Description

Book Synopsis
Uses finite field theory as a hook to introduce the reader to a range of ideas from algebra and number theory. The book constructs all finite fields from scratch and shows that they are unique up to isomorphism.

Table of Contents
  • Primes and factorization
  • Primes in the integers
  • Congruences in rings
  • Primes in polynomial rings: Constructing finite fields
  • The additive and multiplicative structures of finite fields
  • Understanding the structures of $\mathbb{Z}/n\mathbb{Z}$
  • Combinatorial applications of finite fields
  • The AKS primality test
  • Synopsis of finite fields
  • Bibliography
  • Index

Finite Fields with Applications to Combinatorics

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    £999.99

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    A Paperback by Kannan Soundararajan

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      View other formats and editions of Finite Fields with Applications to Combinatorics by Kannan Soundararajan

      Publisher: MP-AMM American Mathematical
      Publication Date: 2/18/2023 12:00:00 AM
      ISBN13: 9781470469306, 978-1470469306
      ISBN10: 1470469308

      Description

      Book Synopsis
      Uses finite field theory as a hook to introduce the reader to a range of ideas from algebra and number theory. The book constructs all finite fields from scratch and shows that they are unique up to isomorphism.

      Table of Contents
      • Primes and factorization
      • Primes in the integers
      • Congruences in rings
      • Primes in polynomial rings: Constructing finite fields
      • The additive and multiplicative structures of finite fields
      • Understanding the structures of $\mathbb{Z}/n\mathbb{Z}$
      • Combinatorial applications of finite fields
      • The AKS primality test
      • Synopsis of finite fields
      • Bibliography
      • Index

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