Algebra II

Third Degree Equation (Discriminant). Construction With Straight-Edge And Compass. Splitting Field And Galois Group of a Polynomial. Fundamental Theorem of Galois Theory. Symmetric Functions. Cyclotomic Extensions. Solvable Groups. Solvability By Radicals. Transcendental Extensions. Transcendence Base and Degree. Pure Transcendental Extensions, Luröth’s Theorem. Separating Bases.

References:
ARTIN, M. – Algebra. Prentice-Hall, New Jersey, 1991.
ENDLER, O. – Teoria dos Corpos, Rio de Janeiro, (Monografias de Matemática, n° 44), IMPA, 1987.
LANG, S. – Algebra. Reading, Mass., Addison-Wesley, 1965.
VAN DER WAERDEN, B. L. – Álgebra Moderna. Vol. 1, Lisboa, Sociedade Portuguesa de Matemática, 1948.

* Standard program. The teacher has the autonomy to make any changes.