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Abstract Algebra for Polynomial Operations by Maya Mohsin Ahmed



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About this book :-
The focus of this book is applications of Abstract Algebra to polynomial systems. It explores basic problems like polynomial division, solving systems of polynomials, formulas for roots of polynomials. The first five chapters explore basic problems like polynomial division, solving systems of polynomials, formulas for roots of polynomials, and counting integral roots of equations. The sixth chapter uses the concepts developed in the book to explore coding theory and other applications.

Book Detail :-
This book has following details information.
Title: Abstract Algebra for Polynomial Operations by Maya Mohsin Ahmed by NA
Publisher: Maya Mohsin Ahmed
Series: eBooksDirectory
Year: 2009
Pages: 210
Type: PDF
Language: English
ISBN-10 #: N\A
ISBN-13 #: N\A
Country: Pakistan
License: N\A
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About Author :-
The author NA NA

Book Contents :-
conver the following topics.
1. Polynomial Division 1.1 Rings and Fields 1.2 Polynomial division 1.3 Gr¨obner bases 2. Solving Systems of Polynomial Equations 2.1 Ideals and Varieties 2.2 Elimination Theory 2.3 Resultants 3. Finding Roots of polynomials in Extension Fields 3.1 Modular Arithmetic and Polynomial irreducibility in Q 3.2 Field Extensions 3.3 Quotient Rings 3.4 Splitting fields of polynomials 4. Formulas to find roots of polynomials 4.1 Groups 4.2 Cyclic groups 4.3 Normal Subgroups and Quotient Groups 4.4 Basic properties of finite groups 4.5 Finite Abelian Groups 4.6 Galois theory 4.7 Proof of Galois’ Criterion for solvability 5. Constructing and Enumerating integral roots of systems of polynomials 5.1 Magic Squares 5.2 Polyhedral con

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