Hello,I am a teacher of Computer Science, from India.

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Books on mathematics which dont teach maths !
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No. I don't mean the kind of books we usually see in our Indian
market. I wish to introduce two useful and very well written books.
All our students (and our teachers) should own and read these two
best-sellers:

How to solve it. G. Polya, Pub.: Prentice Hall of India (Princeton
Univ. Press)

Induction and analogy in mathematics. G. Polya, Princeton University
Press, Princteon, NJ-USA.

George POLYA (1887-1985), an eminent mathematican (of Hungarian
origin), and Professor at Stanford University has given us two jewels,
which will help everyone of us improve our understanding of the hidden
principles of good mathematics. It will help teachers (like me) to
help students (like you) improve their students' ability to solve
problems. It will also help us all appreciate certain poorly
understood concepts which form the basis of mathematical reasoning.
The author is famous for his deft -- indeed brilliant -- approach to
stripping away non-essentials and going straight to the heart of the
problem.

How to solve it -- is an essay on the need to follow a systematic and
oriented approach to solving problems in mathematics. It gives a whole
lot of advise on approaching a mathematically defined problem. This
book is different. Many books on maths give you the solution to
problems. This book tells you how to obtain the solution, on your own.
One such advise is on the need to be able to devise an auxilliary
problem when the main problem seems to be insoluble. Every idea given
in this book, is accompanied by very striking examples. Simple
examples, but ones which drive home the point. In many books on
mathematics, the examples are more difficult to understand than the
concept which the examples are aimed at descibing. The best part of
the book is the last chapter. Here you find real problems which you
can solve using the techniques given earlier. Okay, you are not able
to get the answer in your first try. You are given hints which will
nudge you further. And finally, you are given the answers also, in
detail, so you can see how well you solved the problem. My only
regret, after reading this book was why I did not have teachers like
this, or why I did not get to see this book while I was a student.

Induction and analogy in mathematics -- This is the first volume in a
series on "mathematics and plausible reasoning". Why "induction" and
"analogy" ? These are two important tools out of the tools for
mathematical discovery : generalization, specialization, analogy,
induction. When used correctly, these tools can produce dramatic
results. When used foolishly, these same tools can produce equally
dramatic (but wrong) results. The book starts with a familiar story of
the engineer, logician, mathematician and physicist. This style is
visible throughout the book, as the author effortlessly conveys
several important mathematical principles using simple but convincing
examples. The book gives you many many exercise problems in each
chapter. And, also gives solutions at the end of the book. This book
will enhance the reader's capacity for plausible, and logical
reasoning. If you want to be a good mathematician, or a good engineer,
(or a good teacher), you will profit dramatically by reading this book
thoroughly.

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