• Journal of the Korean School Mathematics Society
• /
• v.18 no.2
• /
• pp.223-240
• /
• 2015

This paper deals with how to design and develop white-box based e-learning contents which are equipped with conceptual understanding and step-by-step computational procedures for studying vector calculus for science-engineering majors who might need supplementary mathematics learning. Noting that rewriting rules are often used in school mathematics for students' problem solving, the theoretical aspects of rewriting rules are reviewed for developing supplementary e-learning contents for them. The software design of step-by-step problem solving requires careful arrangement of rewriting rules and pattern matching techniques for white-box procedures using a computer algebra system such as Mathematica. Several modules for step-by-step problem solving as well as producing dynamic display of e-learning contents was coded by Mathematica in order to find the length of a curve in vector calculus after implementing several rules for differentiation and integration. The developed contents are equipped with diagnostic modules and immediate feedback for supplementary learning in terms of a tutorial. At the end, this paper indicates the strengths and features of the developed contents for college students who need to increase math learning capabilities, and suggests future research directions.

• Communications of Mathematical Education
• /
• v.23 no.1
• /
• pp.109-128
• /
• 2009

This study aimed to investigate students' learning process by examining their perception process of problem structure and mathematization, and further to suggest an effective teaching and learning of mathematics to improve students' problem-solving ability. Using the qualitative research method, the researcher observed the collaborative learning of two middle school students by providing problem-posing activities of five lessons and interviewed the students during their performance. The results indicated the student with a high achievement tended to make a similar problem and a new problem where a problem structure should be found first, had a flexible approach in changing its variability of the problem because he had advanced algebraic thinking of quantitative reasoning and reversibility in dealing with making a formula, which related to developing creativity. In conclusion, it was observed that the process of problem posing required accurate understanding of problem structures, providing students an opportunity to understand elements and principles of the problem to find the relation of the problem. Teachers may use a strategy of simplifying external structure of the problem and analyzing algebraical thinking necessary to internal structure according to students' level so that students are able to recognize the problem.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.12 no.4
• /
• pp.642-651
• /
• 1988

The present paper develops finite element procedures to calculate displacements, strains and stresses in initially stressed elastic solids subjected to static or time-dependent loading conditions. As a point of departure, we employ Hamilton's principle to obtain nonlinear equations of motion characterizing the displacement in a solid. The equations of motion reduce to linear equations of motion if incremental stresses are assumed to be infinitesimal. In the case of linear problem, finite element solutions are obtained by Newmark's direct integration method and by modal analysis. An analytic solution is referred to compare with the linear finite element solution. In the case of nonlinear problem, finite element solutions are obtained by Newton-Raphson iteration method and compared with the linear solution. Finally, the effect of the order of Gauss-Legendre numerical integration on the nonlinear finite element solution, has been investigated.

• School Mathematics
• /
• v.16 no.1
• /
• pp.57-81
• /
• 2014

This study was to investigate how the underachievers of mathematics in a non-leveling excellent high school would overcome the errors through the lessons based on the inductive thinking model in the equation of a circle. The results showed that when there were many stages to solve the problem, the students gave it up or forgot the stage they reached. In this case, if they had a revisit-opportunity to review their thinking process by planning ahead the stage to solve the problem and recording it, the omission error of the solving process and the error of wrong conclusions would be dramatically decreased. Moreover, they understood the mathematical concept, principle, and formula and remembered the learning contents extremely well through thinking by themselves in exploration-based activities and by using visualization for the problem and could solve the problem through these pictures besides algebraic expressions.

• Journal of the Korea Society of Computer and Information
• /
• v.16 no.12
• /
• pp.139-155
• /
• 2011

In recent years, parents of students and government have been taking a growing interest in education for the gifted students and there are many research reports about the gifted education. Most of the reports, however, focuses on the conceptional feature of the gifted education program such as organization, operation, management, evaluation, etc,. In other words, there are very few researches on instructional materials for gifted students even though the materials is a critical factor for successful education programs. So, this paper introduces a lecture notes used in a personal education for gifted students to contribute in developing education contents in computer science area. The instructional materials titled as "The Necessity and Application of Matrix in Computer Science" is based on linear equation to usher the students into creative problem recognition and groping for solutions. Also, the instructional materials is useful for students to understand the tight mathematics-computer science relationship and the basic concept of liner algebra.

• Journal of the Korea Institute of Information Security & Cryptology
• /
• v.31 no.3
• /
• pp.533-544
• /
• 2021

Using Shor algorithm, factoring and discrete logarithm problem can be solved effectively. The public key cryptography, such as RSA and ECC, based on factoring and discrete logarithm problem can be broken in polynomial time using Shor algorithm. NIST has been conducting a PQC(Post Quantum Cryptography) standardization process to select quantum-resistant public key cryptography. The multivariate quadratic based signature scheme, which is one of the PQC candidates, is suitable for IoT devices with limited resources due to its short signature and fast sign and verify process. We analyzes classic attacks and quantum attacks for Rainbow which is the only multivatiate quadratic based signature scheme to be finalized up to the round 3. Also we compute the attack complexity for the round 3 Rainbow parameters, and analyzes the security level of Rainbow, one of the PQC standardization candidates.

• Journal of the Korea Society of Computer and Information
• /
• v.26 no.9
• /
• pp.143-153
• /
• 2021

In this paper, we propose "flexible routing with flex" to provide fast delivery by using the flexible routing for the delivery vehicle and crowd-shipper named flex. To this end, we have introduced an algorithm that can build the delivery plan for delivery vehicles and flexes. The introduced algorithm uses the 2-opt algorithm to construct routes with low complexity and acceptable quality, and the revised saving algorithm to assign customer orders to the flex. The algorithm allows the vehicle and the flex to function complement each other without separating the delivery vehicle from the flex. The experiments consider the 3 different instances named Random, Mixed, Cluster, and show that "the flexible routing with flex" has a better result than "vehicle only". The sensitivity analysis of the flex cost and time penalty shows "the flexible routing with flex" can provide better service not only to the customers who are serviced by flex but also to the customers who are serviced by the delivery vehicle.

• Journal of the Korean Geographical Society
• /
• v.39 no.3
• /
• pp.360-373
• /
• 2004

The purpose of this study is establishing how to build the area of local agents and regional offices in the oil company using GIS technique by reviewing on the spatial distribution pattern and characteristics of the sales area of oil products. Location-allocation and spatial interaction model are cooperated in order to establish sales area of petroleum products distribution system. Location-allocation model is used in the capital region where local agents are concentrated on like Kyoung-gi local agent. Spatial interaction model is used in the rest of the area in Korea to analyze the sales range of the regional offices in oil company. Each office made a big difference in registered cars and population because of the level of petroleum consumption in each sales area.

• Korean Journal of Weed Science
• /
• v.18 no.2
• /
• pp.154-160
• /
• 1998

This study was conducted to develop a foliar applied herbicide mixture covering wide spectrum weeds in dry direct seeded rice. Uniform precision central composite design(UPCCD) was employed to evaluate the effect of herbicide mixture among cyhalofop-butyl(cyhalofop), bispyribenzoxim and pyrazosulfuron-ethyl(pyrazosulfuron) having different weed control spectrum and to determine the best application rates of the three herbicide mixtures. The partial additive effect was observed in the mixture of cyhalofop and bispyribenzoxim with pyrazosulfron against Echinochloa crus-galli Beauv var crus-galli L., attributed to the negative interaction between cyhalofop and bispyribenzoxim system. Additive effect was observed in the mixture of bispyribenzoxim and pyrazosulfuron against Cyperus serotinus R. and Aneilema keisak H. but cyhalofop had no effect on these weeds. The most appropriate rate of the mixture of cyhalofop with bispyribenzoxim and pyrazosulfuron was 100 : 12 : 10g ai/ha exhibiting $ED_{90}$ against three weeds such as E. crus-galli, C. serotinus and A. keisak.

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