The Art and Craft of Problem Solving!

Preface to the Fi rst Ed ition
Why This Book?
This is a book about mathematical problem solving for college-level novices. By this
I mean bright people who know some mathematics (ideally, at least some calculus),
who enjoy mathematics, who have at least a vague notion of proof, but who have spent
most of their time doing exercises rather than problems.
An exercise is a question that tests the student 's mastery of a narrowly focused





technique, usually one that was recently "covered." Exercises may be hard or easy, but
they are never puzzling, for it is always immediately clear how to proceed. Getting
the solution may involve hairy technical work, but the path towards solution is always
apparent. In contrast, a problem is a question that cannot be answered immediately.
Problems are often open-ended, paradoxical, and sometimes unsolvable, and require
investigation before one can come close to a solution. Problems and problem solving
are at the heart of mathematics. Research mathematicians do nothing but open-ended
problem solving. In industry, being able to solve a poorly defined problem is much
more important to an employer than being able to, say, invert a matrix. A computer
can do the latter, but not the former.
Link Download ↓
Download