- Volume 26 Issue 4
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Grassmann's Mathematical Epistemology and Generalization of Vector Spaces
그라스만의 수학 인식과 벡터공간의 일반화
- Lee, Hee Jung (Dept. of Applied Math., Kangnam Univ.) ;
- Shin, Kyunghee (Graduate School of Edu., Ajou Univ.)
- Received : 2013.04.05
- Accepted : 2013.05.27
- Published : 2013.08.31
Hermann Grassmann classified mathematics and extended the dimension of vector spaces by using dialectics of contrasts. In this paper, we investigate his mathematical idea and its background, and the process of the classification of mathematics. He made a synthetic concept of mathematics based on his idea of 'equal' and 'inequal', 'discrete' and 'indiscrete' mathematics. Also, he showed a creation of new mathematics and a process of generalization using a dialectic of contrast of 'special' and 'general', 'real' and 'formal'. In addition, we examine his unique development in using 'real' and 'formal' in a process of generalization of basis and dimension of a vector space. This research on Grassmann will give meaningful suggestion to an effective teaching and learning of linear algebra.
Supported by : 강남대학교
- Henk J. M. Bos, Lectures in the History of Mathematics, Amer, Math. Soc., 1993.
- Michael J. Crowe, A History of Vector Analysis, University of Notre Dame Press, 1967.
- Jean-Luc Dorier,"A General Outline of the Genesis of Vector Space Theory", Historia Mathematica 22(1995), 227-261.
- Jean-Luc Dorier,"Epistemological Analysis of the Genesis of the Theory of Vector Spaces", On the Teaching of Linear Algebra, Edited by Dorier, Kluwer Academic Publishers, 2000, 1-82.
- H. Eves, Great Moments in Mathematics, 1978. 허민 외 역,수학의 위대한 순간들, 경문사.
- Lewis & Albert C. H.,"Grassmann's 1844 Ausdehnungslehre and Schleiermacher's Dialektik", Annals of Science 34(2) (1977), 103-162. https://doi.org/10.1080/00033797700200171
- Albert C. Lewis,"The unity of logic, pedagogy and foundations in Grassmann's mathematical work", History and philosophy of logic 25(2004), 15-36. https://doi.org/10.1080/01445340310001613824
- Michael Otte,"The ideas of Hermann Grassmann in the Context of the Mathematical and Philosophical Tradition since Leibniz", Historia Mathematica 16(1989), 1-35. https://doi.org/10.1016/0315-0860(89)90096-7
- Mircea Radu, "Justus Grassmann's Contributions to the Foundations of Mathematics: Mathematical and Philosophical Aspects", Historia Mathematica 27(1) (2000), 4-35. https://doi.org/10.1006/hmat.1999.2266