From the forward, "With rare exceptions, the mathematics that I have found most useful was learned in science and engineering classes [or] on my own". This has

From the forward, "With rare exceptions, the mathematics that I have found most useful was learned in science and engineering classes [or] on my own". This has been the case for me too. I never learned this in a class in school, but one of the most important things I've always done when learning some mathematic topic is try to #1 associate it with something in the real world and #2 find a way to "guestimate" without a calculator what the answers will be. For instance, take square roots. The sqrt of 137 will be between 11 and 12 more precisely about 11.7 and I can visualize it in my head as one side of a 2D square shape. Also squares and square roots allow me to easily think about the area covered (size/shape) by N-dimensions in relation to the size of just one dimension. A real world application which is interesting to note is that the time it takes a falling object to hit the ground is equal to the square root of the distance traveled (really 2 times the square root divided by gravity but the general relationship is the same).