Thread: Which preposition?

I want to say: "Я сдал экзамен по функциональному анализу".
I've passed the exam <???> functional analysis.

I passed the exam in functional analysis.

I passed the exam on Functional Analysis.

BTW, what is Functional Analysis?

I passed the exam OF Functional Analysis

I passed the exam IN funtional analysis (the class).

I passed the exam ON functional analysis (topic itself).

What is functional analysis?

http://www.google.com/search?hl=en&lr=& ... l+Analysis

I would have said "I passed the Functional Analysis exam."

I am not sure about the rules for capital letters but I think that classes should have capital letters.
Anyway, here are some more examples:

I passed the exam in History.

I passed the exam on history. (this sounds a bit strange)

I passed the exam on history of the world.

I passed the exam in History of the World.

I passed the exam about the history of the world.

Thank you all! How many different variants Does "in" preposition correct in all cases?

What is functional analysis?

http://www.google.com/search?hl=en&lr=& ... l+Analysis

See the last definition:

Functional analysis is that branch of mathematics and specifically of analysis which is concerned with the study of spaces of functions. It has its historical roots in the study of transformations such as the Fourier transform and in the study of differential and integral equations. The word 'functional' goes back to the calculus of variations, implying a function whose argument is a function. Its use in general has been attributed to Volterra.

I think that "in" seems the best here.