According to an actual performance in an experimental course, we reviewed or taught a major scope of mathematics -- from arithmetic through algebra, geometry, trigonometry, differential, integral and multivariate calculus, linear algebra, differential and integral equations, to statistical topics including probability, distributions, regression and optimization -- within an accelerated programme during a summer term; these topics (and others to slight extents) represent all the mathematics that a professor of chemistry would hope and expect that a student would learn in courses traditionally offered in a department of mathematics.  The prerequisites for this course included calculus II, but no previous experience of computer algebra by the students existed or was assumed.  In 24 sessions over eight weeks, in each of which 75 minutes was devoted to a lecture demonstration and the remainder of four hours to supervised practice, the above topics were introduced, based on an interactive electronic textbook Mathematics for Chemistry with Symbolic Computation, and exercises were assigned -- 10 average per session -- for practice and to test the extent of understanding.   The review of mathematical topics during the first half of the course served to introduce and to settle the language of the processor for computer algebra, and the slower progress through the new topics emphasized both the mathematical concepts and principles and the implementation of the mathematics with the software provided.  Despite the heavy demands of this course, the reception by the students was overwhelmingly positive.