The change from high school mathematics to college mathematics involves not merely a step upward in difficulty; it also involves a change from a narrow view of mathematics to a broader view. In high school mathematics you were concerned primarily with manipulations, and you probably fell naturally into the view that mathematics is a study of fixed, immutable laws of nature...In college you will see that the laws of mathematics are not immutable, and that one set of laws can be abandoned and another set adapted in its place whenever it appears that the new set will be more useful for a particular purpose. The study of college mathematics requires a more flexible mind, ready for new ideas and free from preconceived notions.
Carl Denbow & Victor Goedicke
Foundations of Mathematics, 1959, p. 47
