Mathematical Language Research Articles

Methodical conditions which are conducive to improving the education of pupils to solve their context-based mathematics task

Relevance. The research's relevance is due to the need to explore optimal ways to improve the education of pupils in mathematics for the formation of mathematical literacy, by independently solving text-based tasks in mathematics regardless of the orientation of their interests and the chosen specialty. Purpose. The purpose of the article is the characterization of methodical conditions conducive to teaching pupils to solve mathematical tasks on their own. Methodology. The methodology of the research consisted of the use of a set of theoretical methods (general scientific, specific-scientific), which allowed processing of the scientific literature, distributing the information array, studying and clarifying terms and concepts, and structuring the collected information. And empirical methods – interviews and sociological surveys with teachers and experts in the field under study. The participants in this study were 70 primary school mathematics teachers in 2-5 grades. Results. The article analyzes the process of the collaboration between teacher and students during solving textual problems in various ways, which allows students to form not only knowledge and skills on the relevant issue, and also to develop such elements of mathematical literacy as logical thinking and form a literate mathematical language. Conclusions. The study's applied value is that the main points, factual materials, and conclusions can be used in the school system by teachers, methodologists, and research educators to develop recommendations for improving the teaching of schoolchildren's autonomy in solving text-based problems in mathematics.

BioModME for building and simulating dynamic computational models of complex biological systems.

Molecular mechanisms of biological functions and disease processes are exceptionally complex, and our ability to interrogate and understand relationships is becoming increasingly dependent on the use of computational modeling. We have developed "BioModME," a standalone R-based web application package, providing an intuitive and comprehensive graphical user interface to help investigators build, solve, visualize, and analyze computational models of complex biological systems. Some important features of the application package include multi-region system modeling, custom reaction rate laws and equations, unit conversion, model parameter estimation utilizing experimental data, and import and export of model information in the Systems Biology Matkup Language format. The users can also export models to MATLAB, R, and Python languages and the equations to LaTeX and Mathematical Markup Language formats. Other important features include an online model development platform, multi-modality visualization tool, and efficient numerical solvers for differential-algebraic equations and optimization. All relevant software information including documentation and tutorials can be found at https://mcw.marquette.edu/biomedical-engineering/computational-systems-biology-lab/biomodme.php. Deployed software can be accessed at https://biomodme.ctsi.mcw.edu/. Source code is freely available for download at https://github.com/MCWComputationalBiologyLab/BioModME.

Evaluation of school achievements in adolescents with primary hypertension.

Primary hypertension (HT) is a global public health problem with increasing prevalence in recent years. HT may have caused decreased neurocognitive functions and learning difficulties. In this study, clinical characteristics of adolescents with primary HT were examined and the relationship between semester grade point average (GPA) and HT was evaluated. This is an observational, cross-sectional, descriptive study conducted on adolescents with primary HT attending high school. Patient records (number of hospital visits, HT-related complaints, blood pressure measurements, and laboratory tests) were evaluated retrospectively. End-of-semester report card grades of Mathematics, Turkish Language and Literature and English courses were noted, and compared with the clinical characteristics of the patients. The study included 83 patients with a mean age of 15.6±1.2 years. Patients with higher body mass index had lower grades in Mathematics (p=0.007) and Turkish Language and Literature (p=0.004). Patients with HT-related symptoms such as headache, epistaxis and palpitations had lower GPAs for all courses. Also, patients with hyperuricemia or proteinuria had lower semester GPAs compared to patients with normal serum uric acid levels or without proteinuria (p<0.05). GPAs for Mathematics (p=0.000) and Turkish Language and Literature (p=0.006) decrease as the number of hospital visits increases. HT may cause not only cardiovascular complications but also decreased neurocognitive functions through various mechanisms and may have a negative impact on academic skills. Therefore, HT should be followed up with a multidisciplinary approach and intensive efforts should be made to approach the goal of normotension.

Application Strategies of Computer Technology in the Field of Mathematical Modeling

The era of big data has arrived in society, and the technology behind com-puter networks has not only raised the general level of people's living stand-ards but is also making steady headway in the direction of artificial intelli-gence. The most important theoretical basis for it is mathematics. The pro-cess of abstracting and synthesizing the laws of reality through the use of mathematical techniques is known as mathematical modeling. The applica-tion of mathematical modeling in the natural sciences seeks to approach a problem with more precision by employing mathematical rigor and a mathe-matical language that is systematically complete. At this point in time, the progression of mathematical modeling just can't happen without the assis-tance of advances in computer technology. The significance of computer technology in mathematical modeling is demonstrated by a detailed examina-tion of the formula underlying the computer technology model. After con-ducting research on the results of the mathematical modeling competition held over the course of several years, utilizing the artificial neural network (ANN) algorithm to analyze the data, and coming to the conclusion that the implementation of computer technology plays a role in the dissemination of mathematical modeling, we say that computer technology has a part to play in the dissemination of mathematical modeling.

Machine learning and deep learning-based approach to categorize Bengali comments on social networks using fused dataset.

Through the advancement of the contemporary web and the rapid adoption of social media platforms such as YouTube, Twitter, and Facebook, for example, life has become much easier when dealing with certain highly personal problems. The far-reaching consequences of online harassment require immediate preventative steps to safeguard psychological wellness and scholarly achievement via detection at an earlier stage. This piece of writing aims to eliminate online harassment and create a criticism-free online environment. In the paper, we have used a variety of attributes to evaluate a large number of Bengali comments. We communicate cleansed data utilizing machine learning (ML) methods and natural language processing techniques, which must be followed using term frequency and reverse document frequency (TF-IDF) with a count vectorizer. In addition, we used tokenization with padding to feed our deep learning (DL) models. Using mathematical visualization and natural language processing, online bullying could be detected quickly. Multi-layer Perceptron (MLP), K-Nearest Neighbors (K-NN), Extreme Gradient Boosting (XGBoost), Adaptive Boosting Classifier (AdaBoost), Logistic Regression Classifier (LR), Random Forest Classifier (RF), Bagging Classifier, Stochastic Gradient Descent (SGD), Voting Classifier, and Stacking are employed in the research we conducted. We expanded our investigation to include different DL frameworks. Deep Neural Networks (DNN), Convolutional Neural Networks (CNN), Convolutional-Long Short-Term Memory (C-LSTM), and Bidirectional Long Short-Term Memory (BiLSTM) are all implemented. A large amount of data is required to precisely recognize harassing behavior. To rapidly recognize internet harassment written material, we combined two sets of data, producing 94,000 Bengali comments from different points of view. After understanding the ML and DL models, we can see that a hybrid model (MLP+SGD+LR) performed more effectively when compared to other models, its evaluation accuracy is 99.34%, precision is 99.34%, recall rate is 99.33%, and F1 score is 99.34% on multi-label class. For the binary classification model, we got 99.41% of accuracy.

Terminology in the Age of AI: The Transformation of Terminology Theory and Practice

Abstract This article explores the necessary transformation of terminology theory and practice induced by advances in artificial intelligence (AI), in particular generative AI and large language models (LLMs). It underlines the centrality of terminology for accurate and efficient multilingual communication, and it studies the interaction between two different forms of language, the embodied language of humans and the algorithmic and mathematical language of AI. The analysis traces the evolution of terminology, from its normative, concept-centric origins to contemporary challenges such as the concept-context gap, multilingual conceptual modeling and enriching terminologies with contextual relations. The article then highlights how AI and LLM are revolutionizing terminology work, by proposing the construction of relations between terms around prototypical contexts. This innovative approach aims to infuse a more deterministic understanding into human-AI interactions, guiding the latter to generate responses more aligned with human intent and context. Advocating a re-evaluation of current methodologies to interact better with AI's algorithmic mathematical interpretation of natural language, the article envisions a future in which terminology science and AI co-create a framework for improving multilingual knowledge exchange and understanding.

Experimental simulation of quantum superchannels

Simulating quantum physical processes has been one of the major motivations for quantum information science. Quantum channels, which are completely positive and trace preserving processes, are the standard mathematical language to describe quantum evolution, while in recent years quantum superchannels have emerged as the substantial extension. Superchannels capture effects of quantum memory and non-Markovianality more precisely, and have found broad applications in universal models, algorithm, metrology, discrimination tasks, as examples. Here, we report an experimental simulation of qubit superchannels in a nuclear magnetic resonance (NMR) system with high accuracy, based on a recently developed quantum algorithm for superchannel simulation. Our algorithm applies to arbitrary target superchannels, and our experiment shows the high quality of NMR simulators for near-term usage. Our approach can also be adapted to other experimental systems and demonstrates prospects for more applications of superchannels.

Unique and combined effects of quantitative mathematical language and numeracy instruction within a picture book intervention: A registered report.

Unique and combined effects of quantitative mathematical language and numeracy instruction within a picture book intervention: A registered report.

Describing growing tissues in the language of thermodynamics

New analysis shows how key properties of biological tissues can be accurately described in the mathematical language of Onsager’s variational principle, widely used to describe continually changing systems in thermodynamics.

Various Flow in a Slender Tube: Mach Number and Domain Shape Influenced by Boundary Obstacles Via Small Disturbance Equations

With the exponential advancements in computer hardware and software in recent years, computational fluid dynamics (CFD) has emerged as a highly efficient alternative to traditional fluid mechanics studies. Its prowess in accurately predicting and analyzing flow mechanics has led to widespread adoption across diverse engineering disciplines. This research delves into a numerical analysis of flow conditions utilizing the small disturbance equation (SDE). The study bridges the gap between mathematical formulations and computational language, exemplified through Python code, by harnessing the successive over-relaxation (SOR) method, Neumann boundary conditions (BC), and the ghost point technique. The research underscores its predictions' precision in subsonic and supersonic scenarios by meticulously evaluating the resultant errors. This accuracy is further corroborated by examining overarching flow patterns and Mach number distributions. However, the program's outputs indicate a discernible lack of precision in the transonic case, with errors surpassing acceptable thresholds. This discrepancy is hypothesized to stem from potential mischaracterizations of points at the inflow and outflow boundaries. This study, thus, offers invaluable insights while also highlighting areas necessitating further refinement.

Intensification of a methodological approach for mathematical expressions using diverse software: A review study

This current paper attempted to review the methodical intensification of diverse software to teach and learn mathematical expression. The intention is to use this software to solve and create dynamic visualization of expressions in 2D or 3D for various topics in mathematics. The difficulties in teaching mathematical expressions by conventional methods are replicated in this work, to which pertinent topics. One of the main issues, which should have some consequences, is the description of the difficulties in teaching mathematical expressions. It should be addressed with some findings and discussion; highlighted results are included to set the scene. To make the mathematics classroom transition between the topics and the session easier, the software system also presents mathematical language in a manner that is congruent with handwritten notations and textbooks. These elements emphasized that the educational system needed a paradigm change in technique, and the particular subsections would provide detailed justifications for the use of software to teach expressions. The exposures of certain topics in mathematics that assisted with the relevant software will then be drawn by different researchers and highlighted for better comprehension. To enable a software system, its modular architecture divides symbolic math software components from math display components. The relevant software undertaken is such as SciLab, Maxima, and Microsoft Mathematics, and some importance of this software is recorded with suitable themes. Thus, the theme includes the explosion of SciLab, Maxima, and Microsoft Mathematics, thus represented in text and diagrammatic format. Finally, a conclusion and recommendation insist on the specification of diverse software to perform calculations on expression in mathematics.

Kemampuan Siswa SMP dalam Menyelesaikan Persoalan Matematika Dasar

Basic mathematical abilities are having the basic ability (being able) to think deductively in building theories and communicating the results of scientific activities correctly and being able to communicate accurate, precise, artificial language in mathematics. Basic mathematical abilities also include the basic skills needed to understand and solve mathematical problems at a basic level. This research was conducted with the aim of describing the profile of students' basic mathematical abilities in solving basic problems. Elementary schools have a key role in building the foundations of mathematics education for students. Basic mathematics is taught at this level to help students understand basic mathematical concepts necessary in everyday life and to prepare them for further mathematics learning at higher levels. It is important to ensure that the mathematics foundation built at the primary school level is strong, as this will influence students' understanding and success at higher levels of education. Junior high school is the second level of school after elementary school, and at this stage students are taught about basic mathematics or easy mathematics that usually occurs in everyday life. Such as calculations which develop students' basic calculation skills, understanding number concepts such as fractions, decimal numbers and whole numbers, addition, multiplication and division. Using mathematics in real contexts, so that students can see the relevance and usefulness of mathematics in everyday life.

Training of engineers on a bilingual basis: specifics of the English mathematical language

Due to globalization processes in higher education, the use of English as the medium of instruction is becoming more widespread in non-English-speaking countries. Bilingual education is actively being implemented in Ukraine, where professional disciplines are taught in a foreign language, primarily English. This article emphasizes that in bilingual education, the foreign language serves not only as a goal but also as a means of comprehending specialized knowledge. Consequently, the issues related to the nuances of employing a foreign language within specific subject areas, especially when teaching professional disciplines at technical universities, are highly relevant. The article underscores that, at present, only specific aspects of the challenges associated with bilingual higher education have been identified. A comprehensive concept of bilingual professional education in Ukraine has yet to be fully developed. In particular, the methodological and technological foundations for bilingual education in professional engineering and technical disciplines remain underdeveloped. The primary objective of this work is to explore the distinctive features of the English mathematical language within the context of bilingual training for future engineers. The article also analyzes the use of mathematical symbols in acquiring relevant linguistic conventions. It highlights various linguistic aspects of mathematical English texts and conducts a comparative analysis between mathematical and general literary language, examining their shared characteristics and differences. From this perspective, the article delves into the semantic and syntactic aspects of mathematical language, its vocabulary, terminology, and the role of symbols in mathematical expressions. Particular attention is devoted to the use of variables in standard expressions. Various types of variables are identified, including terms, characteristics, and references. The article introduces the concept of “highlighting a form in mathematical language and filling this form with variables”, essentially associating structure with content. The practical application of this concept results in the creation of mathematical templates or clichés, which are utilized in bilingual mathematics education. The article provides examples of such templates and illustrates how they can be employed. Practical experience confirms the effectiveness of this approach, especially when teaching higher mathematics in English to students pursuing engineering and technical specialties. It demonstrates that students can quickly grasp the fundamentals of the English mathematical language through this method

An artificial neural network approach for the language learning model

The current study provides the numerical solutions of the language-based model through the artificial intelligence (AI) procedure based on the scale conjugate gradient neural network (SCJGNN). The mathematical learning language differential model is characterized into three classes, named as unknown, familiar, and mastered. A dataset is generalized by using the performance of the Adam scheme, which is used to reduce to mean square error. The AI based SCJGNN procedure works by taking the data with the ratio of testing (12%), validation (13%), and training (75%). An activation log-sigmoid function, twelve numbers of neurons, SCJG optimization, hidden and output layers are presented in this stochastic computing work for solving the learning language model. The correctness of AI based SCJGNN is noted through the overlapping of the results along with the small calculated absolute error that are around 10–06 to 10–08 for each class of the model. Moreover, the regression performances for each case of the model is performed as one that shows the perfect model. Additionally, the dependability of AI based SCJGNN is approved using the histogram, and function fitness.

Professional learning in moments of whole-class discussion in a lesson study

This article aims to present 1st cycle of basic education Portuguese teachers’ learning of teaching pupils between 6 and 7 years of age, when they plan, lead and reflect on the moment of whole-class discussion, during a lesson study in mathematics. It is a qualitative research, and data collection was carried out by non-participant observation with the elaboration of a logbook and audio and video recording of sessions. The results show that, when planning the whole-class discussion, the teachers became aware of the importance of planning teaching in detail, paying attention to the objectives that are intended to achieve and the role of the teacher in the whole-class discussion. When they conducted and reflected on the discussion, the teachers understood the need to act during the undertaking of the task, in order to support pupils in terms of mathematical language so that they could better communicate their reasoning to their colleagues.

METHOD OF "CHOOSING AN ARBITRARY POINT"

The vector method is one of the most general approaches for solving geometric problems. The universality of this method is so broad that it is applied in algebra, mathematical analysis, geometry, and physics. It is used to solve problems of increased complexity, entrance exams for universities, and high-level mathematical Olympiad problems. The vector method is relatively new in mathematics. Primarily, I propose using it to solve problems that involve vectors in their statements. Such problems will be discussed below in this article. The solutions obtained through this method often have a more concise form, unlike traditional solutions, which can sometimes appear too cumbersome. However, I want to emphasize that comparing classical and vector methods is inappropriate. These are different "languages of mathematics," and we are learning to "speak" in one of them.

MAXWELL’S UNIFICATION OF OPTICS AND ELECTROMAGNETISM AND THE INCOMMENSURABILITY TENET

It is contended that one of the promising directions for solving the problem of incommensurability of paradigms, coined by T. Kuhn and P. Feyerabend, can be associated with the trend of advancement of neo-Kantian epistemology, presented by the writings of Ernst Cassirer. According to Cassirer, the statements fixing connections and relationships between mathematical ideal constructs form a “neutral language” that can serve as a firm ground for comparing the “old” and “new” paradigms. A case study of the genesis and functioning of a neutral mathematical language related to the Maxwellian synthesis of optics and electromagnetism isprovided. It is elicited that its basis is constituted by the mathematical language of continuum mechanics. The main function of the neutral language was to project the consequences of all the unified theories onto the mathematical model, “rewrite” all known laws in this mathematical language, compare their conclusions with each other to eliminate contradictions and generalize the stuff in a self-consistent system of equations.

NCS 수리능력 영역의 대수 문장제 해결 과정에서 나타난 오류 분석에 관한 연구

Objectives The purpose of this study is to analyze errors that arise during the problem-solving process of alge-braic word problems in the mathematical reasoning domain of NCS(National Competency Standards) for speci-alized high school students and to explore instructional strategies to address these errors.&#x0D; Methods A test consisting of six items was administered to 70 students attending specialized high schools lo-cated in medium city. After conducting the test using the questionnaire, the response sheets were analyzed by error type. Additionally, in-depth interviews were conducted with five participants, and the content of these inter-views was recorded, transcribed, and analyzed.&#x0D; Results Many students in specialized high schools experienced difficulties in solving algebraic word problems in the NCS mathematical competency domain. The types of errors observed during the problem-solving process in-cluded errors in skipping solution steps, difficulties arising from mathematical language, errors in problem com-prehension, and errors stemming from inadequate mastery of prerequisite skills, facts, and concepts.&#x0D; Conclusions To address significant errors in solving algebraic word problems, it is crucial to focus on algebraic translation, fundamental computational skills, acquiring prerequisite knowledge, and systematic problem-solving writing. Instruction should be centered around vocational foundational abilities, particularly emphasizing algebraic word problems within the context of vocational math competency assessment. Moreover, it is necessary to in-corporate algebraic word problems into the mathematical application domain of specialized high school vocational foundational assessments and develop and implement an education curriculum tailored to the specialized voca-tional context, preparing students for the NCS mathematical ability assessment.

Теорема Геделя о неполноте: говорит ли она о неполноте математики?

The report will propose some methodological approach (“method of eliminating monsters”) going back to Lakatos (“Proof and refutation”) to the analysis of Godel’s theorem, which shows that despite its mathematical correctness, Godel’s theorem is not applicable to mathematics (recursive arithmetic), since the Gödel expression is not a formula, but a formulaoid (Yesenin-Volpin), or a mathematical “monster” that must be eliminated from the field (language) of mathematics. This makes it possible to “remove” Godel's thesis about the incompleteness of mathematics, although it does not cancel the task of positively proving its completeness.

On solving some stochastic delay differential equations by Daubechies wavelet

There are numerous phenomena in real world that their practical modeling in mathematics language deals with differential equations. Stochastic terms have significant roles in estimating behavior of these events such as machine tool vibrations, biology, traffic dynamics, neural networks and so on, it cannot be reasonable to consider an event without its past information, and it ends up with equations including time delays. The numerical solution of stochastic delay differential equations has always been of interest to researchers. In this paper, by using scaling function of the Daubechies wavelet, a collocation method is presented to solve a class of stochastic delay differential equations and it is tried to demonstrate the advantages of using this type of wavelet. Convergence of the method is provided and numerical experiments are reported to show application of the method in practice.