Students should achieve an advanced mastery of the topics listed in the minimal learning outcomes section of the Math 571 Wiki page. This means that they should know all relevant definitions, correct statements and proofs of the major theorems (including their hypotheses and limitations), and examples and non-examples of the various concepts. The students should be able to demonstrate their mastery by solving difficult problems related to this content, and by proving theorems about these important concepts, even if the theorems go beyond the material in the text.

1. Group Theory
2. Ring Theory
3. Module Theory