000			a
999			_c33610 _d33610
008			250317b xxu||||| |||| 00| 0 eng d
020			_a9781470469306
082			_a512.74 _bSOU
100			_aSoundararajan, Kannan
245			_aFinite fields, with applications to combinatorics
260			_bAmerican Mathematical Society, _c2022 _aProvidence :
300			_axii, 170 p. ; _bill., _c22 cm
365			_b59.00 _c$ _d90.60
490			_aStudent mathematical library ; _vv.99
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.
650			_aCombinatorial analysis
650			_aBertrand's postulate
650			_aCyclic group
650			_aEuclidean domain
650			_aGaussian integers
650			_aGeneral field theory
650			_aIntegral domain
650			_aPolynomial ring
650			_aQuotient ring
650			_aSidon set
942			_2ddc _cBK