The Challenges of Teaching Elementary Linear Algebra in a Modern Matrix Based Way
We assess the situation of our elementary Linear Algebra classes in the US holistically and through personal history recollections. Possible remedies for our elementary Linear Algebra's teaching problems are discussed and a change from abstract algebraic taught classes to a concrete matrix base...
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| Main Author | |
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| Format | Journal Article |
| Language | English |
| Published |
07.03.2023
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| Subjects | |
| Online Access | Get full text |
| DOI | 10.48550/arxiv.2303.03957 |
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| Summary: | We assess the situation of our elementary Linear Algebra classes in the US
holistically and through personal history recollections. Possible remedies for
our elementary Linear Algebra's teaching problems are discussed and a change
from abstract algebraic taught classes to a concrete matrix based first course
is considered. The challenges of such modernization attempts for this course
are laid out in light of our increased after-Covid use of e-books and
e-primers. We specifically address the useless and needless, but ubiquitous use
of determinants, characteristic polynomials and polynomial root finding methods
that are propagated in our elementary text books and are used in the majority
of our elementary Linear Algebra classes for the matrix eigenvalue problem but
that have no practical use whatsoever and offer no solution for finding matrix
eigenvalues. This paper challenges all mathematicians as we have misinformed
and miseducated our students badly for decades in elementary Linear Algebra now
and urges a switch to a new, fully matrix theoretical approach that covers all
classical subjects in a practical and computable way. |
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| DOI: | 10.48550/arxiv.2303.03957 |