• The Mathematical Education
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• v.63 no.2
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• pp.123-138
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• 2024

This study described the utilization of ChatGPT in teaching and students' learning processes for the course "Introductory Mathematics for Artificial Intelligence (Math4AI)" at 'S' University. We developed a customized ChatGPT and presented a learning model in which students supplement their knowledge of the topic at hand by utilizing this model. More specifically, first, students learn the concepts and questions of the course textbook by themselves. Then, for any question they are unsure of, students may submit any questions (keywords or open problem numbers from the textbook) to our own ChatGPT at https://math4ai.solgitmath.com/ to get help. Notably, we optimized ChatGPT and minimized inaccurate information by fully utilizing various types of data related to the subject, such as textbooks, labs, discussion records, and codes at http://matrix.skku.ac.kr/Math4AI-ChatGPT/. In this model, when students have questions while studying the textbook by themselves, they can ask mathematical concepts, keywords, theorems, examples, and problems in natural language through the ChatGPT interface. Our customized ChatGPT then provides the relevant terms, concepts, and sample answers based on previous students' discussions and/or samples of Python or R code that have been used in the discussion. Furthermore, by providing students with real-time, optimized advice based on their level, we can provide personalized education not only for the Math4AI course, but also for any other courses in college math education. The present study, which incorporates our ChatGPT model into the teaching and learning process in the course, shows promising applicability of AI technology to other college math courses (for instance, calculus, linear algebra, discrete mathematics, engineering mathematics, and basic statistics) and in K-12 math education as well as the Lifespan Learning and Continuing Education.

• The KIPS Transactions:PartD
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• v.12D no.6 s.102
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• pp.869-874
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• 2005

In the recent years there has been an increase of service competition in the activity of product selling, especially in the extension of warranty coverage and qualify. The variables in connection with the service competition are not crisp, and required the expertise of the production line. It thus becomes all the more necessary to use subtler tools as decision supports. These problems are typical not only of product companies but also of financial organizations, credit institutions, insurance, which need predictions of credibility for firms or persons in which they have any kind of interest. A suitable approach for minimizing the risk is to use a knowledge-based system. Most often expert systems are not standalone programs, but are embedded into a larger application. The aim of this paper is to discuss an approach for developing an embedded fuzzy expert system with respect to the product selling policy, especially to present the decision system of automobile selling activity around the extension of warranty coverage and quality. We use the MATLAB tools which integrates computation, visualization, and programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation. Also, we present the API functions embedding into the existing application.

• Journal of Technology Innovation
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• v.23 no.4
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• pp.33-61
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• 2015

The global economy is rapidly changing by technological innovation and diffusion of knowledge across nations. Therefore it is still important issue to find a major variables for convergence and divergence of economic development. The studies up to present on the relationship between innovation and institution has limitations that they have dealt with this issue only in term of cross-sectional study or mathematical research models. This paper aims at analyzing the impact of innovation capabilities and institutional quality on the economic growth. Empirically this paper will explore the relationship among human capital capacity and FDI, R&D expenditures and innovation capabilities and institutional quality. This paper analyzes 64 countries, which were divided into 4 groups depending on the level of economic development. Based on the data from 1995 to 2011 and by using a panel model, we look at the structural implications of the research questions. According to our analysis, the weight of R&D and the innovation capabilities were identified as important determinants of economic growth, and FDI was significant factor for economic growth in the upper middle group countries. In case of the innovation capabilities of countries, the diffusion and openness of innovation were most meaningful variables for economic growth. Also, institutional quality has a significantly positive impact. However, in the low-level economic group, innovation capabilities and institutions have a negative impact on economic growth. This paper identifies an important policy implications that of national innovation and institutional factors should be properly invested in accordance with the level of a country's economic growth.

• Journal of Educational Research in Mathematics
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• v.26 no.2
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• pp.247-267
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• 2016

It has been pointed out that the mathematics textbooks according to 2009 revised national curriculum cause difficulty not by mathematical knowledge but concomitantly by words and sentences for the first graders who just started learning Korean alphabets. This study focused on the suitability of words and sentences in mathematics textbooks for elementary first grade. We analyzed the degree of difficulty and familiarity in terms of words and the structure, length, and expression in terms of sentences. The results show some causes that lead the first graders to the difficulty. In more detail, we found 108 difficult words and 6 unfamiliar words for the first graders. And it is noticed that the textbooks contain 37 compound sentences, 727 complex sentences, and 38 compound-complex sentences. They also contain 237 long sentences that are composed of 9 words or more, 168 sentences that assign two activities or more, and 52 sentences that contain three nouns or adjectives or more successively. Based on these results and discussions, we suggested several implications for writing mathematics textbooks for the lower grades in elementary school.

• Korean Journal of Child Education & Care
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• v.17 no.4
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• pp.145-161
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• 2017

The purpose of this study was to analyze the relationship among NCS basic vocational competencies, Teaching Personality Aptitude and DISC behavior type of pre-preschool teachers. The subjects were 110 pre-preschool teachers attended in D university located in Kyonggido. 'NCS basic vocational competencies scale', 'Teaching Personality and Aptitude scale', and 'DISC behavior type scale' were used in the collection of data. It used Pearson's correlation Analysis to analyze the data. The results of this study are as follows; first, there was positive correlations between dominance trait and mathematical competency. And, there was positive correlations between interaction trait and self-development competency. And there were negative correlations between support traits and NCS basic vocational competencies. Second, it was revealed that positive correlations between almost sub scale's of NCS basic vocational competencies and teacher teaching personality aptitude. Third, there was positive correlations between dominance trait and sub scale of teaching personality aptitude(e.g.: problem solving/ inquiry skills, judgment, creativity/practical ability, leadership, knowledge/information ability, planning ability, sincerity/responsibility). And there were negative correlations between support traits and sub scale of teaching personality aptitude(e.g.: problem solving/ inquiry skills, judgment, creativity/practical ability, leadership, sincerity/responsibility).

• Journal of Elementary Mathematics Education in Korea
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• v.20 no.1
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• pp.163-192
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• 2016

In this study, we analyzed what STEAM-related subject contents, except mathematical knowledge, are contained in 2009 revised elementary mathematics 6th grade textbooks and teacher's manuals. The STEAM-related subject contents in the textbooks and the teacher's manuals were examined by unit, by semester, and by strand of the content in the elementary school mathematics curriculum. The results are the following: First, in each unit and in each strand of mathematics, the most frequent STEAM-related subject content is storytelling, followed by the STEAM-related subject contents of technology and engineering, natural science, and social studies in order. On the other hand, the number of culture, physical education, music and fine arts contents is very small. Second, the number of STEAM-related subject contents in the textbook for the second semester(textbook 6-2) of the 6th grade year is 61 more than that in the textbook for the first semester(textbook 6-1). The number of non-storytelling STEAM-related subject contents in textbook 6-2 is 107, 2.7 times more than that in textbook 6-1. Third, the teacher's manual for textbook 6-1 is insufficient in complementing the textbook units which lack in STEAM-related subject contents, while the teacher's manual for textbook 6-2 is comparatively good in its complementing role. Therefore, it is recommended that we develop different STEAM materials for our 6th grade mathematics classes.

• Journal of Educational Research in Mathematics
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• v.14 no.2
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• pp.207-219
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• 2004

There have been studies reporting the increase in student confidence in mathematics when using technology. However, past studies indicating a positive correlation between technology and confidence in mathematics do not explain why they see this positive outcome. With increased availability and easy access to the Internet in schools and the development of free online virtual manipulatives, this research was interested in how the use of virtual manipulatives in mathematics can affect students confidence in their mathematical abilities. Our hypothesis was that the classes using virtual manipulatives which allows students to connecting dynamic visual image with abstract symbols will help students gain a deeper conceptual understanding of math concept thus increasing their confidence and ability in mathematics. The participants in this study were 46 fifth-grade students in three ability groups: one high, one middle and one low. During a two-week unit on fractions, students in three groups interacted with several virtual manipulative applets in a computer lab. Data sources in the project included a pre and posttest of students mathematics content knowledge, Confidence in Learning Mathematics Scale, field notes and student interviews, and classroom videotapes. Our aim was to find evidence for increased level of confidence in mathematics as students strengthened their understanding of fraction concepts. Results from the achievement score indicated an overall main effect showing significant improvement for all ability groups following the treatment and an increase in the confidence level from the preassessment of the Confidence in Learning Mathematics Scale in the middle and high ability groups. An interesting finding was that the confidence level for the low ability group students who had the highest confidence level in the beginning did not change much in the final confidence scale assessment. In the middle and high ability groups, the confidence level did increase according to the improvement of the contest posttest. Through interviews, students expressed how the virtual manipulatives assisted their understanding by verifying their answers as they worked and facilitated their ability to figure out math concept in their mind and visually.

• Journal of the Korean Institute of Gas
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• v.1 no.1
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• pp.27-32
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• 1997

Continual monitoring of abnormal operating conditions i a key issue in maintaining high product quality and safe operation, since the undetected process abnormality may lead to the undesirable operations, finally producing low quality products, or breakdown of equipment. The statistical projection method recently highlighted has the advantage of easily building reference model with the historical measurement data in the statistically in-control state and not requiring any detailed mathematical model or knowledge-base of process. As the complexity of process increases, however, we have more measurement variables and recycle streams. This situation may not only result in the frequent occurrence of process Perturbation, but make it difficult to pinpoint trouble-making causes or at most assignable source unit due to the confusing candidates. Consequently, an ad hoc skill to monitor and diagnose in plat-wide scale is needed. In this paper, we propose a hierarchical plant-wide monitoring methodology based on hierarchical decomposition and principal component analysis for handling the complexity and interactions among process units. This have the effect of preventing special events in a specific sub-block from propagating to other sub-blocks or at least delaying the transfer of undesired state, and so make it possible to quickly detect and diagnose the process malfunctions. To prove the performance of the proposed methodology, we simulate the Tennessee Eastman benchmark process which is operated continuously with 41 measurement variables of five major units. Simulation results have shown that the proposed methodology offers a fast and reliable monitoring and diagnosis for a large scale chemical plant.

• Progress in Medical Physics
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• v.15 no.2
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• pp.84-93
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• 2004

Stereotactic radiosurgery (SRS) is a technique that delivers a high dose to a target legion and a low dose to a critical organ through only one or a few irradiations. For this purpose, many mathematical methods for optimization have been proposed. There are some limitations to using these methods: the long calculation time and difficulty in finding a unique solution due to different tumor shapes. In this study, many clinical target shapes were examined to find a typical pattern of tumor shapes from which some possible ideal geometrical shapes, such as spheres, cylinders, cones or a combination, are assumed to approximate real tumor shapes. Using the arrangement of multiple isocenters, optimum variables, such as isocenter positions or collimator size, were determined. A database was formed from these results. The optimization procedure consisted of the following steps: Any shape of tumor was first assumed to an ideal model through a geometry comparison algorithm, then optimum variables for ideal geometry chosen from the predetermined database, followed by a final adjustment of the optimum parameters using the real tumor shape. Although the result of applying the database to other patients was not superior to the result of optimization in each case, it can be acceptable as a plan starling point.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.3 no.3
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• pp.1-7
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• 1983

In spite of extensive knowledge of the surface chemistry and the transport mechanism in filtration systems, there is still insufficient understanding of the physical characteristics of suspensions and the system components. Because of this, no filtration mechanisms are mathematically generalized to the full extent. The purpose of this paper is to propose experimental equations for the filtration process. using the tracer study in filter layer. Some of results are as follows. (1) The Volume of the specific deposit (${\sigma}$) in filtration was directly measurable using the tracer study without interrupting the filtration. (2) It was also confirmed that the head loss in filtration was greatly in fluenced by the micro-air babbles. (3) The correction coefficient(f) was introduced into the Kozeny-Carman equation in order to apply it for the clogging filter media. The coefficient(f) was experimentally obtained. The total head loss of the filter media is given by next equation. $${\frac{h}{h_0}}={\frac{1}{L}}{\int}^{z=L}_{z=0}f({\sigma})g({\varepsilon}_0,{\sigma})dz$$ $$f=aexp(-b{\sigma})$$ The above equation was applicable without regard to the variation of the suspension concentration, the filter medium diameter, the filter depth, the filtration velocity, and the amount of aluminum in all continuous filtration experiments. (4) The total head loss was graphically generalized assuming mathematical filtration models I II (see fig. 7,8) (5) The total head loss was obtained from the filtration model in the field filtration conditions. (see fig. 9,10)