The basic premise of this book is that understanding difficult abstract concepts is best achieved through illustrative examples and challenging exercises, so problem solving is a central theme of our approach.
Solving a difficult problem normally involves two distinct steps. First we must understand the issues, decide what theorems and results apply, and how to put it all together to arrive at a solution. This tends to be the most difficult part and often requires insight and inventiveness. But once we have a clear understanding of the solution process, a more routine step is still necessary ...
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