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Viser: Algebra - Polynomials, Galois Theory, and Applications

Algebra: Polynomials, Galois Theory and Applications
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Algebra: Polynomials, Galois Theory and Applications Vital Source e-bog

Frédéric Butin
(2017)
Dover Publications
398,00 kr.
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Algebra - Polynomials, Galois Theory, and Applications

Algebra

Polynomials, Galois Theory, and Applications
édéric Butin
(2017)
Sprog: Engelsk
Dover Publications, Incorporated
345,00 kr.
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Detaljer om varen

  • Vital Source searchable e-book (Reflowable pages)
  • Udgiver: Dover Publications (Januar 2017)
  • ISBN: 9780486818849
Suitable for advanced undergraduates and graduate students in mathematics and computer science, this precise, self-contained treatment of Galois theory features detailed proofs and complete solutions to exercises. Originally published in French as Algèbre — Polynômes, théorie de Galois et applications informatiques, this 2017 Dover Aurora edition marks the volume's first English-language publication. The three-part treatment begins by providing the essential introduction to Galois theory. The second part is devoted to the algebraic, normal, and separable Galois extensions that constitute the center of the theory and examines abelian, cyclic, cyclotomic, and radical extensions. This section enables readers to acquire a comprehensive understanding of the Galois group of a polynomial. The third part deals with applications of Galois theory, including excellent discussions of several important real-world applications of these ideas, including cryptography and error-control coding theory. Symbolic computation via the Maple computer algebra system is incorporated throughout the text (though other software of symbolic computation could be used as well), along with a large number of very interesting exercises with full solutions.
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Detaljer om varen

  • Paperback: 288 sider
  • Udgiver: Dover Publications, Incorporated (Marts 2017)
  • ISBN: 9780486810157
Suitable for advanced undergraduates and graduate students in mathematics and computer science, this precise, self-contained treatment of Galois theory features detailed proofs and complete solutions to exercises. This 2017 Dover Aurora edition marks the volume's first English-language publication. The three-part treatment begins by providing the essential introduction to Galois theory. The second part is devoted to the algebraic, normal, and separable Galois extensions that constitute the centre of the theory and examines abelian, cyclic, cyclotomic, and radical extensions. This section enables readers to acquire a comprehensive understanding of the Galois group of a polynomial. The third part deals with applications of Galois theory, including excellent discussions of several important real-world applications of these ideas, including cryptography and error-control coding theory. Symbolic computation via the Maple computer algebra system is incorporated throughout the text (though other software of symbolic computation could be used as well), along with a large number of very interesting exercises with full solutions.
I. Arithmetic, rings and polynomials
1. Arithmetic and the symmetric group
2. Rings and polynomials II. Galois theory
3. Algebraic extensions
4. Normal extensions and separable extensions
5. Galois theory
6. Abelian, cyclic, cyclotomic, radical extensions
7. Galois group of a polynomial III. Applications
8. Ruler and compass constructions
9. Finite fields and applications
10. Norm, trace and algebraic integers Biography of quoted mathematicians Index References About the Author
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