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Introduction# Solution of Equations of Third and Fourth Degrees By Radicals. Composite Extensions, Algebraic Extensions, Algebraically Closed Fields, Splitting Field of a Polynomial. Extensions Of Embeddings, Uniqueness of The Root Field and of The Splitting Field of a Polynomial. Uniqueness of Finite Field. Normal Extensions, Separable Extensions, Counting Embeddings. Galois Extensions and Galois Groups. The Theorem of The Primitive Element. The Funfamenral Theorem of Galois Theory. Solvable Groups and Solvability By Radicals. Cyclotomic Extensions, Realization of Abelian Groups As Galois Groups Over The Rational Number Field. Existence of The Algebraic Closure of a Field, And Additional Topics# "constructions With Straightedge And Compass", The Fundamental Theorem On Symmetric Polynomials, Norm, And Trace in Finite Extensions, Separability and Trace Form Kummer Theory.

Faculty: Mathematics
|Undergraduate Studies

Pre-required courses

104279 - Introduction to Rings and Fields

Course with no extra credit

104278

• Abstract algebra - Dummit, David S.
• Abstract algebra - Dummit, David S.
• Algebra - Lang, Serge
• Algebra - Lang, Serge
• Algebra - Lang, Serge.
• Algebra - Waerden, Bartel L. van der
• Algebra with Galois theory - Artin, Emil
• Algebra. - Lang, Serge
• Basic algebra - Jacobson, Nathan
• Basic algebra - Jacobson, Nathan
• Modern algebra - Waerden, Bartel L. van der
• Topics in algebra. - Herstein, I. N.
• Topics in algebra. - Herstein, I. N.