• Journal of the Korean School Mathematics Society
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• v.23 no.2
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• pp.179-201
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• 2020

The purpose of this study is to analyze tasks reflected in Korean and US textbooks according to the mathematical modeling perspectives, and then to compare the diversity of learning opportunities given to students from both countries. For this, we analyzed mathematical modeling tasks of textbooks based on three aspects: mathematical modeling process, data, and expression. Results are as follows. First, with respect to modeling process, Korean textbook provides a high percentage of the task at all stages of modeling than US textbook. Second, with respect to data, both countries' textbooks have the highest percentage of matching task. Korean textbooks have a large gap in data characteristics by textbook. Third, with respect to expression, both countries' textbooks have the highest percentage of text and picture. Korean textbooks have a large gap in the type of expression than US textbooks, and some textbooks have no other expression except for text and picture. Fourth, tasks were analyzed by integrating the three features. The three features were not combined in various ways. It is necessary to diversify the integration of the three features.

• Electronics and Telecommunications Trends
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• v.33 no.2
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• pp.39-47
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• 2018

The fundamental problem of communication is that of transmitting a message from a source to a destination over a channel through the use of a transmitter and receiver. To derive a theoretically optimal solution, the transmitter and receiver can be divided into several processing blocks, with each component analyzed and optimized. The idea of machine learning (or deep learning) communications systems goes back to the original definition of the communi-cation problem, and optimizes the transmitter and receiver jointly. Although today's systems have been optimized over the last decades, and it seems difficult to compete with their performance, deep learning based communication is attractive owing to its simplicity and the fact that it can learn to communicate over any type of channel without the need for mathematical modeling or analysis.

• Journal of Korea Artificial Intelligence Association
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• v.1 no.1
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• pp.11-16
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• 2023

Accurate hospital case modeling and prediction are crucial for efficient healthcare. In this study, we demonstrate the implementation of regression analysis methods in machine learning systems utilizing mathematical statics and machine learning techniques. The developed machine learning model includes Bayesian linear, artificial neural network, decision tree, decision forest, and linear regression analysis models. Through the application of these algorithms, corresponding regression models were constructed and analyzed. The results suggest the potential of leveraging machine learning systems for medical research. The experiment aimed to create an Azure Machine Learning Studio tool for the speedy evaluation of multiple regression models. The tool faciliates the comparision of 5 types of regression models in a unified experiment and presents assessment results with performance metrics. Evaluation of regression machine learning models highlighted the advantages of boosted decision tree regression, and decision forest regression in hospital case prediction. These findings could lay the groundwork for the deliberate development of new directions in medical data processing and decision making. Furthermore, potential avenues for future research may include exploring methods such as clustering, classification, and anomaly detection in healthcare systems.

• Journal of Educational Research in Mathematics
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• v.20 no.3
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• pp.221-239
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• 2010

Attention to Korean perspective mathematics education has been increasingly paid m international academic meetings or international comparative studies. Personal or intuitive, vague explanation has been given based on limited literature or observations. This increasing attention and Jack of studies warrant the necessity of systematic researches on it. This article aims at clarifying the research issues in searching for Korean perspective on mathematics education and finding the starting point through discussion on mathematical modeling by teacher on researchers and researchers. Firstly, hypothetical perspective will be described. Secondly, Fourteen teacher educators' and seven researchers' opinion on it will be discussed. Findings imply that strong responsibility for Korean mathematics teachers to reveal theoretical aspects of mathematical knowledge, i.e., structure or essence, as well as to pursue efficiency and effectiveness in mathematics teaching and learning is the main aspect of Korean perspective on mathematics education.

• School Mathematics
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• v.7 no.1
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• pp.77-101
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• 2005

This study is a discussion of the teaching and learning of discrete mathematics in school mathematics. In this study, we summarized the importance of discrete mathematics m school mathematics. And we examined instruction methods of discrete mathematics expressed in the 7th mathematics curriculum. On the basis of analysis for teaching cases in previous studies, we proposed four suggestions to organize discrete mathematics classroom. That is as follows. First, discrete mathematics needs to be introduced as a mathematical modeling of real-world problem. Second, algorithm learning in discrete mathematics have to be accomplished with computer experiments. Third, when we solve a problem with discrete data, we need to consider discrete property of given data. Forth, discrete mathematics class must be full of investigation and discussion among students. In each suggestion, we dealt with detailed examples including educational ideas in order to helping mathematics teacher orgainzing discrete mathematics classroom.

• Structural Engineering and Mechanics
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• v.12 no.5
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• pp.527-540
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• 2001

A new sort of learning algorithm named whole learning algorithm is proposed to simulate the nonlinear and dynamic behavior of RC members for the estimation of structural integrity. A mathematical technique to solve the multi-objective optimization problem is applied for the learning of the feedforward neural network, which is formulated so as to minimize the Euclidean norm of the error vector defined as the difference between the outputs and the target values for all the learning data sets. The change of the outputs is approximated in the first-order with respect to the amount of weight modification of the network. The governing equation for weight modification to make the error vector null is constituted with the consideration of the approximated outputs for all the learning data sets. The solution is neatly determined by means of the Moore-Penrose generalized inverse after summarization of the governing equation into the linear simultaneous equations with a rectangular matrix of coefficients. The learning efficiency of the proposed algorithm from the viewpoint of computational cost is verified in three types of problems to learn the truth table for exclusive or, the stress-strain relationship described by the Ramberg-Osgood model and the nonlinear and dynamic behavior of RC members observed under an earthquake.

• Proceedings of the KIEE Conference
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• 2003.07d
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• pp.2176-2178
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• 2003

This paper presents the intelligent modeling method of chaotic systems using a DNA coding based wavelet neural network(WNN). Generally the mathematical teaming method such as gradient descent method is used to adjust the parameters of WNN, which has much computational cost. To overcome this kind of problem, we use the DNA coding method as the learning method of WNN, and then combine it with the WNN. Finally, to verify the efficiency of our method, we apply the proposed DNA coding based wavelet neural network for modeling of Duffing system, which is a representative continuous-time chaotic system.

• The Mathematical Education
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• v.60 no.2
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• pp.133-157
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• 2021

Ill-structured problems have drawn attention in that they can enhance problem-solving skills, which are essential in future societies. The purpose of this study is to analyze and evaluate students' spatial reasoning(Intrinsic-Static, Intrinsic-Dynamic, Extrinsic-Static, and Extrinsic-Dynamic reasoning) and problem solving abilities(understanding problems and exploring strategies, executing plans and reflecting, collaborative problem-solving, mathematical modeling) that appear in ill-structured problem-solving. To solve the research questions, two ill-structured problems based on the geometry domain were created and 11 lessons were given. The results are as follows. First, spatial reasoning ability of sixth-graders was mainly distributed at the mid-upper level. Students solved the extrinsic reasoning activities more easily than the intrinsic reasoning activities. Also, more analytical and higher level of spatial reasoning are shown when students applied functions of other mathematical domains, such as computation and measurement. This shows that geometric learning with high connectivity is valuable. Second, the 'problem-solving ability' was mainly distributed at the median level. A number of errors were found in the strategy exploration and the reflection processes. Also, students exchanged there opinion well, but the decision making was not. There were differences in participation and quality of interaction depending on the face-to-face and web-based environment. Furthermore, mathematical modeling element was generally performed successfully.

• Structural Engineering and Mechanics
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• v.85 no.3
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• pp.315-335
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• 2023

Limited studies are available on the mathematical estimates of the compressive strength (CS) of glass fiber-embedded polymer (glass-FRP) compressive elements. The present study has endeavored to estimate the CS of glass-FRP normal strength concrete (NSTC) compression elements (glass-FRP-NSTC) employing two various methodologies; mathematical modeling and artificial neural networks (ANNs). The dataset of 288 glass-FRP-NSTC compression elements was constructed from the various testing investigations available in the literature. Diverse equations for CS of glass-FRP-NSTC compression elements suggested in the previous research studies were evaluated employing the constructed dataset to examine their correctness. A new mathematical equation for the CS of glass-FRP-NSTC compression elements was put forwarded employing the procedures of curve-fitting and general regression in MATLAB. The newly suggested ANN equation was calibrated for various hidden layers and neurons to secure the optimized estimates. The suggested equations reported a good correlation among themselves and presented precise estimates compared with the estimates of the equations available in the literature with R²= 0.769, and R² =0.9702 for the mathematical and ANN equations, respectively. The statistical comparison of diverse factors for the estimates of the projected equations also authenticated their high correctness for apprehending the CS of glass-FRP-NSTC compression elements. A broad parametric examination employing the projected ANN equation was also performed to examine the effect of diverse factors of the glass-FRP-NSTC compression elements.

• Structural Engineering and Mechanics
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• v.45 no.1
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• pp.53-67
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• 2013

This study aimed to develop a model to accurately predict the acceleration of structural systems during an earthquake. The acceleration and applied force of a structure were measured at current time step and the velocity and displacement were estimated through linear integration. These data were used as input to predict the structural acceleration at next time step. The computation tool used was the Volterra/Wiener neural network (VWNN) which contained the mathematical model to predict the acceleration. For alleviating problems of relatively large-dimensional and nonlinear systems, the VWNN model was utilized as the signal processing tool, including the Taylor series components in the input nodes of the neural network. The number of the intermediate layer nodes in the neural network model, containing the training and simulation stage, was evaluated and optimized. Discussions on the influences of the gradient descent with adaptive learning rate algorithm and the Levenberg-Marquardt algorithm, both for determining the network weights, on prediction errors were provided. During the simulation stage, different earthquake excitations were tested with the optimized settings acquired from the training stage to find out which of the algorithms would result in the smallest error, to determine a proper simulation model.