Jerry P. King

In the introduction, Jerry King says that, "In the mathematical field, a single notion precisely learned is worth a textbook of partially digested material." and I suppose that many of his readers, like myself, have plenty of half digested material that they hope to sort out by reading this book.
The presentation is excellent, and repays reading and understanding each line, but the 10 lessons of this true mathematics course require the same major effort and time as would a good mathematics education beyond the basics. Rather like reading music, many symbols have to be understood first, and then manipulated with ease before anything can be played with pleasure.
I doubt that this book will bring many readers to that level, but for those who are already mathematicians, it should be a great summary of what they already know.
It does illustrate the power of mathematics in the generalization of problems and manipulation of symbols to produce very neat results with surprising real life applications. King sees a separate mathematical world which is essential to scientific progress and he would probably agree with Richard Feynman's statement that, "The only true physical description is that describing the experimental meaning of the quantities in the equation - or better, the way the equations are to be used in describing experimental observations. This being the case perhaps the best way to proceed is to try to guess equations, and disregard physical models or descriptions."… (mais)