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Number Theory and Algebra by Victor Shoup
Number theory and algebra play an increasingly significant role in computing and communications, as evidenced by the striking applications of these subjects to such fields as cryptography and coding theory. My goal in writing this book was to provide an introduction to number theory and algebra, with an emphasis on algorithms and applications, that would be accessible to a broad audience. In particular, I wanted to write a book that would be accessible to typical students in computer science or mathematics who have a some amount of general mathematical experience, but without presuming too much specific mathematical knowledge.