Self Study Galois Theory
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:
JS Milne Galois theory notes: https://jmilne.org/math/CourseNotes/f...
Thomas Judson textbook: https://abstract.ups.edu/aata/aata.html
Herstein textbook: https://amazon.com/exec/obidos/ASIN/0...
Ben1994 Field Theory: • Field theory
Example Syllabus:
Do Milne exercises last, they will be the hardest.
Textbooks:
https://www.jmilne.org/math/CourseNot...
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)
3. Read 30 - 37 and do exercises 2-1, 2-3, and 2-6 from Milne (p. 33) and exercises 22, 23, and 25 from abstract.ups.edu (chapter 21)
4. Read 37 - 45, end of chapter 3, and do 1, 2, 3, 8, 9, and 10 from abstract.ups.edu (chapter 23) and 3-1 from Milne (p. 45)
5. Read 45 - 52 (stops before finite fields) and do 18 and 19 from abstract.ups.edu (chapter 23) and 3-3, 3-4, and 3-5 from Milne (p. 45) and 4-4 from Milne (p. 57)
6. Read 52 - 62 and do 4-1, 4-5 [can be liberal changing the wording; the point is to characterize the polynomials well], and 4-8 [could be hard, try reading the paper] from Milne (p. 57) and 20 from abstract.ups.edu (chapter 23) and 16, 19, 20, 21, 22, 23 from abstract.ups.edu (chapter 22)
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.