For the final exam you need to study the material that is included  for Test 1, Test 2 and Test 3 PLUS:

• The statement of the Fundamental Theorem of Galois Theory.
• Be able to find the Galois groups and structure of the lattice of intermediate fields, exhibiting the Galois correspondence,  for examples similar to those worked out in class.
• The definition of normal extension as a separable extension that is a splitting field (i.e., a splitting field of separable polynomials) and its importance to the Galois correspondence.
• Extension by radicals.
• Solvable groups.
• Understand how the Galois correspondence relates to the insolvability of the general quintic.

This last material will comprise about 50% of the test, for a total of 100 points. 

Good Luck. If you have questions ask in class, see me or send me e-mail at ebarbut@uidaho.edu.