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A new unified, balanced, and conceptual approach to teaching linear algebra. (English) Zbl 1042.00005

The author reports on his efforts to “rethink and retool” the elementary linear algebra course at Auburn University. He suggests using the fundamental equation \(f(\alpha x+\beta y)= \alpha f(x)+\beta f(y)\) as the conceptual core and beginning of the course. After a philosophical prolegomenon, he concludes with a detailed syllabus based on this suggested beginning.

MSC:

00A35 Methodology of mathematics
15-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to linear algebra
97D30 Objectives and goals of mathematics teaching

Keywords:

linear algebra
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References:

[1] Anton, H., Elementary Linear Algebra (1973), Wiley: Wiley New York · Zbl 0277.15001
[2] Halmos, P. R., Finite-Dimensional Vector Spaces (1942, 1958), Princeton: Princeton van Nostrand
[3] Lay, D. C., Linear Algebra and its Applications (1994), Addison-Wesley: Addison-Wesley Reading, MA
[7] Uhlig, F., Transform Linear Algebra (2002), Prentice-Hall: Prentice-Hall Upper Saddle River · Zbl 1083.15002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.