. Not only does this book show you how to solve these problem, it also explains why the solution works, which enables you to apply that solution to other problems that may crop up. Put another way, this book doesn't just show you how to solve problems; it teaches you how to think in order to solve problems.
. In other words, these techniques will do a lot for you, but they will not perform miracles. Shuffling money cannot turn losses into profits. You must have a winning approach to start with.
. It is written mainly for students with a limited experience in mathematics, but determined to study the subject actively. The material is presented in a concise form, proofs are omitted.
s. Thirty-exercises develop familiarity with the definitions and consolidate understanding of the main proof techniques.
. Some are chosen for their value in other areas of mathematics: Ramsey's Theorem, the Tarski-Seidenberg Theorem.
We discuss the properties of p-adic analogues of the logistic and Smale horseshoe maps, and adapt them to form possible practical pseudo-random number generators. The properties of these practical modifications are studied in detail in the case P = 2.
. Further explanations have been included and, on occasion, the appropriate terminology to support them.

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