Books
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My lecture notes will be on sale in the front office, and are available
from the preceding weblink. Other books include:
IT Adamson, Introduction to Field Theory, Oliver and Boyd.
E Artin, Galois Theory, University of Notre Dame.
DJH Garling, A course in Galois theory, CUP.
IN Stewart, Galois Theory, Chapman and Hall.
BL van der Waerden, Algebra (or Modern algebra), vol.~1
S Lang, Algebra, Springer
IR Shafarevich, Basic notions of algebra, Springer (strongly recommended
as an extended essay in philosophical terms on the meaning of algebra --
but it won't help much for the exam)
J-P Tignol, Galois' theory of algebraic equations, World scientific
(historically aware treatment of all the main issues)