• School Mathematics
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• v.10 no.4
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• pp.557-571
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• 2008

The objective of this paper is to study De Morgan's thoughts on teaching and learning negative numbers. We studied De Morgan's point of view on negative numbers, and analyzed his didactical approaches for negative numbers. De Morgan make students explore impossible subtractions, investigate the rule of the impossible subtractions, and construct the signification of the impossible subtractions in succession. In De Morgan' approach, teaching and learning negative numbers are connected with that of linear equations, the signs of impossible subtractions are used, and the concept of negative numbers is developed gradually following the historic genesis of negative numbers. Also, we analyzed the strengths and weaknesses of the De Morgan's approaches compared with the mathematics curriculum.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.47 no.2
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• pp.51-59
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• 2010

Two logic transformations, De Morgan and re-substitution, are sufficient to convert a unate gate network (UGN) to a more general balanced inversion parity (BIP) network. Circuit classes of interest are discussed in detail. We prove that De Morgan and re-substitution transformations are test-set preserving for path delay faults. Using the results of this paper, we can easily show that a high-level test set for a function z that detects all path delay faults in any UGN realizing z also detects all path delay faults in any BIP realization of z.

• Journal for History of Mathematics
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• v.17 no.2
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• pp.73-84
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• 2004

Stone introduced extremally disconnected spaces as the image of complete Boolean algebras under his famous duality between Bool and ZComp and they turn out to be projective objects in various categories of Hausdorff spaces and completely regular ones are exactly those X with Dedekind complete C(X, ). In the pointfree setting, extremally disconnected frame (= De Morgan frame) are those with De Morgan condition. In this paper, we investigate a historical aspect of De Morgan frame together with that of De Morgan.

• Journal for History of Mathematics
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• v.22 no.4
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• pp.129-144
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• 2009

The purpose of this study is what exactly De Morgan contributed to abstract algebra and mathematical logic. He recognised the purely symbolic nature of algebra and was aware of the existence of algebras other than ordinary algebra. He madealgebra as a science by introducing the ordered field and made the base for abstract algebra. He was one of the reformer of classical mathematical logic. Looking into De Morgan's works, we made it clear that the developments of algebra and mathematical logic in 19C.

• Journal for History of Mathematics
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• v.21 no.4
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• pp.61-78
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• 2008

In this paper, we discuss about De Morgan's view on the development of algebra according to following distinctions: arithmetic, universal arithmetic, symbolic algebra, significant algebra. De Morgan thought that the differences between arithmetic and universal arithmetic lie in the usage of letters and the immediate performance of computation. In his viewpoint, universal arithmetic is a transitional phase, in which absurd phenomena occur, from arithmetic to algebra and these absurd phenomena call for algebra. The feature of De Morgan's view on the development of algebra is that symbolic calculus which consist of symbol system without symbol's meaning is acquired, then as extended meanings are furnished to symbols, symbolic calculus become logical so significant calculus is developed. For example, Single algebra is developed, as an extended meaning is furnished to a symbol -1, and double algebra is developed, as an extended meaning is furnished to a symbol $\sqrt{-1}$. According to De Morgan, a symbol system is derived from the incompleteness of a prior symbol system.

• The Mathematical Education
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• v.51 no.2
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• pp.115-129
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• 2012

The values and methods of mathematics education which mathematics teachers tried to impart to their students have varied historically according to the situations of each institution. The cases of the mathematics education in Cambridge University and University College, London show that the peculiar meanings or values of mathematics education were transmitted on students and the methods or focus of the teaching were uniquely determined under the influences of university examinations or conditions of students. In specific, the characteristic education of Augustus De Morgan who studied in Cambridge University and then taught in University College, London reveals better the different institutional contexts. In this paper, I suggest mathematics teachers reconsider mathematics learning motivations on their institutional contexts.

• Journal of Educational Research in Mathematics
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• v.18 no.2
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• pp.223-237
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• 2008

In this paper, We focus on grasping De Morgan's perspectives on mathematics education systematically. His perspectives can be summarized as followings. First, historico-genesis of mathematics must be considered in the teaching and learning of mathematics. Second, mathematical conception of students must be formulated progressively. Third, it is important to use errors which come out continually in the process of passing from inductive stage to deductive stage. Fourth, personal knowledge of students is important in the teaching and learning of mathematics. These De Morgan's four perspectives are the way of approach for experiencing moral certainty first of all to get to mathematical certainty. Moral certainty which he presented is a combination of rationality and humanity to fill up gaps between Platonism and general public education.

• Journal of Korean Philosophical Society
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• v.139
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• pp.1-21
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• 2016

To quickly and accurately grasp the consistency and the true/false of sentence description, we may require the help of a computer. It is thus necessary to research and quickly and accurately grasp the consistency and the true/false of sentence description by computer processing techniques. This requires research and planning for the whole study, namely a plan for the necessary tables and those of processing, and development of the table of the five logic rules. In future research, it will be necessary to create and develop the table of ten basic inference rules and the eleven kinds of derived inference rules, and it will be necessary to build a DB of those tables and the computer processing of sentence logic using server programming JSP and client programming JAVA over its foundation. In this paper we present the overall research plan in referring to the logic operation table, dividing the logic and inference rules, and preparing the listed process sequentially by dividing the combination of their use. These jobs are shown as a variable table and a symbol table, and in subsequent studies, will input a processing table and will perform the utilization of server programming JSP, client programming JAVA in the construction of subject/predicate part activated DB, and will prove the true/false of a sentence. In considering the table prepared in chapter 2 as a guide, chapter 3 shows the creation and development of the table of the five logic rules, i.e, The Rule of Double Negation, De Morgan's Rule, The Commutative Rule, The Associative Rule, and The Distributive Rule. These five logic rules are used in Propositional Calculus, Sentential Logic Calculus, and Statement Logic Calculus for sentence logic.