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
Kac-Moody algebras
Representation of Finite Groups
algbraic number theory
elliptic curves
Automorphic Forms
complex analysis
To choose what makes me pass the qual easily, or to choose what makes me study a lot : that is the question.
Félicitations!