This book is about algebra. This is a very old science and its gems have
lost their charm for us through everyday use. We have tried in this book
to refresh them for you. The main part of the book is made up of
problems. The best way to deal with them is: Solve the problem by
yourself - compare your solution with the solution in the book (if it
exists) - go to the next problem. However, if you have difficulties
solving a problem (and some of them are quite difficult), you may read
the hint or start to read the solution. If there is no solution in the
book for some problem, you may skip it (it is not heavily used in the
sequel) and return to it later. The book is divided into sections
devoted to different topics. Some of them are very short, others are
rather long. Of course, you know arithmetic pretty well. However, we
shall go through it once more, starting with easy things. 2 Exchange of
terms in addition Let's add 3 and 5: 3+5=8. And now change the order:
5+3=8. We get the same result. Adding three apples to five apples is the
same as adding five apples to three - apples do not disappear and we get
eight of them in both cases. 3 Exchange of terms in multiplication
Multiplication has a similar property. But let us first agree on
notation.
