• 제목/요약/키워드: theorem

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미적분학의 기본정리에 대한 역사-발생적 고찰 (A study on a genetic history of the fundamental theorem of calculus)

  • 한대희
    • 대한수학교육학회지:수학교육학연구
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    • 제9권1호
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    • pp.217-228
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    • 1999
  • The fundamental theorem of calculus is the most 'fundamental' content in teaching calculus. Since the aim of teaching the theorem goes beyond simple application of it, it is difficult to teach it meaningfully. Hence, for the meaningful teaching of the fundamental theorem of calculus, this article seeks to find the educational implication of the fundamental theorem of calculus through reviewing the genetic history of it. A genetic history of the fundamental theorem of calculus can be divided into the following five phases: 1. The deductive discovery of the fundamental theorem of calculus 2. Galileo's Law of falling body and the idea of the fundamental theorem of calculus 3. The discovery of the fundamental theorem of calculus and Barrow's proof 4. Newton's mensuration 5. the development of calculus in 19th century and the fundamental theorem of calculus The developmental phases of the fundamental theorem of calculus discussed above provides the three educational implications. first, we can rediscover this theorem through deductive methods and get the ideas of it in relation to kinetic problems. Second, the developmental phases of the fundamental theorem of calculus shows that the value of this theorem lies in the harmony of its theoretical beauty and practicality. Third, Newton's dynamic image of this theorem can be a typical way of understanding the theorem. We have different aims of teaching the fundamental theorem of calculus, according to which the teaching methods can be adopted. But it is self-evident that the simple application of the theorem is just a part of teaching the fundamental theorem of calculus. Hence we must try to put the educational implications reviewed above into practice.

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ON BASIC ANALOGUE OF CLASSICAL SUMMATION THEOREMS DUE TO ANDREWS

  • Harsh, Harsh Vardhan;Rathie, Arjun K.;Purohit, Sunil Dutt
    • 호남수학학술지
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    • 제38권1호
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    • pp.25-37
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    • 2016
  • In 1972, Andrews derived the basic analogue of Gauss's second summation theorem and Bailey's theorem by implementing basic analogue of Kummer's theorem into identity due to Jackson. Recently Lavoie et.al. derived many results closely related to Kummer's theorem, Gauss's second summation theorem and Bailey's theorem and also Rakha et. al. derive the basic analogues of results closely related Kummer's theorem. The aim of this paper is to derive basic analogues of results closely related Gauss's second summation theorem and Bailey's theorem. Some applications and limiting cases are also considered.

NONLINEAR VARIATIONAL INEQUALITIES AND FIXED POINT THEOREMS

  • Park, Sehie;Kim, Ilhyung
    • 대한수학회보
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    • 제26권2호
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    • pp.139-149
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    • 1989
  • pp.Hartman and G. Stampacchia [6] proved the following theorem in 1966: If f:X.rarw. $R^{n}$ is a continuous map on a compact convex subset X of $R^{n}$ , then there exists $x_{0}$ ..mem.X such that $x_{0}$ , $x_{0}$ -x>.geq.0 for all x.mem.X. This remarkable result has been investigated and generalized by F.E. Browder [1], [2], W. Takahashi [9], S. Park [8] and others. For example, Browder extended this theorem to a map f defined on a compact convex subser X of a topological vector space E into the dual space $E^{*}$; see [2, Theorem 2]. And Takahashi extended Browder's theorem to closed convex sets in topological vector space; see [9, Theorem 3]. In Section 2, we obtain some variational inequalities, especially, generalizations of Browder's and Takahashi's theorems. The generalization of Browder's is an earlier result of the first author [8]. In Section 3, using Theorem 1, we improve and extend some known fixed pint theorems. Theorems 4 and 8 improve Takahashi's results [9, Theorems 5 and 9], respectively. Theorem 4 extends the first author's fixed point theorem [8, Theorem 8] (Theorem 5 in this paper) which is a generalization of Browder [1, Theroem 1]. Theorem 8 extends Theorem 9 which is a generalization of Browder [2, Theorem 3]. Finally, in Section 4, we obtain variational inequalities for multivalued maps by using Theorem 1. We improve Takahashi's results [9, Theorems 21 and 22] which are generalization of Browder [2, Theorem 6] and the Kakutani fixed point theorem [7], respectively.ani fixed point theorem [7], respectively.

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TOUCHE ROUCHE

  • Harte, Robin;Keogh, Gary
    • 대한수학회보
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    • 제40권2호
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    • pp.215-221
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    • 2003
  • There seems to be a love-hate relationship between Brouwer's fixed point theorem and the fundamental theorem of algebra; in this note we offer one more tweak at it, and give a version of Rouches theorem.

SECOND MAIN THEOREM WITH WEIGHTED COUNTING FUNCTIONS AND UNIQUENESS THEOREM

  • Yang, Liu
    • 대한수학회보
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    • 제59권5호
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    • pp.1105-1117
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    • 2022
  • In this paper, we obtain a second main theorem for holomorphic curves and moving hyperplanes of Pn(C) where the counting functions are truncated multiplicity and have different weights. As its application, we prove a uniqueness theorem for holomorphic curves of finite growth index sharing moving hyperplanes with different multiple values.

피타고라스 정리와 증명의 발견 과정 재구성 (A study on the rediscovery of the Pythagorean theorem)

  • 한대희
    • 대한수학교육학회지:학교수학
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    • 제4권3호
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    • pp.401-413
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    • 2002
  • The Pythagorean theorem is one of the most important theorem which appeared in school mathematics. Allowing our pupils to rediscover it in classroom, we must know how this theorem was discovered and proved. Further, we should recompose that historical knowledge to practical program which might be suitable to them So, firstly this paper surveyed the history of mathematics on discovering the Pyth-agorean theorem. This theorem was known to many ancient civilizatons: There are evidences that Babylonian and Indian had the knowledges on the relationship among the sides of a right triangle. In Zhoubi suanjing, which was ancient Chinese text book, was the proof of the Pythagorean theorem in special case. And then this paper proposed a teaching program that is composed following five tasks : 1) To draw up squares on geo-board that are various in size and shape, 2) To invent squares that are n-times bigger than a given square, 3) Discovering the Pyth-agorean theorem through the previous activity, 4) To prove the Pythagorean theorem in special case, 5) To prove the Pythagorean theorem in general case.

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