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Grassmann's Mathematical Epistemology and Generalization of Vector Spaces

그라스만의 수학 인식과 벡터공간의 일반화

  • Received : 2013.04.05
  • Accepted : 2013.05.27
  • Published : 2013.08.31

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.

Acknowledgement

Supported by : 강남대학교

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