This is a book about mathematics
appreciation via discovery, rather than about practical mathematics. It
considers several problems that don't appear to be amenable to ordinary
arithmetic, algebraic or geometric techniques. It then guides the reader
through the process of discovering the solution to each problem, using
creative methods and simple techniques that arise naturally. It also
indicates how each solution leads to new questions, provides a bit of
history of the problem, and discusses a few related problems of current
interest that have not yet been solved.
" I often wondered what math was all about 
whether there was more math to be discovered 
and if so, how can mathematicians discover more math 
Even with my
minimal math background, I found my curiosity and my participation in
the discovery process enough for me to get a good sense of the answers
to my questions  and an appreciation of the beauty of math"
 anonymous student evaluation of a course based on the material in this book.
The
book contains numerous examples, illustrations, problems and projects
that advance the discovery process. There is an extensive section at the
end of each chapter that gives answers to the problems posed in the
chapter, as well as an additional section that provides supplementary
material.
Each topic is divided into many short sections. The Table of Contents shows the topics covered, and lists the titles of the sections and subsections. More about the goals and use of the book can be found in the Preface.
The
book comes in two versions  one with more than one hundred full color
illustrations, and a less expensive edition with black and white
illustrations.
Mathematical Discovery
COLOR EDITION
by Andrew M. Bruckner, Brian S. Thomson, Judith B. Bruckner
266 pages, 4 Chapters, 2 Appendices, Bibliography and Index
ISBN10: 1463730578
ISBN13: 9781463730574 (CreateSpaceAssigned)
BISAC: Mathematics/ General
List Price: $39.39
Mathematical Discovery
Black/White Edition
by Andrew M. Bruckner, Brian S. Thomson, Judith B. Bruckner
266 pages, 4 Chapters, 2 Appendices, Bibliography and Index
ISBN10: 1453892923
ISBN13: 9781453892923(CreateSpaceAssigned)
BISAC: Mathematics/ General
© A.M .Bruckner, J.B. Bruckner, and B.S.Thomson (2012).

