions, biomedical research, and public health. TC identified the following educational challenges experienced by Mississippi high school students: inadequate exposure to reading, writing, logic, and quantitative skills; inadequate course work in science and mathematics; lack of mentors and role models in science-related fields as well as for exploration and identification of career options in the health professions and biomedical research. To this end, the JHS Undergraduate Training and Education Center (JHS UTEC) developed three four-week summer workshops in Science, Language Arts, and Mathematics (SLAM) for high school students in grades 9 through 11. Since SLAM's inception, more than 900 students have completed the program, and more than 90% have enrolled in college. In addition, according to National Student Clearinghouse and participant-reported data, many of the SLAM participants have earned not only undergraduate degrees in science, but also graduate degrees in a health-related and STEM fields. This article details the SLAM curricula and strategies for recruiting, selecting, training, and retaining high school students; we also present data to illustrate the success of the SLAM program.

Investigating the Development of Pre-Service Teachers’ Problem-Solving Strategies via Problem-Solving Mathematics Classes

<p style="text-align:justify">This study investigated the development of problem-solving strategies demonstrated by 42 elementary pre-service mathematics teachers in problem-solving mathematics classes. The study used a mixed methods approach of quantitative and qualitative research by analyzing the collected data.. The quantitative portion calculates the frequencies and percentage of the participants’ responses to the problems posed in three different phases of the intervention: before, during, and after receiving the mathematics lessons. The qualitative approach was used for in-depth investigation to describe various mathematical problem-solving strategies demonstrated by participants across the three different research phases. Findings of the study indicated a limited number of problem-solving strategies present during the first phase of research such as “use arithmetic operation strategy,” and “make a drawing strategy,”. During the implementation of the problem-solving lessons and classroom discussion, the participants began to develop more strategies such as “use logical reasoning,” “solve a simpler problem,” “guess and check,” “organize data in a table or a list,” “look for a pattern,” “work backwards,” and “solve an equation,”. However, the research findings nonetheless revealed participants’ weakness in applying the variety of skills required for success in problem solving, such as interpreting information, mathematical working, and logical thinking. Results also demonstrated a limited and incorrect use of mathematical terminology, as well as a lack of problem comprehension. The discussion of the study addresses different features and issues related to mathematical problem-solving strategies. In light of its findings, this study presents recommendations and suggestions for the future development of pre-service teachers’ problem-solving strategies.</p>

Grasping Mysteries: Girls Who Loved Math by Jeannine Atkins

Reviewed by: Grasping Mysteries: Girls Who Loved Math by Jeannine Atkins Elizabeth Bush Atkins, Jeannine Grasping Mysteries: Girls Who Loved Math. Atheneum, 2020 [320p] Trade ed. ISBN 9781534460683 $17.99 E-book ed. ISBN 9781534460706 $10.99 Reviewed from digital galleys R Gr. 5-8 As she did in Finding Wonders: Three Girls Who Changed Science (BCCB 6/16), Jeannine Atkins presents a distinguished sorority, drawing readers beyond the customary strictures of collective biographies and into a sensitive exploration not only of accomplishments but the resilient inner lives of women who struggled to navigate male-dominated fields. Seven chapters in verse highlight the familiar—Caroline Herschel, whose calculations led to multiple comet discoveries; Marie Tharp, whose sea floor maps forced geologists to take sea floor spread seriously; Katherine Johnson, whose mathematical work at NASA is finally receiving public acclaim. They also shed new light on a familiar name: nurse Florence Nightingale, whose data collection and graphing opened inroads in public health. Three less familiar figures add depth to the field: Hertha Marks Ayrton, for whom math led to a pioneering career in electrical engineering; Edna Lee Paisano, whose analytical work at the Census Bureau led to a career dedicated to redress of the decennial undercount of fellow Native Americans; and Vera Rubin, whose groundbreaking research on the speed of outer stars in spiral galaxies provided evidence for the existence of dark matter. Although longer biographical works are seldom grist for readalouds, Atkins' respect for the particularities of each life manifests in the image-rich poetry that recommends itself to oral presentation. For Caroline Herschel, for instance, "Winter offers long nights with more time/to sweep the sky, moving the telescope like a broom/meant to gather every star." Notes and bibliographies are appended for each entry. This is a must-buy for STEAM collections. Copyright © 2020 The Board of Trustees of the University of Illinois

Kritička recepcija Raselove "Historije zapadne filozofije" i "Mudrosti Zapada"

In this paper, the author critically considers the reception of one of the greatest thinkers of modern Western civilization, Bertrand Russell (1872-1970), analyzing his epochal works "History of Western Philosophy", "Wisdom of the West" and other writings. In addition to his other works in logic, mathematics and other scientific disciplines, I paid special attention to the political and legal dimension.

Dynamique du travail mathématique en classe entre un enseignant et des groupes d’élèves sur la simulation en probabilités : une étude de cas

The purpose of this contribution is to characterize the work of a teacher on simulations in probability in grade 9 course in France (14-15 year-old students). In a case study, we report in particular on what is at stake in the solving of a probability task with simulations when the teacher decides to organize small group work. Methodological tools, such as the chronogram, related to the specificity of this type of work in class are defined in the article. We have used the theory of Mathematical Work Spaces (MWS) and concepts such as potential suitable MWS and actual suitable MWS have been defined to conduct our study. The analysis of the teacher's interventions in the classroom revealed a standardization of the probabilistic model produced by the teacher during the simulation. The role of the teacher and the choice of the digital artefact transformed the students' work. We matched blockages, rebounds or identified containments in the actual MWS with the potential MWS. Our research has clarified first cognitive task routes in probability on The Hare and the Tortoise game.

Mary Somerville's early contributions to the circulation of differential calculus

In 1831, with the publication of her translation of Laplace's Mécanique Céleste, Mary Somerville (1780–1872) solidified her reputation throughout Western Europe as a highly proficient mathematician, and an expert in ‘French analysis’. To shed light on her preliminary studies, we here examine Somerville's earliest known mathematical work, namely her published and unpublished solutions to questions posed in the New Series of the Mathematical Repository, alongside her contemporary correspondence with mathematicians John and William Wallace. These submissions demonstrate her active engagement in the circulation of the differential calculus twenty years earlier than previously appreciated.

El camino cubista hacia la experiencia n-dimensional

El acercamiento metodológico del lenguaje cubista hacia las ciencias contemporáneas les llevó a interesarse por aquellas cuestiones que eran más novedosas y que estaban siendo más debatidas a principios del siglo XX, entre ellas, la temática relacionada con la Cuarta Dimensión y todo lo relativo a lo n-dimensional, tanto desde una perspectiva positivista como filosófica, lo que les inducirá a consultar no sólo publicaciones herméticas, sino especialmente los trabajos matemáticos de Esprit Jouffret y Henri Poincaré, cuyas nociones técnicas serán transmitidas especialmente por parte del matemático Maurice Princet. Dichos encuentros especulativos y toma de contacto con lo n-dimensional impulsaran una reorientación representativa en los trabajos de Marcel Duchamp, Juan Gris, Kazimir Malevich y especialmente las aportaciones de Albert Gleizes y Jean Metzinger, entre otros.

Collaborative group work in mathematics in the UK and Japan: use of group thinking measure tests

ABSTRACT This paper reports on a study of collaborative group work in mathematics. Although collaborative group work is known as one of the important approaches in education, it is still uncertain how group thinking can be measured in various learning contexts. We used the Group Thinking Measure (GTM) test developed by [Wegerif, R., T. Fujita, J. Doney, J. Perez Linares, A. Richards, and C. van Rhyn. 2017. “Developing and Trialing a Measure of Group Thinking.” Learning and Instruction 48: 40–50.] alongside mathematics tests to measure group thinking and group mathematical thinking. Our participants from Japan (134 pupils, 10–12 year old) and the UK (30 pupils, 11–12 year old) schools undertook the GTM individually and then in a group of three (triad), following which, the same group also solved sets of mathematics problems. From the quantitative results we found that examining whether a group is a Value Added Group or not in their GTM scores is a useful way to identify more mathematically effective groups. From a qualitative analysis of video data of pupils’ group work, we also found that successful problem solving might be due to the use of certain strategies. In conclusion, we consider that GTM can be used to indicate which groups are effective in subject areas such as mathematics.