Galois theory and applications : solved exercises and problems

The book provides exercises and problems with solutions in Galois Theory and its applications, which include finite fields, permutation polynomials, derivations and algebraic number theory. It will be useful to the audience below: Students who want to learn the material around the arithmetic of polynomials and field extensions. Teachers who want to work on problems with their students. Researchers who require a reference book. The book contains some useful results generally known by specialists, but for which a detailed proof is not always in the literature. Contents Preface 1. Polynomials, Fields, Generalities 2. Algebraic extension, Algebraic closure 3. Separability, Inseparability 4. Normal extensions 5. Galois extensions, Galois groups 6. Finite fields 7. Permutation polynomials 8. Transcendental extensions, Linearly disjoint extensions, Luroth's theorem 9. Multivariate polynomials 10. Integral elements, Algebraic number theory 11. Derivations Notations Bibliography