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040			_aNISER LIBRARY _beng _cNISER LIBRARY
082			_a512.624 _bSOU-F
100			_aSoundararajan, Kannan
245			_aFinite fields, with applications to combinatorics
260			_aIndia : _bUniversities Press, _c2025.
300			_axii, 170p. : _bill. ; _c22 cm.
490			_aStudent mathematical library, _vv. 99 _x1520-9121 ;
504			_aIncludes bibliographical references and index.
520			_aThis book uses finite field theory as a hook to introduce the reader to a range of ideas from algebra and number theory. It constructs all finite fields from scratch and shows that they are unique up to isomorphism. As a payoff, several combinatorial applications of finite fields are given: Sidon sets and perfect difference sets, de Bruijn sequences and a magic trick of Persi Diaconis, and the polynomial time algorithm for primality testing due to Agrawal, Kayal and Saxena. The book forms the basis for a one term intensive course with students meeting weekly for multiple lectures and a discussion session. Readers can expect to develop familiarity with ideas in algebra (groups, rings and fields), and elementary number theory, which would help with later classes where these are developed in greater detail. And they will enjoy seeing the AKS primality test application tying together the many disparate topics from the book. The pre-requisites for reading this book are minimal: familiarity with proof writing, some linear algebra, and one variable calculus is assumed. This book is aimed at incoming undergraduate students with a strong interest in mathematics or computer science.
521			_aReadership: Undergraduate students interested in finite fields and combinatorics.
650			_aFinite fields (Algebra)
650			_aCombinatorial analysis
650			_aNumber theory
650			_aCombinatorics
650			_aField theory and polynomials
650			_aElementary number theory _xCongruences
650			_aElementary number theory _xFactorization
856			_3Table of Contents _uhttps://www.ams.org/bookstore/pspdf/stml-99-toc.pdf?_gl=1*1khgh4w*_ga*NzkyMDE0ODczLjE3NTAwNDYzMjU.*_ga_26G4XFTR63*czE3NTAyMTk3MDQkbzMkZzEkdDE3NTAyMTk3NTckajckbDAkaDA.
856			_3Reviews _uhttps://www.goodreads.com/book/show/122889858-finite-fields-with-applications-to-combinatorics?from_search=true&from_srp=true&qid=A0MPKmKz6r&rank=1#CommunityReviews
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