In order to promote the growth of contemporary music and the reform of music, this article designs an improved collaborative filtering (CF) algorithm to solve the problem of sparse matrix in traditional recommendation algorithms. The data matrix is dimensionally reduced to find the nearest neighbor, so as to realize personalized recommendation of…

Described are ways that errors of magnitude can be unwittingly caused when using various supercalculator algorithms to solve linear systems of equations that are represented by nearly singular matrices. Precautionary measures for the unwary student are included. (JJK)

How to use the electronic spreadsheet (e.g., VisiCalc) creatively is discussed, with computer printouts for a number of algorithms. (MNS)

Chio's method of evaluating determinants by successive reduction of size is explained. (MN)

The author presents two examples of lattice multiplication followed by a computer algorithm to perform this multiplication. The algorithm is given in psuedocode but could easily be given in Pascal. (PK)

The article discusses the use of computers to teacher college level mathematics. In particular, the Gaussian elimination procedure for solving a system of n linear equations in n unknowns, using a computer, is examined. (PK)

Presented is a method where a quadratic equation is solved and from its roots the eigenvalues and corresponding eigenvectors are determined immediately. Included are the proposition, the procedure, and comments. (KR)

This yearbook provides the mathematics education community with specific perceptions about discrete mathematics concerning its importance, its composition at various grade levels, and ideas about how to teach it. Many practical suggestions with respect to the implementation of a discrete mathematics school program are included. A unifying thread…

Presented is a scheduling algorithm that uses all the busses at each step for any rectangular array. Included are two lemmas, proofs, a theorem, the solution, and variations on this problem. (KR)