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http://dx.doi.org/10.14477/jhm.2013.26.4.245
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Grassmann's Mathematical Epistemology and Generalization of Vector Spaces |

Lee, Hee Jung
(Dept. of Applied Math., Kangnam Univ.)
Shin, Kyunghee (Graduate School of Edu., Ajou Univ.) |

Publication Information

Abstract

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.

Keywords

Grassmann; contrast; dialectics; real and formal; vector space; basis; dimension; generalization;

Citations & Related Records

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