• Journal of the Korean School Mathematics Society
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• v.19 no.1
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• pp.1-19
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• 2016

This study investigated the mathematical notation used today in terms of skip ping the parenthesis. At first we have studied the elementary and secondary curriculum content related to omitted rules. As a result, it is difficult to find explicit evidence to answer that question 'What is the calculation of the $48{\div}2(9+3)$?'. In order to inquire the notation fundamentally, we checked the characteristics on prefix, infix and postfix, and looked into the advantages and disadvantages on infix. At the same time we illuminated the development of mathematical notation from the point of view of skipping the parenthesis. From this investigation, we could check that this interpretation was smooth in the point of view that skipping the parentheses are the image of the function. Through this we proposed some teaching methods including 'teaching mathematical notation based on historic genetic principle', 'reproduction of efforts to overcome the disadvantages of infix and understand the context to choose infix', 'finding the omitted parentheses to identify the fundamental formula' and 'specifying the viewpoint that skipping the multiplication notation can be considered as an image of the function'.

• The KIPS Transactions:PartB
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• v.9B no.6
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• pp.827-834
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• 2002

In this paper, we proposed the formation of Korean-Roman alphabet notation conversion table for the generation of Korean-Roman alphabet notation that also meets revised Roman alphabet notation. Introduced a mathematical analyzing method of the natural language which used a petrinet model so that a base of Roman alphabet notation analyzed standard pronunciation and Roman alphabet notation to work mathematically. It display the practical example through a petrinet modeling of a plan and Roman alphabet notation to create a Korean Roman alphabet notation conversion table with the method of the analysis that used a petrinet model, and present a mathematical modeling plan and application method of Korean. We developed application program based on window in order to verify a created Korean-Roman alphabet notation conversion table, and compared the result of an application program with Roman alphabet notation of an Roman alphabet notation example dictionary.

• Journal for History of Mathematics
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• v.22 no.3
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• pp.187-206
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• 2009

On this study, the historical flow of the notation was briefly examined and the direction of mathematical investigation activity of the content of notation by analogy was explored and teaching learning materials were developed. Diverse mathematical facts were investigated on the basis of decimal system and binary system which are learned in middle school. First, the way of progressing analytic activity with algebraic material was examined. Second, on the basis of the notation which are learned in the first grade of middle school, the definition of the scale of a -notation, -a -notation, $\frac{1}{a}$notation, $\sqrt{a}$-notation was extended by analogy. The result of this study will be expected to establish the curriculum of mathematics and provide teaching and learning with the meaningful current events.

• Journal of the Korean School Mathematics Society
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• v.19 no.1
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• pp.63-82
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• 2016

Mathematical notation is the main means to realize the power of mathematics. Under this perspective, this study analyzed the difficulties of learning an irrational number concept in terms of notation. I tried to find ways to overcome the difficulties arising from the notation. There are two primary ideas in the notation of irrational number using root. The first is that an irrational number should be represented by letter because it can not be expressed by decimal or fraction. The second is that $\sqrt{2}$ is a notation added the number in order to highlight the features that it can be 2 when it is squared. However it is difficult for learner to notice the reasons for using the root because the textbook does not provide the opportunity to discover. Furthermore, the reduction of the transparency for the letter in the development of history is more difficult to access from the conceptual aspects. Thus 'epistemological obstacles resulting from the double context' and 'epistemological obstacles originated by strengthening the transparency of the number' is expected. To overcome such epistemological obstacles, it is necessary to premise 'providing opportunities for development of notation' and 'an experience using the notation enhanced the transparency of the letter that the existing'. Based on these principles, this study proposed a plan consisting of six steps.

• Honam Mathematical Journal
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• v.4 no.1
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• pp.147-154
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• 1982

Estimation methods of missing points for an experimental design are described. Formulae are provided for the estimation of missing points using matrix notation. The correct analysis of variance table is given. Estimation methods of a single missing point and two missing points in $2^{n}$ factorial designs are described.

• Journal of Educational Research in Mathematics
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• v.13 no.4
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• pp.429-446
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• 2003

Gu-il-jip is a mathematical book of Chosun dynasty in the 18c. It consists of nine chapters including more than 473 problems and their solutions. Analyzing the problems and their solutions, we can appreciate the mathematical researches by the professional mathematicians of Chosun. Especially, it is worth noting the followings: - units for measuring and decimal notations - $\pi$, area of circle, volume of sphere - naming the powers - counting rods - excess and deficit: calculation technique for excess-deficit relations among quantities - rectangular arrays: calculation technique for simultaneous linear equations - 'Thien Yuan' notation: method for representing equations - 'Khai Fang': algorithm for numerical solution of quadratic, cubic and higher equations Based on these analyses, some pedagogical applications are proposed.

• Communications of Mathematical Education
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• v.28 no.3
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• pp.375-394
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• 2014

The purpose of this study is to examine the transition of mathematical representation in Joseon mathematics, which is focused on numbers and operations, letters and expressions. In Joseon mathematics, there had been two numeral systems, one by chinese character and the other by counting rods. These systems were changed into the decimal notation which used Indian-Arabic numerals in the late 19th century passing the stage of positional notation by Chinese character. The transition of the representation of operation and expressions was analogous to that of representation of numbers. In particular, Joseon mathematics represented the polynomials and equations by denoting the coefficients with counting rods. But the representation of European algebra was introduced in late Joseon Dynasty passing the transitional representation which used Chinese character. In conclusion, Joseon mathematics had the indigenous representation of numbers and mathematical symbols on our own. The transitional representation was found before the acceptance of European mathematical representations.

• The KIPS Transactions:PartC
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• v.8C no.5
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• pp.607-614
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• 2001

With a remarkable growth and expansion of Internet, the security issues emerged from intrusions and attacks such as computer viruses, denial of services and hackings to destroy information have been considered as serious threats for Internet and the private networks. To protect networks from those attacks, many vendors have developed various security systems such as firewalls, intrusion detection systems, and access control systems. However, managing those systems individually requires too much work and high cost. Thus, in order to manage integrated security management and establish consistent security management for various security products, the policy model of PN-ISMS (Policy Based Integrated Security Management System) has become very important. In this paper, present the hierarchical policy model which explore the refinement of high-level/conceptual policies into a number of more specific policies to form a policy hierarchy. A formal method of policy description was used as the basis of the mode in order to achieve precision and generality. Z-Notation was chosen for this propose. The Z-Notation is mathematical notation for expressing and communicating the specifications of computer programs. Z uses conventional notations of logic and set theory organized into expressions called schemas.

• Proceedings of the IEEK Conference
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• 2002.07a
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• pp.321-324
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• 2002

For a rule-based conversion of Hangout into the Roman alphabet rather than a word-for-word conversion, one must come up with a faultless model for the Korean standard pronunciation rules, which are the basis of the Romanization. It is on this foundation that the Korean-Roman alphabet conversion table can be created. For linguistic modeling using PetriNet, modeling boundary and notation of modeling can be defined. In order to describe PetriNet, which is a dynamic modeling tool, as a static one, one can model the standard Korean pronunciation rules and the Hangout-Roman alphabet notation by conversion into incident matrix Thus, this research attempts to develop a mathematical modeling tool for a natural language using PetriNet, and create a Korean-Roman alphabet conversion table.

• Journal of the Korean School Mathematics Society
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• v.20 no.3
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• pp.211-237
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• 2017

Depending on the type of textbook, the word and mathematical notation expression used in high school mathematics textbooks varied and there were also some differences on the mathematical definition and the content description methods. Not only the composition of textbooks but also various expressing ways of textbooks have significant impacts on teaching and learning of teacher and student. The diversity of expression had pros and cons like both sides of a coin. There is a positive aspect that we can pursue pedagogical diversity. Simultaneously there is a negative aspect that the possibility of acting as a learning burden exists in the viewpoint of the student and the equality of evaluation may be undermined. In this study, Preferentially we focused on analyzing the actual situation rather than judging what is more appropriate about the diversity of words and notation expressions used in mathematics textbooks which is based on the current curriculum. For this purpose, we analyzed 56 kinds of mathematics textbooks based on the 2009 revised mathematics curriculum, and presented four aspects(terms expressing, notations expression, mathematical definition, content description method) with examples about differences of the various expressions used in textbooks including 'terms and notations'.