• Journal of Wetlands Research
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• v.19 no.2
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• pp.216-222
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• 2017

Recently, opinions on the need for revision regarding the nitrogen effluent standard of nitrogen from sewage treatment plant(STP) are consistently suggested. However, it is axiomatic that if nitrogen effluent standard is strengthened without a clear basis, it will cause confusion in domestic STP. In this research, nitrogen fraction was analyzed based on a long-term incubation method, according to STP capacity, and the linked treatment of industrial wastewater. As a result, NBDDON, which is difficult to treat in STP, ranged from 1.0 to 1.9 mg/L. larger DON and NBDDON/DON was detected in small STP (under 10,000 m3 /d) as opposed to the large STP. NBDDON/DON in industrial STP was about 0.7 and it was higher than municipal STP. This research result will be used in the important raw data for revision of nitrogen effluent standard of nitrogen from STP.

• The Mathematical Education
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• v.44 no.4 s.111
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• pp.547-563
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• 2005

There have been many papers reporting that the axiomatic approach in Abstract Algebra is a big obstacle to overcome for the students who are not trained to think in an abstract way. Therefore an instructor must seek for ways to help students grasp mathematical concepts in Abstract Algebra and select the ones suitable for students. Mathematics faculty and students generally consider Abstract Algebra in general and quotient groups in particular to be one of the most troublesome undergraduate subjects. For, an individual's knowledge of the concept of group should include an understanding of various mathematical properties and constructions including groups consisting of undefined elements and a binary operation satisfying the axioms. Even if one begins with a very concrete group, the transition from the group to one of its quotient changes the nature of the elements and forces a student to deal with elements that are undefined. In fact, we also have found through running abstract algebra courses for several years that students have considerable difficulty in understanding the concept of quotient groups. Based on the above observation, we explore and analyze the nature of students' knowledge about $Z_n$ that is the set of congruence classes modulo n. Applying the genetic decomposition method, we propose a model to lead students to achieve the correct concept of $Z_n$.

• Journal for History of Mathematics
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• v.24 no.3
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• pp.37-58
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• 2011

The development of recent Mathematical Logic is mostly originated in Hilbert's Proof Theory. The purpose of the plan so called Hilbert's Program lies in the formalization of mathematics by formal axiomatic method, rescuing classical mathematics by means of verifying completeness and consistency of the formal system and solidifying the foundations of mathematics. In 1931, the completeness encounters crisis by the existence of undecidable proposition through the 1st Theorem of G?del, and the establishment of consistency faces a risk of invalidation by the 2nd Theorem. However, relative of partial realization of Hilbert's Program still exists as a fruitful research program. We have tried to bring into relief through Curry-Howard Correspondence the fact that Hilbert's program serves as source of power for the growth of mathematical constructivism today. That proof in natural deduction is in truth equivalent to computer program has allowed the formalization of mathematics to be seen in new light. In other words, Hilbert's program conforms best to the concept of algorithm, the central idea in computer science.

• Journal of Educational Research in Mathematics
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• v.11 no.2
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• pp.363-384
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• 2001

The purpose of this thesis is, through analysing the characteristics of the definitions in Korean school mathematics textbooks, to explore the levels of them and to make suggestions for definition - teaching as a mathematising activity, Definitions used in academic mathematics are rigorous. But they should be transformed into various types, which are presented in school mathematics textbooks, with didactical purposes. In this thesis we investigated such types of transformation. With the result of this investigation we tried to identify the levels of the definitions in school mathematics textbooks. And in school mathematics textbooks there are definitions which carry out special functions in mathematical contexts or situations. We can say that we understand those definitions, only if we also understand the functions of definitions in those contexts or situations. In this thesis we investigated the cases in school mathematics textbooks, when such functions of definition are accompanied. With the result of this investigation we tried to make suggestions for definition-teaching as an intellectual activity. To begin with we considered definition from two aspects, methods of definition and functions of definition. We tried to construct, with consideration about methods of definition, frame for analysing the types of the definitions in school mathematics and search for a method for definition-teaching through mathematization. Methods of definition are classified as connotative method, denotative method, and synonymous method. Especially we identified that connotative method contains logical definition, genetic definition, relational definition, operational definition, and axiomatic definition. Functions of definition are classified as, description-function, stipulation-function, discrimination-function, analysis-function, demonstration-function, improvement-function. With these analyses we made a frame for investigating the characteristics of the definitions in school mathematics textbooks. With this frame we identified concrete types of transformations of methods of definition. We tried to analyse this result with van Hieles' theory about levels of geometry learning and the mathematical language levels described by Freudenthal, and identify the levels of definitions in school mathematics. We showed the levels of definitions in the geometry area of the Korean school mathematics. And as a result of analysing functions of definition we found that functions of definition appear more often in geometry than in algebra or analysis and that improvement-function, demonstration-function appear regularly after demonstrative geometry while other functions appear before demonstrative geometry. Also, we found that generally speaking, the functions of definition are not explained adequately in school mathematics textbooks. So it is required that the textbook authors should be careful not to miss an opportunity for the functional understanding. And the mathematics teachers should be aware of the functions of definitions. As mentioned above, in this thesis we analysed definitions in school mathematics, identified various types of didactical transformations of definitions, and presented a basis for future researches on definition teaching in school mathematics.

• (The)Study of the Eastern Classic
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• no.71
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• pp.99-128
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• 2018

Zhōuyì周易 is intended to explain the affairs of human beings by observing the images and works of all things in the universe, abstracting them into the $b{\bar{a}}gu{\grave{a}}$八卦, calculating the process and inducing the outcome by the method of stalk divination, in which this paper finds the origin of natural scientific thought of Zhōuyì. The way of Zhōuyì's thought on the natural science is distinguished from that of the Western's. In the West, people dismantled the objects into the parts until they reached the atom and analyzed them by the principle of causality to draw an axiomatic truth. In the meantime Zhōuyì observed and studied the dynamic functions and changes of all things for the convergence of the whole. While the way of Zhōuyì's thinking could have not contributed to the development of modern scientific development, that of the West overwhelmed Asian development passing through the period of enlightenment during 16-17 century. This paper tries to articulate the points where Zhōuyì can share its theory with the contemporary science by finding the traces of scientific thoughts in Zhōuyì. It encounters its ground from the methodology of natural science and scientific statements proposed by Zhōuyì. The essential concepts of Zhōuyì are induced from all things in nature. This can be considered as the idea of '法自然'(emulating the patterns and examples from nature). Also they observed the images and changes seen by the habits of animals, plants and human beings to sense and perceive their laws. These are regarded as the methodology of natural science in Zhōuyì. As a book of divination, the way of stalk divination is designed to calculate the future by using the system of 'numbers'. 'tàijí太極', ' yīnyáng陰陽', 'four symbols四象', '$b{\bar{a}}gu{\grave{a}}$八卦' and 'wǔxíng五行' are the essential concepts of Zhōuyì to represents the dynamic phenomena and changes of the natural order. Among them '$b{\bar{a}}gu{\grave{a}}$八卦' is a presentment to explain the structure of the world not by the individual analysis of things but by the unification of the whole through the contradictions and interchanges among them to reach the new orders. As of now, the studies of Zhōuyì in Korea have focused on the traditional perspectives, such as political and ethical philosophy. Some of recent studies, having interpreted Zhōuyì with scientific inclination have generated controversy 'Can Zhōuyì be a science?', for which scholars have hard time to reach the agreement. This paper tries to find the headwaters of the contemporary natural science by elaborating the methodology of natural science stated in Zhōuyì.