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The present textbook is a lively, problem-oriented and carefully written introduction to classical modern algebra. The author leads the reader through interesting subject matter, while assuming only the background provided by a first course in linear algebra. The first volume focuses on field extensions. Galois theory and its applications are treated more thoroughly than in most texts. It also covers basic applications to number theory, ring extensions and algebraic geometry. The main focus of the second volume is on additional structure of fields and related topics. Much material not usually covered in textbooks appears here, including real fields and quadratic forms, the Tsen rank of a field, the calculus of Witt vectors, the Schur group of a field, and local class field theory. Both volumes contain numerous exercises and can be used as a textbook for advanced undergraduate students. From Reviews of the German version: This is a charming textbook, introducing the reader to the classical parts of algebra. The exposition is admirably clear and lucidly written with only minimal prerequisites from linear algebra. The new concepts are, at least in the first part of the book, defined in the framework of the development of carefully selected problems. - Stefan Porubsky, Mathematical Reviews.

Algebra --- Algebraic fields --- Galois theory --- Equations, Theory of --- Group theory --- Number theory --- Algebraic number fields --- Algebraic numbers --- Fields, Algebraic --- Algebra, Abstract --- Algebraic number theory --- Rings (Algebra) --- Algebra. --- Field theory (Physics). --- Matrix theory. --- Number theory. --- Commutative Rings and Algebras. --- Field Theory and Polynomials. --- Linear and Multilinear Algebras, Matrix Theory. --- Number Theory. --- Number study --- Numbers, Theory of --- Classical field theory --- Continuum physics --- Physics --- Continuum mechanics --- Mathematics --- Mathematical analysis --- Commutative algebra. --- Commutative rings. --- Field theory (Physics)

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Number theory --- Ordered algebraic structures --- Algebra --- Classical mechanics. Field theory --- algebra --- matrices --- mechanica --- getallenleer

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• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The present textbook is a lively, problem-oriented and carefully written introduction to classical modern algebra. The author leads the reader through interesting subject matter, while assuming only the background provided by a first course in linear algebra. The first volume focuses on field extensions. Galois theory and its applications are treated more thoroughly than in most texts. It also covers basic applications to number theory, ring extensions and algebraic geometry. The main focus of the second volume is on additional structure of fields and related topics. Much material not usually covered in textbooks appears here, including real fields and quadratic forms, diophantine dimensions of a field, the calculus of Witt vectors, the Schur group of a field, and local class field theory. Both volumes contain numerous exercises and can be used as a textbook for advanced undergraduate students. From Reviews of the German version: This is a charming textbook, introducing the reader to the classical parts of algebra. The exposition is admirably clear and lucidly written with only minimal prerequisites from linear algebra. The new concepts are, at least in the first part of the book, defined in the framework of the development of carefully selected problems. - Stefan Porubsky, Mathematical Reviews.

Algebra --- Algebraic fields --- Galois theory --- Algebra. --- Field theory (Physics). --- Number theory. --- Field Theory and Polynomials. --- Commutative Rings and Algebras. --- Number Theory. --- Number study --- Numbers, Theory of --- Classical field theory --- Continuum physics --- Physics --- Continuum mechanics --- Mathematics --- Mathematical analysis --- Field theory (Physics) --- Commutative algebra. --- Commutative rings. --- Rings (Algebra) --- Algebra - Textbooks --- Algebraic fields - Textbooks --- Galois theory - Textbooks --- Algebra - Problems, exercises, etc