The book begins with a detailed discussion of two problems that have played an extremely important role in the emergence of theoretical programming as an independent discipline. The principal goals in this book are to explain the line of thought that was followed in solving these problems, demonstrate the workings of the mathematical way of thinking, carefully analyze the different stages of descriptive analysis and problem formulation, and reveal the aesthetic component in the search for solutions - in other words, to try to turn the reader into a true witness of the process of discovering...