• Journal for History of Mathematics
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• v.17 no.4
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• pp.37-44
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• 2004

Homological algebra has emerged and developed since 1950s. However, in 1890's Hilbert investigated the resolutions in his Syzygy Theorem which is a vital ingredient in homological algebra. In 1956 Serre has proved the finite global dimension of regular local rings. His result give a basic tool in homological algebra. This paper also deals with the depth formula that was raised by Auslander in 1961.

• Journal for History of Mathematics
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• v.30 no.4
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• pp.247-258
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• 2017

The goal of this essay is to examine metaphors for mathematics and to discuss philosophical problems related to them. Two metaphors for mathematics are well known. One is a tree and the other is a building. The former was proposed by Pasch, and the latter by Hilbert. The difference between these metaphors comes from different philosophies. Pasch's philosophy is a combination of empiricism and deductivism, and Hilbert's is formalism whose final task is to prove the consistency of mathematics. In this essay, I try to combine two metaphors from the standpoint that 'mathematics is a part of the ecosystem of science', because each of them is not good enough to reflect the holistic mathematics. In order to understand mathematics holistically, I suggest the criteria of the desirable philosophy of mathematics. The criteria consists of three categories: philosophy, history, and practice. According to the criteria, I argue that it is necessary to pay attention to Pasch's philosophy of mathematics as having more explanatory power than Hilbert's, though formalism is the dominant paradigm of modern mathematics. The reason why Pasch's philosophy is more explanatory is that it contains empirical nature. Modern philosophy of mathematics also tends to emphasize the empirical nature, and the synthesis of forms with contents agrees with the ecological analogy for mathematics.

• Communications of Mathematical Education
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• v.28 no.3
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• pp.321-338
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• 2014

In this paper, we introduce the history and the present status of the Mathematics Genealogy Project (MGP). The cases of David Hilbert and the first author were used to show how it works. As an example, we explain how to gain useful information such as the granting year of mathematics Ph. D degree holders, the title of dissertation, advisors and descendants from the MGP website. Through a survey of three different groups in MGP on 20~30 significant Korean mathematicians, we found that Korean records in the academic genealogy project are missing or poorly presented in the database of the MGP website. In conclusion, we found a way to improve the situation and provide instructions to submit our information to MGP. We expect our effort can help Korean mathematics and mathematicians to become better exposed to the world. It will help others to understand both the modern history and the future prospect of Korean mathematics.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.50 no.6
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• pp.413-422
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• 2022

In this paper, the fault analysis of the momentum wheel, which is a high-speed rotary machinery of 'Control Moment Gyro' for medium and large satellite, was described. For fault diagnosis, envelope spectrum analysis was performed using Hilbert transformation method and signal demodulation method to find the impact signals periodically generated from amplitude modulated signals. Through this, the fault of the momentum wheel was diagnosed by analyzing whether there was a harmonic component of the rotational frequency and a bearing fault frequency in a specific frequency band with a high peak.