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Withers, Christopher S.; Nadarajah, Saralees – International Journal of Mathematical Education in Science and Technology, 2012
We show that there are exactly four quadratic polynomials, Q(x) = x [superscript 2] + ax + b, such that (x[superscript 2] + ax + b) (x[superscript 2] - ax + b) = (x[superscript 4] + ax[superscript 2] + b). For n = 1, 2, ..., these quadratic polynomials can be written as the product of N = 2[superscript n] quadratic polynomials in x[superscript…
Descriptors: Mathematics Instruction, Equations (Mathematics), Validity, Mathematical Logic
Withers, Christopher S.; Nadarajah, Saralees – International Journal of Mathematical Education in Science and Technology, 2012
For n = 1, 2, ... , we give a solution (x[subscript 1], ... , x[subscript n], N) to the Diophantine integer equation [image omitted]. Our solution has N of the form n!, in contrast to other solutions in the literature that are extensions of Euler's solution for N, a sum of squares. More generally, for given n and given integer weights m[subscript…
Descriptors: Statistical Analysis, Geometric Concepts, Numbers, Equations (Mathematics)
Withers, Christopher S.; Nadarajah, Saralees – International Journal of Mathematical Education in Science and Technology, 2011
The linear regression model is one of the most popular models in statistics. It is also one of the simplest models in statistics. It has received applications in almost every area of science, engineering and medicine. In this article, the authors show that adding a predictor to a linear model increases the variance of the estimated regression…
Descriptors: Regression (Statistics), Computation, Models, Prediction
Withers, Christopher S.; Nadarajah, Saralees – International Journal of Mathematical Education in Science and Technology, 2010
We extend the well-known identity, log det A = tr log A, for any square non-singular matrix A.
Descriptors: Algebra, Matrices, Equations (Mathematics)