Finite fields, with applications to combinatorics
Soundararajan, Kannan
Finite fields, with applications to combinatorics - India : Universities Press, 2025. - xii, 170p. : ill. ; 22 cm. - Student mathematical library, v. 99 1520-9121 ; .
Includes bibliographical references and index.
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.
Readership: Undergraduate students interested in finite fields and combinatorics.
9789349750357
Finite fields (Algebra)
Combinatorial analysis
Number theory
Combinatorics
Field theory and polynomials
Elementary number theory--Congruences
Elementary number theory--Factorization
512.624 / SOU-F
Finite fields, with applications to combinatorics - India : Universities Press, 2025. - xii, 170p. : ill. ; 22 cm. - Student mathematical library, v. 99 1520-9121 ; .
Includes bibliographical references and index.
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.
Readership: Undergraduate students interested in finite fields and combinatorics.
9789349750357
Finite fields (Algebra)
Combinatorial analysis
Number theory
Combinatorics
Field theory and polynomials
Elementary number theory--Congruences
Elementary number theory--Factorization
512.624 / SOU-F
