This manual outlines an advanced mathematics course for secondary school students in Manitoba (Canada). Included are eight different topics for a total of ten modules, with each module accounting for 18 40-minute periods. Teachers, or teachers and students cooperatively, should select the equivalent of five modules from the eight topics covered. The course is designed to be of interest to highly motivated students who wish some introduction to areas of mathematics which will be studied in depth in post-secondary programs. Six general objectives are listed. Included are an introduction, examples, objectives, and notes to teachers. The topics covered are: complex numbers and polar coordinates; statistics; number theory; linear programming; theory of equations; matrices and systems of linear equations; three-dimensional geometry; and vectors. Appendices contain annotations of primary and supplementary references. (MNS)