• Journal for History of Mathematics
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• v.30 no.1
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• pp.1-15
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• 2017

The original proof-argument of Riemann in 1851 for the Riemann mapping theorem, one of the most central theorems in Complex analysis, was found faulty and essentially buried underneath the proof by $Carath{\acute{e}}odory$ of 1929, now accepted as the "textbook" proof. On the other hand, the original Riemann's "proof" was rediscovered and made correct by R.E. Greene and the author of this article in 2016. In this article, we try to shed lights onto the history related to the Riemann mapping theorem and the surrounding developments of 1850-1930 by reflecting upon the main flow of ideas and methods of the proof by R. E. Greene and K.-T. Kim.

• Proceedings of the Korea Information Processing Society Conference
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• 2012.04a
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• pp.1176-1179
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• 2012

To ensure the correctness of high performance satisfiability (SAT) solvers, several proof formats have been proposed. SAT solvers can report a formula being unsatisfiable with a proof, which can be independently verified by a trusted proof checker. Among the proof formats accepted at the SAT competition, the Reverse Unit Propagation (RUP) format is considered the most popular. However, the official proof checker was not efficient and failed to check many of the proofs at the competition. This inefficiency is one of the drawbacks of SAT proof checking. In this paper, I introduce a work-in-progress project, vercheck to implement an efficient RUP checker using modern SAT solving techniques. Even though my implementation is larger and more complex, the level of trust is preserved by statically verifying the correctness of the code. The vercheck program is written in GURU, a dependently typed functional programming language with a low-level resource management feature.

• 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 Korea Institute of Information Security & Cryptology
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• v.21 no.5
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• pp.83-94
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• 2011

Yoking proof is a concept proposed by A. Juels in 2004. It proves that a pair of tags are scanned simultaneously by one reader. After the first yoking proof protocol is proposed by A. Juels, replay attack vulnerabilities of yoking proof are considered and many other yoking proof schemes are proposed to improve it. However, compared with the first yoking proof scheme which emphasizes protocol efficiency due to the limited performance of tags, other yoking proof protocols need more computing power and storage of the tags. We propose two security protocols that consider both the general condition and limited performance of tags. The proposed scheme can protect the tags from replay attack and Brute-force attack as well. Moreover, many pairs of tags or several tag groups can be proved at the same time by executing the protocol only once.

• Journal of the Korean School Mathematics Society
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• v.11 no.1
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• pp.55-68
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• 2008

In this paper, we investigated difficulties that middle school students face in the teaming process of proof, and then inquired how does learning of proof using GSP ease students' difficulties. Throughout the inspection, we identified that students have difficulties in understanding process of premise and conclusion, use of notation, process of reasoning. And we identified, throughout learning process of proof using GSP, students can be feedbacked for their guess or reasoning, generalize the special case to general properties and have attitude checking ideas needed in proof by themselves.

• Journal of Korean Society of Steel Construction
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• v.14 no.2
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• pp.329-337
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• 2002

The skid proof pavement is used for safety driving on curved bridges and high level roads. This study analyzed the effect of skid proof pavement on the bridge using actual spot test and computer analysis. In the actual spot test, the natural frequency and dynamic deflection of steel box girder bridges were measured before and after skid proof pavement. Likewise, in the computer analysis, the dynamic response of the finite element model was evaluated. The model was based on real steel box girder bridge according to the skid proof pavement. The analyzed results provide basic data on the effect of skid proof pavement on road structure.

• Fashion & Textile Research Journal
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• v.8 no.6
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• pp.727-732
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• 2006

The purpose of this study was to investigate the effects of flame-proof clothing on physiological responses and subjective sensation. We measured rectal temperatures, local skin temperature, clothing microclimate, blood pressure, heart rate, body weight loss and subjective sensation during 90 minutes (30 min of rest, 45 min of exercise and 15 min of recovery periods). Seven male subjects wore flame-proof clothing or reformed flame-proof clothing under the environmental condition of $35{\pm}1^{\circ}C$, $45{\pm}5%$ RH and $25{\pm}1^{\circ}C$, $50{\pm}5%$ RH. The results of this study were as follows; Rectal temperature, mean skin temperature, clothing microclimate and blood pressure were significantly lower levels in reformed flame-proof clothing. Heart rate and body weight loss were also showed lower levels. Subjects replied less hot, less uncomfortable and less wet in wearing a reformed flame-proof clothing. Our present results suggest that the ventilation through of gusset in underarm seam and zipper in sideseam of slacks are qualitatively useful for physiological needs.

• Education of Primary School Mathematics
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• v.7 no.2
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• pp.85-99
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• 2003

In this paper, firstly examined various proofs types that cover informal empirical justifications by Balacheff, Miyazaki, and Harel ＆ Sowder and Tall. Using these theoretical frameworks, justification activities by 5th graders were analyzed and several conclusions were drawn as follow: 1) Children in 5th grade could justify using various proofs types and method ranged from external proofs schemes by Harel & Sowder to thought experiment by Balacheff This implies that children in elementary school can justify various mathematical statements of ideas for themselves. To improve children's proving abilities, rich experience for justifying should be provided. 2) Activities that make conjectures from cases then justify should be given to students in order to develop a sense of necessity of formal proof. 3) Children have to understand the meaning and usage of mathematical symbol to advance to formal deductive proofs. 4) New theoretical framework is needed to be established to provide a framework for research on elementary school children's justification activities. Research on proof mainly focused on the type of proof in terms of reasoning and activities involved. But proof types are also influenced by the tasks given. In elementary school, tasks that require physical activities or examples are provided. To develop students'various proof types, tasks that require various justification methods should be provided. 5) Children's justification type were influenced not only by development level but also by the concept they had. 6) Justification activities provide useful situation that assess students'mathematical understanding. 7) Teachers understanding toward role of proof(verification, explanation, communication, discovery, systematization) should be the starting point of proof activities.

• Journal of Educational Research in Mathematics
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• v.9 no.1
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• pp.245-261
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• 1999

Proof is an essential characteristic of mathematics and as such should be a key component in mathematics education. But, teaching proof in school mathematics have been unsuccessful for many students. The traditional approach to proofs stresses formal logic and rigorous proof. Thus, most students have difficulties of the concept of proof and students' experiences with proof do not seem meaningful to them. However, different views of proof were asserted in the reassessment of the foundations of mathematics and the nature of mathematical truth. These different views of justification need to be reflected in demonstrative geometry classes. The purpose of this study is to characterize the types of students' justification in demonstrative geometry classes taught using dynamic software. The types of justification can be organized into three categories : empirical justification, deductive justification, and authoritarian justification. Empirical justification are based on evidence from examples, whereas deductive justification are based logical reasoning. If we assume that a strong understanding of demonstrative geometry is shown when empirical justification and deductive justification coexist and benefit from each other, then students' justification should not only some empirical basis but also use chains of deductive reasoning. Thus, interaction between empirical and deductive justification is important. Dynamic geometry software can be used to design the approach to justification that can be successful in moving students toward meaningful justification of ideas. Interactive geometry software can connect visual and empirical justification to higher levels of geometric justification with logical arguments in formal proof.

• Korean Journal of Materials Research
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• v.19 no.7
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• pp.382-385
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• 2009

Efforts to reduce noise in industrial application fields, such as automobiles, aircrafts, and plants have been gaining considerable attention while a sound proof wall to protect people from the noise has been intensively investigated by many researchers. In this study, our research group suggested creating a new sound proof wall composed of scrap aluminum chips and perforated plates in a commercial polyester sound proof wall, which was then successfully fabricated. This wall's sound absorption characteristics were measured by an impedance tube method. The sound absorption property was evaluated by measuring the Noise Reduction Coefficient (NRC) to the standard, ASTM C 423-90a. The noise reduction coefficient of the sound proof wall composed of 3.5 vol.% and 7.5 vol.% of scrap aluminum chips relatively increased to 5% and 8% compared to the commercial polyester sound proof wall. The scrap aluminum perforated plate also relatively increased to 13% compared to the commercial polyester sound proof wall.