Lipson's book is the first I found that combined an introduction to modern, abstract algebra with chapters that apply these abstractions in an actual computing context. Though this is not necessarily the book for those wishing to get the deepest possible understanding of abstract algebra, it is the perfect introduction for those wishing to understand enough to apply the concepts in a computational setting.Perhaps the only really disappointing aspect of this book is that it's out of print, and that no second edition seems to have been written. A shame, given that many of the concepts described within are now the foundation of probabilistic algorithms and encryption schemes, none of which are discussed. Still, what is presented makes an excellent foundation for understanding the what's and why's of these more recent applications.
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