In these lectures we will discuss:

1. (1) Very simple physical or pre-physical problems; problems that could be discussed at the high school level.

2. (2) The relation of mathematics to science and of science to mathematics. This relation is a two-way street. Though more usual, it is not always the case that mathematics is applied to science; also there is traffic in the opposite direction. Good driving takes note of the oncoming traffic.

3. (3) Elementary calculus, for without some calculus one's idea of how mathematics is applied to science is necessarily inadequate.

Also, as their title indicates, these lectures will deal with my ideas about methods. First, let me say that there is no one teaching method which is the method; there are as many good methods as there are good teachers. To teach effectively a teacher must develop a feeling for his subject; he cannot make his students sense its vitality if he does not sense it himself. He cannot share his enthusiasm when he has no enthusiasm to share. How he makes his point may be as important as the point he makes; he must personally feel it to be important; he must develop his personality.

In my presentation I shall, by and large, follow the genetic method. The essential idea of this method is that the order in which knowledge has been acquired by the human race will be a good order for its acquisition by the individual.