To get Ph.D. in UCB math dept, all graduate students have to take and pass two language exams among French, German and Russian. I took French exam ten days ago with two days of intensive (?) preparation and I passed it. Although I do not know either German or Russian at all, I am in favor of German a little more (since Russian alphabets seems too intimidating).
Now I am planning to take my qualifying exam next semester and for that I collected some past qual syllabus of other grad students with the aid of my secretary Google. I have to find three math dept faculty and one outside faculty. The Qual syllabus which I need to make by myself consists of two major topics and one minor topics. Here are my options:
Lie algebras and Lie groups
Representation of Finite Groups
algbraic number theory
To choose what makes me pass the qual easily, or to choose what makes me study a lot : that is the question.