• Title/Summary/Keyword: mathematical expression

Search Result 352, Processing Time 0.026 seconds

A Study of the Representation and Algorithms of Western Mathematics Reflected on the Algebra Domains of Chosun-Sanhak in the 18th Century (18세기 조선산학서의 대수 영역에 나타난 서양수학 표현 및 계산법 연구)

  • Choi, Eunah
    • Journal of the Korean School Mathematics Society
    • /
    • v.23 no.1
    • /
    • pp.25-44
    • /
    • 2020
  • This study investigated the representation and algorithms of western mathematics reflected on the algebra domains of Chosun-Sanhak in the 18th century. I also analyzed the co-occurrences and replacement phenomenon between western algorithms and traditional algorithms. For this purpose, I analyzed nine Chosun mathematics books in the 18th century, including Gusuryak and Gosasibijip. The results of this study are as follows. First, I identified the process of changing to a calculation by writing of western mathematics, from traditional four arithmetical operations using Sandae and the formalized explanation for the proportional concept and proportional expression. Second, I observed the gradual formalization of mathematical representation of the solution for a simultaneous linear equation. Lastly, I identified the change of the solution for square root from traditional Gaebangsul and Jeungseunggaebangbeop to a calculation by the writing of western mathematics.

Mathematical Expressions for Stress-Strain Curve of Metallic Material (금속재료 응력-변형률 곡선의 수학적 표현들)

  • Hyun, Hong-Chul;Lee, Jin-Haeng;Lee, Hyung-Yil
    • Transactions of the Korean Society of Mechanical Engineers A
    • /
    • v.32 no.1
    • /
    • pp.21-28
    • /
    • 2008
  • Stress-strain curves based on Ramberg-Osgood and Hollomon relations are strongly dependent upon the regressed range of strain. This work investigates mathematical expressions of true stress-strain curves of metallic materials. We first observe the variation of yield strength, strain hardening exponent and stress-strain curve with regressed range of stain. Based on sectional regression and expression using one or two parameters, we propose an optimal strain range for which yield strength and nonlinear material behavior are quite appropriate.

The analysis of the concept of equal symbol and the investigation of the students' understanding of it (등호 개념의 분석 및 학생들의 등호 이해 조사)

  • 이종희;김선희
    • Journal of Educational Research in Mathematics
    • /
    • v.13 no.3
    • /
    • pp.287-307
    • /
    • 2003
  • This study analyzed the concept of equal symbol(=) that is the most symbol used in learning of mathematics and investigated students' understanding of that. The equal symbol is endowed with the 'same', 'equal', and 'equivalent' meaning, represented by =, but students interpret the meaning of equal symbol according to the mathematical con text. Thus, we analyzed the equal symbol on the basis of the theory of conceptual fields. In the theory of conceptual fields, concept is a three-tuple of three sets of situation, operational invariants and symbolic representations, and the operational invariants are the concept-in-action and the theorems- in-action. With the analysis contents, we investigated how students read = by korean, what equals in the expression containing = or by what meaning students used =, and which they could correct the error for =. This study imply that we should consider the symbol notation agreed by mathematical society, the meaning, and the situational context that it used, when we teach the mathematics symbols.

  • PDF

A Study on Relation between e-Learning Strategy and Multiple Intelligence of College Students of Engineering Department (공과대 학생들의 e-Learning 전략과 다중지능의 관련성 연구)

  • An, Gwang-Sik;Park, Hae-Ouk;Kim, Mi-Young;Lee, Ja-Hee;Ku, Jin-Hee;Choi, Won-Sik
    • 대한공업교육학회지
    • /
    • v.30 no.2
    • /
    • pp.72-81
    • /
    • 2005
  • The purpose of this study is to do research on correlation between multiple intelligence and e-Learning strategy, which can be used to develop and strengthen e-Learning strategy. The subject was 183 college students of engineering at C university who had ever taken a lesson through e-Learning. Two items are investigated in these college students. One is whether there is a gap and any gender-related difference in multiple intelligence and e-Learning strategy, and the other is what multiple intelligences have an effect on e-Learning strategy. The e-Learning strategy developed by In-Sock Lee and the instrument by Yong-Lin Moon were used. The results of this study are as follows. First, it appeared that there was a difference between gender in musical intelligence and naturalistic intelligence. The average of musical intelligence was higher in female collegian, while the average of naturalistic intelligence was higher in male collegian. But there was no gender-related difference in using e-Learning strategy. Second, it appeared that multiple intelligence gave an explanation of self-direction intelligence up to 31.1%, expression strategy 20.35%, and information processing strategy 16.6%. The results of this study showed that logical-mathematical intelligence affected all of three e-Learning strategies. So, new curriculum which can make use of logical-mathematical intelligence needs to be developed so as to devise efficient e-Learning strategies.

An Analysis on Teaching and Learning Strategies of Inquiry Tasks in the Elementary Moral Textbooks by Multiple Intelligence (다중지능을 이용한 초등학교 도덕 교과서 탐구 과제의 교수·학습 전략 분석)

  • Noh, Jeong-Im;Song, Gi-Ho;Yu, Jong-Youl
    • Journal of the Korean Society for Library and Information Science
    • /
    • v.51 no.2
    • /
    • pp.5-22
    • /
    • 2017
  • The purpose of this study is to analyze the teaching and learning strategies included in the inquiry tasks of elementary moral textbooks with multiple intelligences (M.I), and to propose educational information services of teacher librarians. It was found that the tasks were mainly designed by the linguistic intelligence, logical & mathematical intelligence and spatial intelligence. In terms of the information literacy process, linguistic intelligence and spatial intelligence are mainly applied to the analysis-understanding stage. Logical & mathematical intelligence is applied to the stage of comprehensive-application and linguistic intelligence is applied to expression-delivery step. In order to cultivate the insufficient M.I in inquiry activities, teacher librarians should improve room and teaching materials of their school library and provide workbooks using the graphic organizer after analyzing the linkage of the inquiry tasks between the subjects.

The Core Concepts of Mathematics for AI and An Analysis of Mathematical Contents in the Textbook (수학과 인공지능(AI) 핵심 개념과 <인공지능 수학> 내용 체계 분석)

  • Kim, Changil;Jeon, Youngju
    • Journal of the Korean School Mathematics Society
    • /
    • v.24 no.4
    • /
    • pp.391-405
    • /
    • 2021
  • In this study, 'data collection', 'data expression', 'data analysis, and 'optimization and decision-making' were selected as the core AI concepts to be dealt with in the mathematics for AI education. Based on this, the degree of reflection of AI core concepts was investigated and analyzed compared to the mathematical core concepts and content of each area of the elective course. In addition, the appropriateness of the content of was examined with a focus on core concepts and related learning contents. The results provided some suggestions for answering the following four critical questions. First, How to set the learning path for ? Second, is it necessary to discuss the redefinition of the nature of ? Third, is it appropriate to select core concepts and terms for ? Last, is it appropriate to present the relevant learning contents of the content system of ?

Understanding the Proof of Inverse Square Law of Newton's Principia from a Heuristic Point of View (Newton의 Principia에서 역제곱 법칙 증명에 대한 발견적 관점에서의 이해)

  • Kang, Jeong Gi
    • Communications of Mathematical Education
    • /
    • v.36 no.1
    • /
    • pp.23-38
    • /
    • 2022
  • The study provided a perspective on which readers can see Newton's proof heuristically in order to overcome the difficulty of proof showing 'QT2/QR converges to the latus rectum of ellipse' in the proof of the inverse square law of Newton's Principia. The heuristic perspective is as follows: The starting point of the proof is the belief that if we transform the denominators and numerators of QT2/QR into expression with respect to segments related to diameter and conjugate diameter, we may obtain some constant, the desired value, by their relationship PV × VG/QV2 = PC2/CD2 in Apollonius' Conic sections. The heuristic perspective proposed in this study is meaningful because it can help readers understand Newton's proof more easily by presenting the direction of transformation of QT2/QR.

Performance Analysis of Decode-and-Forward Relaying with Partial Relay Selection for Multihop Transmission over Rayleigh Fading Channels

  • Bao, Vo Nguyen Quoe;Kong, Hyung-Yun
    • Journal of Communications and Networks
    • /
    • v.12 no.5
    • /
    • pp.433-441
    • /
    • 2010
  • Multihop transmission is a promising technique that helps in achieving broader coverage (excellent network connectivity) and preventing the impairment of wireless channels. This paper proposes a cluster-based multihop wireless network that makes use of the advantages of multihop relaying, i.e., path loss gain, and partial relay selection in each hop, i.e., spatial diversity. In this partial relay selection, the node with the maximum instantaneous channel gain will serve as the sender for the next hop. With the proposed protocol, the transmit power and spectral efficiency can be improved over those in the case of direct transmission and conventional multihop transmission. Moreover, at a high signal-to-noise ratio (SNR), the performance of the system with at least two nodes in each cluster is dependent only on the last hop and not on any of the intermediate hops. For a practically feasible decode-and-forward relay strategy, a compact expression for the probability density function of the end-to-end SNR at the destination is derived. This expression is then used to derive closed-form expressions for the outage probability, average symbol error rate, and average bit error rate for M-ary square quadrature amplitude modulation as well as to determine the spectral efficiency of the system. In addition, the probability of SNR gain over direct transmission is investigated for different environments. The mathematical analysis is verified by various simulation results for demonstrating the accuracy of the theoretical approach.

Synergistic inhibition of mesothelioma cell growth by the combination of clofarabine and resveratrol involves Nrf2 downregulation

  • Lee, Yoon-Jin;Im, Jae-Hyuk;Lee, David M.;Park, Ji-Sung;Won, Seong Youn;Cho, Moon-Kyun;Nam, Hae-Seon;Lee, Yong-Jin;Lee, Sang-Han
    • BMB Reports
    • /
    • v.45 no.11
    • /
    • pp.647-652
    • /
    • 2012
  • We previously reported that MSTO-211H cells have a higher capacity to regulate Nrf2 activation in response to changes in the cellular redox environment. To further characterize its biological significance, the response of Nrf2, a transcription factor that regulates ARE-containing genes, on the synergistic cytotoxic effect of clofarabine and resveratrol was investigated in mesothelioma cells. The combination treatment showed a marked growth-inhibitory effect, which was accompanied by suppression of Nrf2 activation and decreased expression of heme oxygenase-1 (HO-1). While transient overexpression of Nrf2 conferred protection against the cytotoxicity caused by their combination, knockdown of Nrf2 expression using siRNA enhanced their cytotoxic effect. Pretreatment with Ly294002, a PI3K inhibitor, augmented the decrease in HO-1 level by their combination, whereas no obvious changes were observed in Nrf2 levels. Altogether, these results suggest that the synergistic cytotoxic effect of clofarabine and resveratrol was mediated, at least in part, through suppression of Nrf2 signaling.

Non-structural Characteristics of Asian Looks in Modern Fashion (현대패션에 나타난 아시안룩의 비구조적 조형성)

  • Lim, Ji-Ah;Kim, Min-Ja
    • Journal of the Korean Society of Costume
    • /
    • v.60 no.6
    • /
    • pp.1-10
    • /
    • 2010
  • The cultures and traditions of Asia has the roots so deep and it is the origin of inspiration. Therefore, it is easy to find a different inspiration when designing, expecially for Western designers who are seeking European tradition and its comparison. The most distinctive feature of the Asian look is non-structural and has no clear form close to the structure of the body or mathematical ratio, but is steric with 2-Dimensional planed textiles, and has a flexible, non-structural formative characteristic related to the movable body. This is base on the vision of the universe that regards the parts as the whole. From this research, generally studying about the Asian look and its non-structural formative characteristics. The study looked closely into the aesthetic value of non-structural formative characteristics formation, with basis on the large dress regulation system of the western reasoning and rationalism and mechanism. At first, my study pointed on the dressing functionalism or Neo-classism considering emotions, Anti-Western aspect observing surrealism dressing and expressionism dressing. Second, with men and women showing similar outer shape without the equivalent element such from wearing a corset, the sexism is abolished. Finally, the designers’ inner intention of art is being delivered, from the aspect that the expression of art, size and no waste of fabric shows effort of communicating with the world, giving value to the possibility of continuance.