As to the need of improvement there can be no question whilst the reign of continues. My own idea of a useful course is to begin with arithmetic, and then not but algebra. Next, not , but practical geometry, solid as well as plane; not demonstration, but to make acquaintance. Then not , but elementary vectors, conjoined with algebra, and applied to geometry. Addition first; then the scalar product. Elementary calculus should go on simultaneously, and come into vector algebraic geometry after a bit. might be an extra course for learned men, like ...