• Communications of Mathematical Education
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• v.22 no.4
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• pp.417-444
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• 2008

Many research papers on the college students' functional concept show they have poor understanding on this topic. To compare the results with that of Korean students, four interrelated topics are chosen: How do they understand the concept of function?; what are their misconceptions including epistemological obstacles?; How do the function concepts develop and are acquired? For this a survey has been conducted to 95 engineering students just before they start Calculus course. We have done research on other major areas including psychology, economics and statistics to see how function is defined in these areas. Function definitions from US math text books are also introduced. Based on the these and the survey, some suggestions are made on the new curriculum which treat function as a correspondence relation. Vertical line test should be added to the Algebra II/Pre calculus course to check the univalent property.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.15 no.1
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• pp.51-59
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• 2004

We design multilevel coding(MLC) with a semi bit-interleaved coded modulation(BICM) scheme based on low density parity check(LDPC) codes. Different from traditional designs, we joint the MLC and BICM together by using the Gray mapping, which can transmit the multimedia data over several equivalent channels with different code rates. To get a good performance from signal-to-noise ratio(SNR) very close to the capacity of the additive white Gaussian noise(AWGN) channel, random regular LDPC code and a simple semi-algebra LDPC(SA-LDPC) code are discussed in MLC with parallel independent decoding(PID). Finally, the numerical results demonstrate that the proposed scheme could achieve both power and bandwidth efficiency for multimedia communication system.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.3 no.1
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• pp.209-221
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• 1999

Several approaches to anlayzing real-time schedulability have been presented, but since these used a fixed priority scheduling scheme and/or traverse all possible state spaces, there take place exponential time and space complexity of these methods. Therefore it is necessary to reduce the state space and detect schedulability at earlier time. This paper proposes and implements an advanced schedulability analysis algorithm to determine that is satisfied a given deadlines for real-time processes. These use a minimum execution time of process, periodic, deadline, and a synchronization time of processes to detect schedulability at earlier time and dynamic scheduling scheme to reduce state space using the transition rules of process algebra. From a result of implementation, we demonstrated the effective performance to determine schedulability analysis.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 1999.11a
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• pp.248-251
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• 1999

We extend the sue of the method of least square to develop a recursive algorithm for the design of adaptive transversal filters such that, given the least-square estimate of this vector of the filter at iteration n-1, we may compute the updated estimate of this vector at i(oration n upon the arrival of new data. The RLS algorithm may be viewed as a special case of the Kalman filter. Indeed this special relationship between the RLS algorithm and the Kalman filter is considered. We begin the development of the RLS algorithm by reviewing some basic relations that pertain to the method of least squares. Then, by exploiting a relation in matrix algebra known as the matrix inversion lemma, we develop the RLS algorithm. An important feature of the RLS algorithm is that it utilizes information contained in the input data, extending back to the instant of time when the algorithm is initiated. The resulting rate of convergence is therefore typically an order of magnitude faster than the simple LMS algorithm. This improvement in performance, however, Is achieved at the expensive of a large increase in computational complexity.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.37A no.12
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• pp.1031-1037
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• 2012

We study an algorithm that can efficiently find square roots and cube roots by modifying Tonelli-Shanks algorithm, which has an application in Number Field Sieve (NFS). The Number Field Sieve, the fastest known factoring algorithm, is a powerful tool for factoring very large integer. NFS first chooses two polynomials having common root modulo N, and it consists of the following four major steps; 1. Polynomial Selection 2. Sieving 3. Matrix 4. Square Root. The last step of NFS needs the process of square root computation in Number Field, which can be computed via square root algorithm over finite field.

• Journal of the Korean Mathematical Society
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• v.42 no.3
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• pp.529-541
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• 2005

An operator T belonging to the algebra B(H) of bounded linear transformations on a Hilbert H into itself is said to be posinormal if there exists a positive operator $P{\in}B(H)$ such that $TT^*\;=\;T^*PT$. A posinormal operator T is said to be conditionally totally posinormal (resp., totally posinormal), shortened to $T{\in}CTP(resp.,\;T{\in}TP)$, if to each complex number, $\lambda$ there corresponds a positive operator $P_\lambda$ such that $|(T-{\lambda}I)^{\ast}|^{2}\;=\;|P_{\lambda}^{\frac{1}{2}}(T-{\lambda}I)|^{2}$ (resp., if there exists a positive operator P such that $|(T-{\lambda}I)^{\ast}|^{2}\;=\;|P^{\frac{1}{2}}(T-{\lambda}I)|^{2}\;for\;all\;\lambda)$. This paper proves Weyl's theorem type results for TP and CTP operators. If $A\;{\in}\;TP$, if $B^*\;{\in}\;CTP$ is isoloid and if $d_{AB}\;{\in}\;B(B(H))$ denotes either of the elementary operators $\delta_{AB}(X)\;=\;AX\;-\;XB\;and\;\Delta_{AB}(X)\;=\;AXB\;-\;X$, then it is proved that $d_{AB}$ satisfies Weyl's theorem and $d^{\ast}_{AB}\;satisfies\;\alpha-Weyl's$ theorem.

• The KIPS Transactions:PartD
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• v.16D no.2
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• pp.185-190
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• 2009

The event sequence of the same type from a set of events having time property can be summarized in one event. But if the event sequence having an interval, It is reasonable to be summarized more than one in independent sub event sequence of each other. In this paper, we suggest a method of temporal data mining that summarizes the interval events based on Allen's interval algebra and finds out interval event association rule from interval events. It provides better knowledge than others by using concept of an independent sub sequence and finding interval event association rules.

• The Mathematical Education
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• v.53 no.1
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• pp.25-40
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• 2014

Mathematical concept exists in the structural form, not in the independent form. The purpose of this study is to consider the network which students actually have for the mathematical concept structure related to the properties of derivatives. First, we analyzed the properties of derivatives in 'Mathematics II' and showed the mathematical concept structure of the relations among derivatives, functions, and primitive functions as a network. Also, we investigated the understanding of high school students for the mathematical concept structure between derivatives and functions, and the structure between functions and second order derivatives when the functional formula is not given, and only the graph is given. The results showed that students mainly focus on the relation of 'function-derivatives', the thinking process for direction of derivative and the thinking style for algebra. On this basis, we suggest the educational implication that is necessary for students to build the network properly.

• The Mathematical Education
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• v.50 no.2
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• pp.135-148
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• 2011

We can say that the history of mathematics is the history on the development of the number system. The number starts from Natural number and is constructed to Integer number and Rational number. The Rational number is not the complete number analytically so that Real number is completed by the idea of the nested interval method. Real number is completed analytically, however, is not by algebra, so the algebraically completed type of the rational number, through the way that similar to the process of completing real number, is Complex number. The purpose of this study is to show the most appropriate way for the development of the human being thinking about the teaching and leaning of Complex number. To do this, We have to consider the proof of the existence of Complex number, the background of the introduction of Complex number and the background knowledge that the teachers to teach Complex number should have. Also, this study analyzes the knowledge to be taught of Complex number based on the anthropological theory of didactics and finally presents the teaching method of Complex number based on this theory.

• Research in Mathematical Education
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• v.18 no.3
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• pp.223-234
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• 2014

Research shows that formative assessment has a more powerful effect on student learning than summative assessment. This case study of an 8th grade algebra classroom focuses on how the implementation of Formative Assessment Lessons (FALs) and the participation in teacher learning communities related to FALs changed in the teacher's instructional practices, over the course of a year, to promote students' mathematical reasoning and justification. Two classroom observations are analyzed to identify how the teacher elicited and built on students' mathematical reasoning, and how the teacher prompted students to respond to and develop one another's mathematical ideas. Findings show that the teacher solicited students' reasoning more often as the academic year progressed, and students also began developing mathematical reasoning in meaningful ways, such as articulating their mathematical thinking, responding to other students' reasoning, and building on those ideas leading by the teacher. However, findings also show that teacher change in teaching practices is complicated and intertwined with various dimensions of teacher development. This study contributes to the understanding of changes in teaching practices, which has significant implications for teacher professional development and frameworks for investigating teacher learning.