• Journal of Educational Research in Mathematics
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• v.13 no.1
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• pp.13-28
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• 2003

Practice of proof is considered in, the view of language and meta-mathematics, recognizing the role of proof that is the means of communication and development of mathematical understanding. Linguistic components in proof texts are symbol, verbal language and visual text, and contain the implicit knowledge in the meta-mathematics view. This study investigates the functions of linguistic elements according to Halliday's functional grammar and the rhetoric skills in proof texts in math textbook, teacher's note, and student's written text. We need to inquire into the aspects of language for mathematics learning process and the understanding and use of students' language.

• International Journal of Internet, Broadcasting and Communication
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• v.13 no.2
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• pp.60-66
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• 2021

Blockchain is a technology that enables trust-based consensus and verification based on a decentralized network. Distributed ID (DID) is based on a decentralized structure, and users have the right to manage their own ID. Recently, interest in self-sovereign identity authentication is increasing. In this paper, as a method for transparent and safe sovereignty management of data, among data pseudonymization techniques for blockchain use, various methods for data encryption processing are examined. The public key technique (homomorphic encryption) has high flexibility and security because different algorithms are applied to the entire sentence for encryption and decryption. As a result, the computational efficiency decreases. The hash function method (MD5) can maintain flexibility and is higher than the security-related two-way encryption method, but there is a threat of collision. Zero-knowledge proof is based on public key encryption based on a mutual proof method, and complex formulas are applied to processes such as personal identification, key distribution, and digital signature. It requires consensus and verification process, so the operation efficiency is lowered to the level of O (log_eN) ~ O(N²). In this paper, data encryption processing for blockchain DID, based on zero-knowledge proof, was proposed and a one-way encryption method considering data use range and frequency of use was proposed. Based on the content presented in the thesis, it is possible to process corrected zero-knowledge proof and to process data efficiently.

• Journal of Educational Research in Mathematics
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• v.18 no.4
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• pp.455-467
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• 2008

We need to reflect the establishment of meaning and level of 'proof and argumentation in middle school mathematics'. It should be considered as human activity through communication in community. Thus, we should design instruction from this standpoint. From this point of view, we had been operated 'Geometry Inquiry Class' aimed at middle school students in eighth grade for two years to improve current geometry class in middle school. In this study, we will observe how individual students' original proof schemes are developed and accepted to the class through the process of mutual negotiation between the teacher and students. The episode with four phases begins with the initial proof schemes students have offered. Through the negotiation of class participants, it gives birth to the proof scheme unique to the current geometry classroom. Why do we pay attention to the process? It is because we think that the value of this type of instruction lies in the process of communication and mutual understanding and mutual reference, not in the completeness of the final product. This is the very appropriate proof in the middle school mathematics classroom.

• School Mathematics
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• v.5 no.4
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• pp.401-420
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• 2003

We have many problems in the teaching and learning of proof, especially in the demonstrative geometry of middle school mathematics introducing the proof for the first time. Above all, it is the serious problem that many students do not understand the meaning of proof. In this paper we intend to show that teaching the meaning of proof in terms of historic-genetic approach will be a method to improve the way of teaching proof. We investigate the development of proof which goes through three stages such as experimental, intuitional, and scientific stage as well as the development of geometry up to the completion of Euclid's Elements as Bran-ford set out, and analyze the teaching process for the purpose of looking for the way of improving the way of teaching proof through the historic-genetic approach. We conducted lessons about the angle-sum property of triangle in accordance with these three stages to the students of seventh grade. We show that the students will understand the meaning of proof meaningfully and properly through the historic-genetic approach.

• The Mathematical Education
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• v.41 no.1
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• pp.79-90
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• 2002

In this article we study on connecting paper 131ding activities of triangle with mathematical proof Folding median, bisector of angle, and hight of paper triangle, we from and extract some ideas that help us to proof some important theorems of plane geometry. In this study using formed ideas in the process of paper folding activities, we suggest some interesting new mathematical proofs of the following theorems: 1. three medians of triangle are intersect in a point; 2. three bisectors of interior angles of triangle are intersect in a point; 3. three heights of triangle are intersect in a point.

• Communications of the Korean Mathematical Society
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• v.25 no.2
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• pp.291-301
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• 2010

This paper consists of two main parts. Firstly, we introduce an evolving binomial process from a binomial stock model and consider various types of limiting behavior of the logarithm of the evolving binomial process. Among others we find that the logarithm of the binomial process converges weakly to a Gaussian process. Secondly, we provide new approaches for proving the limit theorems for an integral process motivated by the evolving binomial process. We provide a new proof for the uniform strong LLN for the integral process. We also provide a simple proof of the functional CLT by using a restriction of Bernstein inequality and a restricted chaining argument. We apply the functional CLT to derive the LIL for the IID random variables from that for Gaussian.

• East Asian mathematical journal
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• v.24 no.5
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• pp.465-476
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• 2008

Even though Godel's theorem is remarkable to mathematics teachers, it is not simple to understand the proof in detail. It would be useful for us to understand the basic ideas and the proving process of the proof. In this note, we suggest a proposal for the purpose.

• Journal of the Semiconductor & Display Technology
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• v.22 no.2
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• pp.56-63
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• 2023

This paper presents a method using finite element analysis and topology optimization to address the issue of overdesign in pressure-explosion proof enclosure doors for semiconductor manufacturing processes. The design conducted in this paper focuses on the pattern design of the enclosure door and its fixation components. The process consists of a solid-filled model, a topology optimization model, and a post-processing model. By applying environmental conditions to each model and comparing the maximum displacement, maximum equivalent stress, and weight values, it was confirmed that a reduction of about 13% in weight is achievable.

• School Mathematics
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• v.18 no.4
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• pp.839-856
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• 2016

In 2009 revision and 2015 revision mathematics national curriculum, 'proof' was moved to high school from middle school in consideration of the cognitive development level of students, and 'proof by contradiction' was stated in the "success criteria of learning contents" of the first year high school subject while it had been not officially introduced in $7^{th}$ and 2007 revision national curriculum. Proof by contradiction is known that it induces a cognitive conflict due to the unique nature of rather assuming the opposite of the statement for proving it. In this article, based on the logical, mathematical and historical analysis of Proof by contradiction, we looked about the introductions and the applications of the current textbooks which had been revised recently, and searched for improvement measures from the viewpoint of discovery, explanation, and consilience. We suggested introducing Proof by contradiction after describing the discovery process earlier, separately but organically describing parts necessary to assume the opposite and parts not necessary, disclosing the relationships with proof by contrapositive, and using the viewpoint of consilience.

• Journal of the Korean Society of Systems Engineering
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• v.15 no.2
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• pp.39-46
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• 2019

The purpose of this paper is to present the results of the study, applying Systems Engineering(SE) method, on the feasibility of developing a Melt-down Proof Modular Micro Reactor(MDP-MMR) for its future deployment in Korea. The reactor is being developed by NCSU (North Carolina State University) due to its advantage of melt-down proof nature of the reactor core. For this paper, the characteristics of the MDP-MMR has been studied in terms of fuel characteristics, inherent safety features and passive safety system. The NCSU's development process has been reviewed applying the SE method, and further research is recommended for the feasibility study on deploying such a modular micro reactor in Korea.