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- W2078722486 abstract "Values of logarithms can be estimated using only their algebraic properties, i.e. without appeal to calculus. College algebra students can achieve estimates that are of the order of 1% error, by solving certain linear systems by hand. Improving the accuracy of the approximations naturally leads in twodirections: to larger linear systems, requiring a computer; or to least squares solutions, which can be made natural and accessible tocollege algebra students in anovel, low-dimensional geometric way. Error bounding, and comparision of the new low-dimensional, geometric least squares method with the traditional higher-dimensional approach to least squares provide useful explorations for linear algebra students. Specifically, error bounding is possible for students who (1) are able to compute the distance from a point in R k to a hyperplane; (2) understand orthogonal matrices, and the basics of the singular value decomposition of a matrix; and (3) know the Taylor series for ln (1+x)." @default.
- W2078722486 created "2016-06-24" @default.
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- W2078722486 date "1999-03-01" @default.
- W2078722486 modified "2023-09-26" @default.
- W2078722486 title "Estimating logarithms with College Algebra students" @default.
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- W2078722486 doi "https://doi.org/10.1080/002073999287987" @default.
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