Errors have been corrected in the third edition and parts of the Fast

Euclidean Algorithm chapter have been refreshed.

Written for elementary school teachers (and presumably teachers in training), this textbook addresses numbers and operations in the mathematics curriculum of grades K-6 (as well as some topics that may be more appropriate for grades 7 and 8, such as rational numbers, the

Euclidean Algorithm, and the conversion of a fraction to a decimal).

Appendices offer background on the

Euclidean algorithm, permutations, polynomials, and analysis in R.

That is, we can use the extended Euclidean algorithm to compute the inverse of any element of Z[[tau]].

Applying Extended Euclidean Algorithm, there exist t, u [member of] Z[[tau]] with [deg.

This facilitates our use of the Euclidean algorithm.

H [subset] {0, 1,2, xxx }) and if deg(g) [less than or equal to] deg(f), the Euclidean algorithm yields

It can be viewed as a generalization of the Euclidean Algorithm to the two dimensional-case.

In this case, the Gauss Algorithm "tends" to the Euclidean Algorithm, and it is important to precisely describe this transition.

One can use the

Euclidean Algorithm to find the Greatest Common Divisor of two polynomial in F[X], for any field F.

Step one involves finding an initial solution to the LDE using Blankinship's Version of the Euclidean Algorithm as its basis.

In the second section, Blankinship's version of the Euclidean Algorithm is demonstrated as an alternative to finding a greatest common divisor (gcd) and solution to a gcd equation of n integers.