• The Mathematical Education
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• v.62 no.2
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• pp.289-302
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• 2023

In today's digital information society, student knowledge and skills to analyze big data and make informed decisions have become an important goal of school mathematics. Integrating big data statistical projects with digital technologies in high school <Artificial Intelligence> mathematics courses has the potential to provide students with a learning experience of high impact that can develop these essential skills. This paper proposes a set of guidelines for designing effective big data statistical project-based tasks and evaluates the tasks in the artificial intelligence mathematics textbook against these criteria. The proposed guidelines recommend that projects should: (1) align knowledge and skills with the national school mathematics curriculum; (2) use preprocessed massive datasets; (3) employ data scientists' problem-solving methods; (4) encourage decision-making; (5) leverage technological tools; and (6) promote collaborative learning. The findings indicate that few textbooks fully align with these guidelines, with most failing to incorporate elements corresponding to Guideline 2 in their project tasks. In addition, most tasks in the textbooks overlook or omit data preprocessing, either by using smaller datasets or by using big data without any form of preprocessing. This can potentially result in misconceptions among students regarding the nature of big data. Furthermore, this paper discusses the relevant mathematical knowledge and skills necessary for artificial intelligence, as well as the potential benefits and pedagogical considerations associated with integrating technology into big data tasks. This research sheds light on teaching mathematical concepts with machine learning algorithms and the effective use of technology tools in big data education.

• Communications for Statistical Applications and Methods
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• v.15 no.1
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• pp.117-124
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• 2008

The liquidity risk is defined as an additional risk in the market due to the timing and size of a trade. A recent work by Cetin et ai. (2003) proposes a rigorous mathematical model incorporating this liquidity risk into the arbitrage pricing theory. A practical problem arising in a real market application is an estimation problem of a liquidity cost. In this paper, we propose to estimate the liquidity cost function in the context of Cetin et al. (2003) using the constrained least square (LS) method, and illustrate it by analyzing the Kellogg company data.

• Journal of the Korean Mathematical Society
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• v.42 no.4
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• pp.773-793
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• 2005

We consider interesting conditions, one of which will be called the disjoint $(A^2,\;D^2)-pair$ property, on genus $g{\geq}2$ Heegaard splittings of compact orient able 3-manifolds. Here a Heegaard splitting $(C_1,\;C_2;\;F)$ admits the disjoint $(A^2,\;D^2)-pair$ property if there are an essential annulus Ai normally embedded in $C_i$ and an essential disk $D_j\;in\;C_j((i,\;j)=(1,\;2)\;or\;(2,\;1))$ such that ${\partial}A_i$ is disjoint from ${\partial}D_j$. It is proved that all genus $g{\geq}2$ Heegaard splittings of toroidal manifolds and Seifert fibered spaces admit the disjoint $(A^2,\;D^2)-pair$ property.

• Journal of Mechanical Science and Technology
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• v.20 no.8
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• pp.1232-1239
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• 2006

In the present study, the unsteady Hartmann flow with heat transfer of a viscous incompressible electrically conducting fluid under the influence of an exponentially decreasing pressure gradient is studied. The parallel plates are assumed to be porous and subjected to a uniform suction from above and injection from below while the fluid is acted upon by an external uniform magnetic field applied perpendicular to the plates. The equations of motion are solved analytically to yield the velocity distributions for both the fluid and dust particles. The energy equations for both the fluid and dust particles including the viscous and Joule dissipation terms, are solved numerically using finite differences to get the temperature distributions.

• Journal of Engineering Education Research
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• v.24 no.6
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• pp.79-85
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• 2021

In a future society where cutting-edge science technology such as artificial intelligence becomes commonplace, the demand for talented people with basic knowledge of mathematics and science is expected to increase continuously, and the educational infrastructure suitable for the characteristics of future generations is still insufficient. In particular, in the case of students taking convergence courses including practical training, there was a problem in communication with the instructor. In this study, we looked at the current status of distance learning at domestic universities that came suddenly due to the global pandemic of COVID-19. In addition, a case study of the use of technology was conducted to facilitate the interaction between instructors and learners through case analysis of distance classes in convergence subjects. Therefore, this study aims to introduce the case of developing lecture contents for smooth convergence education in a non-face-to-face educational environment targeting the developed AI convergence courses and applying them to the education of enrolled students.

• Journal for History of Mathematics
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• v.24 no.4
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• pp.1-6
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• 2011

We investigate a method to find the least common multiples of numbers in the mathematics book GuIlJib(구일집(九一集), 1724) written by the greatest mathematician Hong Jung Ha(홍정하(洪正夏), 1684~?) in Chosun dynasty and then show his achievement on Number Theory. He first noticed that for the greatest common divisor d and the least common multiple l of two natural numbers a, b, l = $a\frac{b}{d}$ = $b\frac{a}{d}$ and $\frac{a}{d}$, $\frac{b}{d}$ are relatively prime and then obtained that for natural numbers $a_1,\;a_2,{\ldots},a_n$, their greatest common divisor D and least common multiple L, $\frac{ai}{D}$($1{\leq}i{\leq}n$) are relatively prime and there are relatively prime numbers $c_i(1{\leq}i{\leq}n)$ with L = $a_ic_i(1{\leq}i{\leq}n)$. The result is one of the most prominent mathematical results Number Theory in Chosun dynasty. The purpose of this paper is to show a process for Hong Jung Ha to capture and reveal a mathematical structure in the theory.

• Communications of Mathematical Education
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• v.36 no.1
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• pp.1-21
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• 2022

The purpose of this study is to analyze the current situation of EduTech, which is proposed as a way to build a flexible learning environment regardless of time and place according to the use of digital technology in mathematics subjects. The process of designing classes to use the EduTech platform, which is still in the development introduction stage, in public education is still difficult, and research to observe its effects and characteristics is also in its early stages. However, in the stage of preparing for future education, it is a meaningful process to grasp the current situation and point out the direction in preparation for the future in which EduTech will be actively applied to education. Accordingly, the current situation and utilization trends of EduTech at home and abroad were confirmed, and the functions and roles of EduTech platforms used in mathematics were analyzed. As a result of the analysis, the EduTech platform was pursuing learners' self-directed learning by constructing its functions so that they could be useful for individual learning of learners in hierarchical mathematics education. In addition, we have confirmed that the platform is evolving to be useful for teachers' work reduction, suitable activities, and evaluations learning management. Therefore, it is necessary to implement instructional design and individual customized learning support measures for students that can efficiently utilize these platforms in the future.

• The Mathematical Education
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• v.63 no.2
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• pp.165-186
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• 2024

Despite the growing attention on artificial intelligence-based automated scoring technology as a support method for the introduction of descriptive items in school environments and large-scale assessments, there is a noticeable lack of foundational research in mathematics compared to other subjects. This study developed an automated scoring model for two descriptive items in first-year middle school mathematics using the Random Forest algorithm, evaluated its performance, and explored ways to enhance this performance. The accuracy of the final models for the two items was found to be between 0.95 to 1.00 and 0.73 to 0.89, respectively, which is relatively high compared to automated scoring models in other subjects. We discovered that the strategic selection of the number of evaluation categories, taking into account the amount of data, is crucial for the effective development and performance of automated scoring models. Additionally, text preprocessing by mathematics education experts proved effective in improving both the performance and interpretability of the automated scoring model. Selecting a vectorization method that matches the characteristics of the items and data was identified as one way to enhance model performance. Furthermore, we confirmed that oversampling is a useful method to supplement performance in situations where practical limitations hinder balanced data collection. To enhance educational utility, further research is needed on how to utilize feature importance derived from the Random Forest-based automated scoring model to generate useful information for teaching and learning, such as feedback. This study is significant as foundational research in the field of mathematics descriptive automatic scoring, and there is a need for various subsequent studies through close collaboration between AI experts and math education experts.

• Journal of the Korea Society for Simulation
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• v.31 no.2
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• pp.11-20
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• 2022

There is a critical need for AI assistance in guard operations of Army base perimeters, which is exacerbated by changes in the national defense and security environment such as force reduction. In addition, the possibility for human error inherent to perimeter guard operations attests to the need for an innovative revamp of current systems. The purpose of this study is to propose a real-time object detection AI tailored to military CCTV surveillance with three unique characteristics. First, training data suitable for situations in which relatively small objects must be recognized is used due to the characteristics of military CCTV. Second, we utilize a data augmentation algorithm suited for military context applied in the data preparation step. Third, a noise reduction algorithm is applied to account for military-specific situations, such as camouflaged targets and unfavorable weather conditions. The proposed system has been field-tested in a real-world setting, and its performance has been verified.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.46 no.3
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• pp.170-185
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• 2023

The advent of big data has brought about the need for analytics. Natural language processing (NLP), a field of big data, has received a lot of attention. Topic modeling among NLP is widely applied to identify key topics in various academic journals. The Korean Society of Industrial and Systems Engineering (KSIE) has published academic journals since 1978. To enhance its status, it is imperative to recognize the diversity of research domains. We have already discovered eight major research topics for papers published by KSIE from 1978 to 1999. As a follow-up study, we aim to identify major topics of research papers published in KSIE from 2000 to 2022. We performed topic modeling on 1,742 research papers during this period by using LDA and BERTopic which has recently attracted attention. BERTopic outperformed LDA by providing a set of coherent topic keywords that can effectively distinguish 36 topics found out this study. In terms of visualization techniques, pyLDAvis presented better two-dimensional scatter plots for the intertopic distance map than BERTopic. However, BERTopic provided much more diverse visualization methods to explore the relevance of 36 topics. BERTopic was also able to classify hot and cold topics by presenting 'topic over time' graphs that can identify topic trends over time.