Section: Other texts (not required for the course) | Galois theory HT24

Section outline

Here are some other texts, either directly about Galois theory, or about its relationship with other subjects, such as algebraic topology, number theory and/or algebraic geometry. These texts are mostly for those of you who are curious to explore beyond the course itself. These texts are not required and should not scare anyone.
- Select activity Undergraduate Algebra by S. Lang
  
  Undergraduate Algebra by S. Lang URL
  
  Slightly more elementary text which covers less material than Dummit & Foote, but covers a substantial part of the course, often using slightly different arguments. For example, I like that Lang puts a stronger emphasis on embeddings than Dummit & Foote, see section VII.2. Also VIII.6 "Where does it all go?" is a nice exposition/motivation for how Galois theory leads to current research in the Langlands Program. (If the link does not work directly, then go to https://link-springer-com.ezp.sub.su.se/, use your SU login and then search for Lang Undergraduate Algebra and you will be able to download the book for free via SU access)
- Select activity Exploratory Galois theory by J. Swallow
  
  Exploratory Galois theory by J. Swallow URL
  
  Another introduction to Galois theory, seems roughly at the same level as Dummit & Foote, maybe some more examples to consider.
- Select activity Algebra and Galois Theories by R. Douady and A. Douady
  
  Algebra and Galois Theories by R. Douady and A. Douady URL
  
  Tries to present simultaneously the Galois theory of field extensions and the analogous theory of covering spaces in topology.
  You might need to go to https://link-springer-com.ezp.sub.su.se/ first, login, and then search for "Douady Galois theories"
- Select activity Idees Galoisiennes by Y. Andre
  
  Idees Galoisiennes by Y. Andre File
  
  Expository article in French about the history of Galois theory and its role in the development of modern mathematics. If there is sufficient demand I will consider translating it.
- Select activity Galois groups and fundamental groups by T. Szamuely
  
  Galois groups and fundamental groups by T. Szamuely URL
  
  A more advanced text about the analogy and common thread between Galois groups and fundamental groups; this one involves more algebraic geometry and less topology.
  You might need to go to https://mathscinet-ams-org.ezp.sub.su.se/ first, use your SU login, then search for Author = Szamuely and Title = Galois fundamental
- Select activity Algebraic theory of numbers by P. Samuel
  
  Algebraic theory of numbers by P. Samuel URL
  
  Does not seem to be available online via SU login (I'm told you can find it online if you look a bit harder)
  Chapter 6 gives a concise introduction to how Galois theory enters in the arithmetic theory of algebraic numbers, via the decomposition and inertia subgroups of the Galois group, and how this is related to the splitting of primes in extensions.