• Journal of Educational Research in Mathematics
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• v.8 no.1
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• pp.381-403
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• 1998

As a researcher engaged in the mathematical education, mathematics teachers are interested in instructional methods. While it is unlikely that the viewpoints of individual mathematics teachers are reflected in making decisions on instructional purposes and instructional contents, a good many parts of instructional methods on mathematical facts are decided by individual teachers. This means that the role of mathematics teachers is given much weight in the mathematical education. Therefore, the mathematics teachers must not be excluded in all parts of the study of mathematical education. We studied the instructional methods of function concept, a central topic in school mathematics from the following perspectives. First, we examined the characteristics of the three(correspondence-centered, middle, dependence centered) viewpoints about the essence of function concept. And we should that which of them should be the viewpoint of instruction of function concept in school mathematics. Second, we investigated the questions regarding the process of function instruction in school mathematics and presented alternative instruction methods of function concept to solve the questions. Third, we postulated the importance of polynomial function, relating college mathematics in order to present the reason why the polynomial function is importantly treated in functional instruction of school mathematics.

• Journal of applied mathematics & informatics
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• v.40 no.5_6
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• pp.1167-1179
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• 2022

In this paper, we obtain some subsets of real numbers (ℝ) on which a fractional part function is defined as a real-valued continuous function. This gives rise to the analysis of the continuous properties of the fractional part function as a real-valued function. The analysis of fractional part function is helpful in the study of the dynamics of circle.

• Kyungpook Mathematical Journal
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• v.55 no.2
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• pp.335-344
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• 2015

In the paper we discuss the value distribution of the product of the derivative of a transcendental meromorphic function and a power of the function.

• Journal of applied mathematics & informatics
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• v.37 no.1_2
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• pp.13-21
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• 2019

In the present research paper, we introduce a further extension of Hurwitz-Lerch zeta function by using the generalized extended Beta function defined by Parmar et al.. We investigate its integral representations, Mellin transform, generating functions and differential formula. In view of diverse applications of the Hurwitz-Lerch Zeta functions, the results presented here may be potentially useful in some related research areas.

• Honam Mathematical Journal
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• v.33 no.2
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• pp.187-206
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• 2011

The main object of this paper is to present generalization of extended beta function, extended hypergeometric and confluent hypergeometric function introduced by Chaudhry et al. and obtained various integral representations, properties of beta function, Mellin transform, beta distribution, differentiation formulas transform formulas, recurrence relations, summation formula for these new generalization.

• Journal of the Korean Mathematical Society
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• v.56 no.2
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• pp.559-578
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• 2019

We list all subfields of cyclotomic function fields over rational function fields with class number three. We also determine all the imaginary abelian extensions with relative class number three, explicitly.

• Journal of applied mathematics & informatics
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• v.37 no.1_2
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• pp.65-71
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• 2019

In this paper we give some properties related to fuzzy functions on complete residuated lattices.

• Journal of applied mathematics & informatics
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• v.10 no.1_2
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• pp.297-308
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• 2002

• School Mathematics
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• v.4 no.2
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• pp.247-260
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• 2002

In recent elementary school mathematics a word 'stipulation' newly appears. The word is used instead of definition. However, there seems to be some differences between definition and stipulation. So, in this paper we investigate those differences through the concept 'function of definition'. In school mathematics textbooks there are definitions which carry out special functions In mathematical contexts or situations. We can say that we understand those definitions, only if we also understand the functions of definitions in those contexts or situations. Functions of definition are classified as, stipulation-function, discrimination-function, analysis-function, demonstration-function, improvement-function. With these analyses we made a frame for investigating the characteristics of the definitions in recent elementary school mathematics textbooks. As a result of analysing functions of definition we found that generally speaking, stipulation-function is excessively emphasized and the other functions of definition are not explained adequately in school mathematics textbooks. So it is required that the textbook authors should be careful not to miss an opportunity for the functional understanding and the mathematics teachers should be aware of the functions of definitions. Finally, we comment that textbook author, teacher, and researcher should be careful in using the word 'stipulation' instead of definition, because, although there are various functions of definitions, students might ream only stipulation-function.

• Journal of applied mathematics & informatics
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• v.37 no.3_4
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• pp.307-315
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• 2019

In this paper we construct orthogonal two-direction scaling function of order 3 and corresponding wavelet function. In this paper we propose a different approach using orthogonal symmetric/antisymmetric multiwavelets of order 3. An example for constructing orthogonal two-direction scaling function of order 3 and corresponding wavelet function is given.