Finite Fields: An introduction through exercises
نویسنده
چکیده
A typical course in “abstract algebra” starts with groups, and then moves on to rings, vector spaces, fields, etc. This sequence may give the impression that fields form an advanced and arcane subject. In fact, however, fields are rather simpler than other structures, by virtue of being more constrained. This holds particularly for the case of finite fields, which arise in many areas of computer science. This sequence of exercises will take you through most of the mathematical theory one needs in order to use finite fields.1 Although none of the steps is difficult by itself, we have quite a few details to go through. When you find yourself stuck, short of “aha!” moments, take a break and come back later. (Or phone a friend, or whatever.)
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