epdf.pub_the-nuts-and-bolts-of-proofs-third-edition-an-intr

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Preface
The purpose of this book is to help the reader to gain a better understanding
of the basic logic of mathematical proofs and to become famihar
with some of the basic steps needed to construct proofs. Thus, the mathematical
statements to be proved have been kept simple with these goals in
mind. It is just Hke learning where the chords are, before being able to play a
nice piece of music!
I would Hke to thank all my students who keep teaching me that there
is always one more way to look at things and one more way to explain
something.
I would Uke to thank the following reviewers for their insight and
suggestions: Rob Beezer, University of Puget Sound; Andy Miller,
University of Oklahoma; David Vella, Skidmore College; and Maria
Girardi, University of South Carolina.
To the Reader
The solutions for all the exercises in this book (except for those in the section
"Exercises without Solutions") can be found in the back of the book. These
solutions should only be used as a guide. Indeed learning to construct proofs
is Hke learning to play tennis. It is useful to have someone teaching us the
basics, and it is useful to look at someone playing, but we need to get into the
court and play, if we really want to learn.
Therefore we suggest that you, the reader, set aside a minimum time limit
for yourself to construct a proof without looking at the solution (as a
starting point, you could give yourself one hour, and then adjust this limit to
fit your abihty). If you do not succeed, read only the first few Hnes of the
proof presented here, and then try again to complete the proof on your own.
If you are not able to do so, read a few more Hnes and try once more. If you
need to read the whole proof, make sure that you understand it, and after a
few days, try the exercises again on your own.
Be aware of the fact that in several cases it is possible to construct proofs
different from the ones presented in the solutions.
Exercises with the symbol (*) require knowledge of calculus and/or Hnear
algebra.