• Journal for History of Mathematics
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• v.15 no.2
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• pp.49-68
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• 2002

One of the characteristics of modem mathematics is to use algebra in every fields of mathematics. But we don't have the exact definition of algebra, and we can't clearly define algebraic thinking. In order to solve this problem, this paper investigate the history of algebra. First, we describe some of the features of proportional Babylonian thinking by analysing some problems. In chapter 4, we consider Greek's analytical method and proportional theory. And in chapter 5, we deal with Diophantus' algebraic method by giving an overview of Arithmetica. Finally we investigate Viete's thinking of algebra through his ‘the analytical art’. By investigating these history of algebra, we reach the following conclusions. 1. The origin of algebra comes from problem solving(various equations). 2. The origin of algebraic thinking is the proportional thinking and the analytical thinking. 3. The thing that plays an important role in transition from arithmetical thinking to algebraic thinking is Babylonian ‘the false value’ idea and Diophantus’ ‘arithmos’ concept.

• Journal of Educational Research in Mathematics
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• v.17 no.3
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• pp.253-270
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• 2007

by A.C. Clairaut was written based on the historico-genetic principle such as his . In this paper, by analyzing his we can induce six principles that Clairaut adopted to teach algebra: necessity and curiosity as a motive of studying algebra, harmony of discovery and proof, complementarity of generalization and specialization, connection of knowledge to be learned with already known facts, semantic approaches to procedural knowledge of mathematics, reversible approach. These can be considered as strategies for teaching algebra accorded with beginner's mind. Some of them correspond with characteristics of , but the others are unique in the domain of algebra. And by comparing Clairaut's approaches with school algebra, we discuss about some mathematical subjects: setting equations in relation to problem situations, operations and signs of letters, rule of signs in multiplication, solving quadratic equations, and general relationship between roots and coefficients of equations.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.3
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• pp.279-286
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• 2007

Using t-norm T and s-norm S, we introduce the notion of intuitionistic (T, S)-normed fuzzy subalgebra in BCK/BCI-algebra, and some related properties are investigated.

• Communications of the Korean Mathematical Society
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• v.20 no.3
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• pp.505-509
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• 2005

We show that every $\varepsilon-approximate$ Jordan functional on a Banach algebra A is continuous. From this result we obtain that every $\varepsilon-approximate$ Jordan mapping from A into a continuous function space C(S) is continuous and it's norm less than or equal $1+\varepsilon$ where S is a compact Hausdorff space. This is a generalization of Jarosz's result [3, Proposition 5.5].

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1489-1492
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• 2009

Nagata[3] and Higman[1] showed that nil-algebra of the nilindex n is nilpotent of finite index. In this paper we show that the bounded degree of the nilpotency is less than or equal to $2^n-1$. Our proof needs only some elementary fact about Vandermonde determinant, which is much simpler than Nagata's or Higman's proof.

• The Mathematical Education
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• v.44 no.3 s.110
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• pp.337-360
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• 2005

In this paper we develop textbook 'Modem Algebra' for training mathematics teacher of secondary schools. In order to understand mathematics teacher's viewpoint about desirable textbook 'Modem Algebra' we created a Questionnaire related with curriculum and textbook for training mathematics teacher of secondary schools. We analyze the result of the questionnaire along with recent studies on teacher education and come up with basic principles of developing textbook 'Modern Algebra'. The first version of 'Modern Algebra for Mathematics Teachers' that we have developed based on our study can be found in website 'www.teacheredu.co.kr'.

• Communications of the Korean Mathematical Society
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• v.9 no.2
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• pp.265-270
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• 1994

In 1966, Iseki [2] introduced the notion of BCI-algebras which is a generalization of BCK-algebras. Lei and Xi [3] discussed a new class of BCI-algebra, which is called a p-semisimple BCI-algebra. For p-semisimple BCI-algebras, a subalgebra is an ideal. But a subalgebra of an arbitrary BCI/BCK-algebra is not necessarily an ideal. In this note, a BCI/BCK-algebra that every subalgebra is an ideal is called a normal BCI/BCK-algebra, and we give characterizations of normal BCI/BCK-algebras. Moreover we give a positive answer to the problem which is posed in [4].(omitted)

• Research in Mathematical Education
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• v.10 no.3 s.27
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• pp.169-187
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• 2006

Ubiquitous errors in algebra like $(x+y)^2=x^2+y^2$ are a constant reminder that most students' manipulation of algebraic symbols has become detached from structural principles. The U.S. mathematics education community (NCTM, 2000) has responded by shying away from algebra as a structural study, preferring instead to ground meaning in empirical domains of reference. A new analysis of such errors shows that students' detachment from structural meaning stems from an inadequate structural curriculum, not from the inherent difficulty of adopting an abstract perspective on expressions and equations. A structural curriculum is outlined that preserves the possibility of students' engaging fully with algebra as both an empirical and a structural study.

• Communications of the Korean Mathematical Society
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• v.11 no.3
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• pp.601-611
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• 1996

In this paper, we introduce the notion of weakly associative BCI-algebras and investigate structure of it. Some of characterizations of elements of the quasi-associative part Q(X) of a BCI-algebra X are shown.

• Journal of applied mathematics & informatics
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• v.34 no.3_4
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• pp.309-317
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• 2016

Let V be a Euclidean Jordan algebra with a symmetric cone K. We show that for a Z-transformation L with the additional property L(K) ⊆ K (which we will call ’cone-preserving’), GUS ⇔ strictly copositive on K ⇔ monotone + P. Specializing the result to the Stein transformation S_A(X) := X - AXA^T on the space of real symmetric matrices with the property $S_A(S^n_+){\subseteq}S^n_+$, we deduce that S_A GUS ⇔ I ± A positive definite.