• Korean Journal of Cognitive Science
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• v.6 no.3
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• pp.5-23
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• 1995

According to a well-known argument (so-called the Godelian argument) proposed by Lucas. Godel's theorem refutes the thesis of mechanism. that is, the thesis that human cognitive system is no more than a Turing machine. The main aim of this paper is to show that this argument is not successful. However. I also argue that many pre-existing objections (by Benacerraf, Slezak. Boyer. Hofstadter etc.) to Gooelian argument are not satisfactory. either. Using Tarski's theorem. I then strengthen what I caII the consistency objection to Godelian argument. In my dilemma objection obtained. Godelian argument doesn't work because the argument has a false premise if we have the concept of global truth and the argument cannot be stated if not.

• Communications of the Korean Mathematical Society
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• v.37 no.4
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• pp.989-993
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• 2022

In this paper, we prove Pascal's hexagon theorem by elementary tools only. We follow the well-known route to prove the theorem by Bezóut's theorem, explaining all the details in elementary argument. In particular, we prove a toy version of Study's lemma.

• Research in Mathematical Education
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• v.27 no.1
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• pp.75-92
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• 2024

Mathematical argument has been given much attention in the research literature as a mediating construct between reasoning and proof. However, there have been relatively less efforts made in the research that examined the nature of empirical arguments represented in textbooks and how students perceive them as proofs. Cases of point include Intermediate Value Theorem [IVT] and Maximum-Minimum theorem [MMT] in grade 11 in Korea. In this study, using Toulmin's framework (1958), the author analyzed the substance of the empirical arguments provided for both MMT and IVT to draw comparisons between the nature of datum, claims, and warrants among empirical arguments offered in textbooks. Also, an online survey was administered to learn about how students view as proofs the empirical arguments provided for MMT and IVT. Results indicate that nearly half of students tended to accept the empirical arguments as proofs. Implications are discussed to suggest alternative approaches for teaching MMT and IVT.

• Journal of applied mathematics & informatics
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• v.33 no.5_6
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• pp.723-738
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• 2015

In this paper, the prescribed mean curvature Rayleigh p-Laplacian equation with a deviating argument

• Korean Journal of Mathematics
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• v.32 no.1
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• pp.73-82
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• 2024

The purpose of this paper is to introduce a new subclass of strongly meromorphic close-to-convex functions by subordinating to generalized Janowski function. We investigate several properties for this class such as coefficient estimates, inclusion relationship, distortion property, argument property and radius of meromorphic convexity. Various earlier known results follow as particular cases.

• 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.

• Honam Mathematical Journal
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• v.41 no.3
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• pp.661-666
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• 2019

In this short research note, we aim to provide a new proof of classical Dixon's summation theorem for the series $_3F_2$ with unit argument. The theorem is obtained by evaluating an infinite integral and making use of classical Gauss's and Kummer's summation theorem for the series $_2F_1$.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.1
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• pp.13-27
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• 2018

By using of the Banach fixed point theorem, the theory of a strongly continuous semigroup of operators and resolvent operator, we investigate the existence and uniqueness of S-asymptotically ${\omega}-periodic$ mild solutions for some differential (integrodifferential) equations with piecewise constant argument when specially ${\omega}$ is an integer.

• The Mathematical Education
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• v.52 no.4
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• pp.549-565
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• 2013

To help students understand the deduction system in the proof, we analyzed the textbook on mathematics at first. As results, we could find that the textbook' system of deduction is similar with the Euclid' system of deduction. The starting point of deduction is different with each other. But the flow of deduction match with each other. Next, we searched for the example of circular argument and analyzed. As results, we classified the circular argument into two groups. The first is an internal circular argument which is a circular argument occurred in a theorem. The second is an external circular argument which is a circular argument occurred between many theorems. We could know that the flow of deduction system is consistent in internal-external dimension. Lastly, we proposed the desirable teaching direction to help students understand the deduction system in the proof.

• Journal of the Korean Statistical Society
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• v.22 no.2
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• pp.353-359
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• 1993

In this note we consider other type of tightness than that of Birkel (1988) and prove an invariance principle for nonstationary associated processes by an application of the central limit theorem of Cox and Grimmett (1984), thus avoiding the argument of uniform integrability. This result is an extension to the nonstationary case of an invariance priciple of Newman and Wright (1981) as well as an improvement of the central limit theorem of Cox and Grimmett (1984).