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At my university there is a debate about whether it is better to require students to have taken a class in Galois theory or to require a class in representation theory for admission into the graduate program. Currently, Galois theory is required for admission and rep theory is not. Many of the professors have argued that representation theory has a broader application and hence should be preferred over Galois theory on admissions applications. There are of course important links between the two topics, so I wanted to see what people at other universities have found to be more helpful in graduate school.

At my university, we teach Galois theory out of Dummit and Foote or a book by Ian Stewart. We teach rep theory out of a book by Martin Liebeck and Gordon James (If you are familiar with those texts).

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closed as primarily opinion-based by rschwieb, Nick Peterson, user63181, Dan Rust, Grigory M Jan 6 '14 at 21:40

Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ Why not require students to have taken a class in Galois theory or a class in representation theory? $\endgroup$ – Magdiragdag Jan 6 '14 at 20:23
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    $\begingroup$ The closest thing I can see to a question here is so I wanted to see what people at other universities have found to be more helpful in graduate school. Is this correct? Questions like "what do you think is more useful" are a little too subjective. You might toss it into the main chatroom though. $\endgroup$ – rschwieb Jan 6 '14 at 20:24
  • $\begingroup$ Yes, To clarify: I want to pick up some comments on what people have found to be more helpful in their graduate level research/classwork, Galois or Rep theory. $\endgroup$ – Vladhagen Jan 6 '14 at 20:27