Finite Fields (Encyclopedia of Mathematics and its Applications Book 20)

This really is a must read for any mathematician (professional, amateur, hobbyist) who is interested in cryptography. Finite fields form the basis of modern cryptography, at least as of the writing of this review. It's not a quick or breezy read, though: quite dense and packed with theorems.

An excellent reference for cryptographers, coding theorists, and others whose research relies on the theory of finite fields. Each chapter is written by a leading expert in specializing in the topic being treated. There is a 150+ page bibliography that provides a wealth of articles and other books supporting and expanding on the arguments presented here.The Big Red Book is more than just a reference, though. It makes an excellent introduction to finite fields accessible to anyone with a first year abstract algebra class under their belt (that is, groups, rings, fields, and some galois theory). The writing style is very down to earth and practical, making sparse use of higher level artillery like category theory or topology. The results are often treated as more combinatorial than algebraic, favoring constructive proofs and counting arguments over algebraic geometry.An excellent addition to the bookshelf of any mathematician, grad student, or undergrad with interests in algebra.

This book is an excellent reference on finite fields. Chapter 1 covers the necessary background material at the right level for someone with a good knowledge of mathematics, but little algebra. Chapter 2 covers the basics of finite fields and chapter 3 goes into more detail on polynomials. The later chapters treat special topics and some applications. The proofs are clear, not over detailed and not overly terse either. If you just want to know the basics then there may be more in this book than you will ever need, but if you want a thorough reference it is recommended.

This is the best book on Galois (Finite) Fields, written by Austrian and Australian professors can be recomended as the most complete reference in the field. It is amazing how helpful it has been to me since time I wrote my MS diploma. Though an instance I was using was borrowed from library, I'd recomend everybody, who is related to deescrete math to have one.

Undoubtedly an excellent book, but comprehensive ... only up to 1983, as this is essentially an IDENTICAL reprint by CUP of the original 1983 book by Addison-Wesley. Don't be misled by the 1997 edition date; second edition = first edition, not a single result from 1983 - 1997.