Calculus is the mathematics of change. ...Change is characteristic of the world. - Richard Hamming

Increasingly... the application of mathematics to the real world involves discrete mathematics... the nature of the discrete is often most clearly revealed through the continuous models of both calculus and probability. Without continuous mathematics, the study of discrete mathematics soon becomes trivial and very limited. ...The two topics, discrete and continuous mathematics, are both ill served by being rigidly separated.

Very few of us in our saner moments believe that the particular postulates that some logicians have dreamed up create the numbers - no, most of us believe that the real numbers are simply there and that it has been an interesting, amusing, and important game to try to find a nice set of postulates to account for them.

Mathematics, being very different from the natural languages, has its corresponding patterns of thought. Learning these patterns is much more important than any particular result... They are learned by the constant use of the language and cannot be taught in any other fashion.