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Self Study Galois Theory
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Do you want to study Galois theory, but you can't take a regular class? Here is self study guide based on the resources I found most helpful when I independently studied Galois theory. If you haven't already, check out my video called "Self Study Strategies for Math" so you know how to turn the resources from this video into a successful self study.
Links:
Example Syllabus:
Do Milne exercises last, they will be the hardest.
Textbooks:
Abstract Algebra: Theory and Applications
Abstract Algebra by I. N. Herstein
Weeks:
1. Read 1 - 20 from Milne (stops before Constructions) and do exercises 1, 8 from Herstein 5.3 (p. 230 and 231) and 5 and 7 from Herstein 5.4 (p. 234) and 1-1, 1-2, and 1-3 from Milne (p. 25)
2. Read 20 - 30 and do exercises 1-4 and 1-6 from Milne (p. 25) and 6, 7, 8, 9, and 14 from Herstein 5.6 (p. 249)
Topics covered:
fields, polynomial rings, extension fields, algebraic and transcendental numbers, constructions with straight-edge and compass, splitting fields, Galois groups, fundamental theorem of Galois Theory, computing Galois groups, insolubility of the quintic
Description:
This is a follow-on course to 18.703 to add elements of Galois Theory into the structure of 18.703. It takes a more traditional approach to Galois Theory than 18.702.
Links:
Example Syllabus:
Do Milne exercises last, they will be the hardest.
Textbooks:
Abstract Algebra: Theory and Applications
Abstract Algebra by I. N. Herstein
Weeks:
1. Read 1 - 20 from Milne (stops before Constructions) and do exercises 1, 8 from Herstein 5.3 (p. 230 and 231) and 5 and 7 from Herstein 5.4 (p. 234) and 1-1, 1-2, and 1-3 from Milne (p. 25)
2. Read 20 - 30 and do exercises 1-4 and 1-6 from Milne (p. 25) and 6, 7, 8, 9, and 14 from Herstein 5.6 (p. 249)
Topics covered:
fields, polynomial rings, extension fields, algebraic and transcendental numbers, constructions with straight-edge and compass, splitting fields, Galois groups, fundamental theorem of Galois Theory, computing Galois groups, insolubility of the quintic
Description:
This is a follow-on course to 18.703 to add elements of Galois Theory into the structure of 18.703. It takes a more traditional approach to Galois Theory than 18.702.
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