TY  - BOOK
AU  - Soundararajan, Kannan
TI  - Finite fields, with applications to combinatorics
T2  - Student mathematical library,
SN  - 9789349750357
U1  - 512.624 
PY  - 2025///
CY  - India
PB  - Universities Press
KW  - Finite fields (Algebra)
KW  - Combinatorial analysis
KW  - Number theory
KW  - Combinatorics
KW  - Field theory and polynomials
KW  - Elementary number theory
KW  - Congruences
KW  - Factorization
N1  - Includes bibliographical references and index; Readership: Undergraduate students interested in finite fields and combinatorics
N2  - This 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
UR  - https://www.ams.org/bookstore/pspdf/stml-99-toc.pdf?_gl=1*1khgh4w*_ga*NzkyMDE0ODczLjE3NTAwNDYzMjU.*_ga_26G4XFTR63*czE3NTAyMTk3MDQkbzMkZzEkdDE3NTAyMTk3NTckajckbDAkaDA.
UR  - https://www.goodreads.com/book/show/122889858-finite-fields-with-applications-to-combinatorics?from_search=true&from_srp=true&qid=A0MPKmKz6r&rank=1#CommunityReviews
ER  -