How Long to Read Infinite Algebraic Extensions of Finite Fields

How Long Does it Take to Read Infinite Algebraic Extensions of Finite Fields?

It takes the average reader 1 hour and 45 minutes to read Infinite Algebraic Extensions of Finite Fields by Joel V. Brawley

Assuming a reading speed of 250 words per minute. Learn more

Description

Over the last several decades there has been a renewed interest in finite field theory, partly as a result of important applications in a number of diverse areas such as electronic communications, coding theory, combinatorics, designs, finite geometries, cryptography, and other portions of discrete mathematics. In addition, a number of recent books have been devoted to the subject. Despite the resurgence in interest, it is not widely known that many results concerning finite fields have natural generalizations to abritrary algebraic extensions of finite fields. The purpose of this book is to describe these generalizations. After an introductory chapter surveying pertinent results about finite fields, the book describes the lattice structure of fields between the finite field $GF(q)$ and its algebraic closure $\Gamma (q)$. The authors introduce a notion, due to Steinitz, of an extended positive integer $N$ which includes each ordinary positive integer $n$ as a special case. With the aid of these Steinitz numbers, the algebraic extensions of $GF(q)$ are represented by symbols of the form $GF(q^N)$. When $N$ is an ordinary integer $n$, this notation agrees with the usual notation $GF(q^n)$ for a dimension $n$ extension of $GF(q)$. The authors then show that many of the finite field results concerning $GF(q^n)$ are also true for $GF(q^N)$. One chapter is devoted to giving explicit algorithms for computing in several of the infinite fields $GF(q^N)$ using the notion of an explicit basis for $GF(q^N)$ over $GF(q)$. Another chapter considers polynomials and polynomial-like functions on $GF(q^N)$ and contains a description of several classes of permutation polynomials, including the $q$-polynomials and the Dickson polynomials. Also included is a brief chapter describing two of many potential applications. Aimed at the level of a beginning graduate student or advanced undergraduate, this book could serve well as a supplementary text for a course in finite field theory.

How long is Infinite Algebraic Extensions of Finite Fields?

Infinite Algebraic Extensions of Finite Fields by Joel V. Brawley is 104 pages long, and a total of 26,416 words.

This makes it 35% the length of the average book. It also has 32% more words than the average book.

How Long Does it Take to Read Infinite Algebraic Extensions of Finite Fields Aloud?

The average oral reading speed is 183 words per minute. This means it takes 2 hours and 24 minutes to read Infinite Algebraic Extensions of Finite Fields aloud.

What Reading Level is Infinite Algebraic Extensions of Finite Fields?

Infinite Algebraic Extensions of Finite Fields is suitable for students ages 10 and up.

Note that there may be other factors that effect this rating besides length that are not factored in on this page. This may include things like complex language or sensitive topics not suitable for students of certain ages.

When deciding what to show young students always use your best judgement and consult a professional.

Where Can I Buy Infinite Algebraic Extensions of Finite Fields?

Infinite Algebraic Extensions of Finite Fields by Joel V. Brawley is sold by several retailers and bookshops. However, Read Time works with Amazon to provide an easier way to purchase books.

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