How “rigorous” is the O/Z approach to calculus?
“Rigor” is commonly used in 2 different ways: (i) in reference to a traditional, Bourbaki-style mathematical sense; (ii) as a rough synonym for “hard” or “challenging”. The O/Z approach is certainly not rigorous in the first sense. (Nor, for that matter, are most other beginning texts. For instance, a rigorous approach to trigonometric functions should be preceded with a proof of existence of arclength for circular segments.) Rigor in this sense is, of course, essential to knowing and doing mathematicsmajor students should certainly encounter it seriously in their courses. But we think that a beginning calculus course is too “early” for this encounter to occur in a concerted way. A pedagogically sounder goal for beginning calculus students (including prospective mathematics majors) is to become familiar and proficient with the objects and methods of calculus. This approach seems more practical for non-major students; it can also help prospective mathematics majors better understand and
