19세기 대수학 및 논리학 발달에서의 드모르간의 위상
De Morgan in the development of algebra and mathematical logic in 19C
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초록
이 연구의 목적은 19세기 대수와 논리 분야에서 드모르간이 구체적으로 어떻게 기여했는지를 살펴보는 것이다. 19세기 대수 분야 발달과정에서 드모르간은, 산술에서 단순히 유추한 형태의 기호대수를 넘어서, 형식으로부터 구성하는 수학의 가능성을 인식하고 이를 명시적으로 나타내어 추상대수학으로 나아갈 수 있는 기초를 닦았다. 드모르간은 19세기 논리학 분야 발달과정에서 아리스토텔레스 논리학의 재구성자인 동시에 수학적 논리학의 창시자로 간주할 수 있다. 그의 연구로 논리학이 철학에서 분리되어 나와 수학과 더욱 긴밀하게 결합하게 되어 수학적 논리학이 하나의 독립적 학문으로 자리 잡게 되었다. 그의 연구 활동을 통하여 우리는 19세기 수학의 발달에서 대수학과 논리학이 현재의 상태로 진화하여 가는 모습을 좀 더 명확하게 알 수 있다.
Abstract
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 made algebra 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.
참고문헌 (33)
- 유미경, "대수 발달의 단계에 관한 드모르간의 관점 연구", 한국수학사학회지, 21(4), pp.61~78 (2008), 한국수학사학회
- Bashmakova, I. G, "Algebra and algebraic number theory. In Mathematics of the 19th century: mathematical logic, algebra, number theory, probability theory", pp.35~135 (2001), Birkhäuser Verlag
- Boyer, C. B, "수학의 역사" (2000), 경문사
- Cajori, F, "A history of mathematics" (1958), The Macmillan company
- Cajori, F, "A history of elementary mathematics with hints on method of teaching" (1917), Macmillan & Co. Ltd
- DeMorgan, A, "Review of a book on geometry", The Athenaeum, 2, pp.71~73 (1868)
- De Morgan, A, "On the study and difficulties of mathematics" (1831), The open court publishing company
- De Morgan, A, "Elements of algebra: preliminary to the differential calculus" (1835), Walton
- De Morgan,A, "Trigonometry and Double Algebra" (1849), Walton & Maberly
- De Morgan, S. E, "Momoir of August De Morgan" (1882), Elibron Classics
- Fisch, M, "‘The Emergency Which Has Arrived’: The Problematic History of Nineteenth-Century British Algebra: A Programmatic Outline", The British Journal for the History of Science, 27(3), pp.247~276 (1994)
- Givant, S, "The calculus of relations as a foundation for mathematics", Journal of Automated Reasoning,, 37, pp.277~322 (2006)
- Guinness, G, "An eye for method: Augustus De Morgan and mathematical education", Paradigm, 9 (1992)
- Kline, M, "Mathematical thought from ancient to modern times" (1972), Oxford University Press
- Kuzicheva, Z. A, "Mathematical logic. In Mathematics of the 19th century: mathematical logic, algebra, number theory, probability theory", pp.1~34 (2001), Birkhäuser Verlag
- Laita, L. M, "Influences on Boole's logic: the controversy between William Hamilton and Augustus De Morgan", Annals of Science, 36(1), pp.45~65 (1979)
- Macfarlane, A, "The Fundamental Principles of Algebra. A report of American Association for the Advancement of Science", Science, 10(246), pp.345~364 (1899)
- Macfarlane, A, "Lectures on ten British mathematicians of the nineteen century. In Mathematical Monographs" (1916), project Gutenberg Archive Foundation
- Maddux, R, "The origin of relation algebras in the development and axiomatization of the calculus of relations", Studia Logica,, 50(3), pp.421~455 (1991)
- Merrill, D.D, "Augustus De Morgan and the logic of relations" (1990), Kluwer Academic Publishers
- Panteki, M, "French "logique" and British "logic"; on the origins of Augustus De Morgan's early logical inquiries 1805-1835", Historia Mathematica, 30, pp.278~340 (1835)
- Peacock, G, "A treatise on algebra vol. II: on symbolic algebra and its applications and the geometry of position" (1842), Cambridge university press
- Pycior, H. M, "Early criticism of the symbolical approach to algebra", Historia Mathematica, 9, pp.392~412 (1982)
- Pycior, H. M, "Augustus De Morgan's algebraic work: the three stage", Isis, 74(1), pp.211~226 (1983)
- Rice, A, "Augustus De Morgan(1806-1871)", The Mathematical Intelligencer, 18(3), pp.40~403 (1996)
- Rice, A, "Augustus De Morgan: Historian of science", History of Science, 34, pp.201~240 (1996)
- Richards, J. L, "Augustus De Morgan, the history of mathematics, and the foundations of algebra", Isis, 78(1), pp.6~30 (1987)
- Styazhkin, N. I, "History of mathematical logic from Leibniz to Peano" (1969), The Colonial Press
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