This week's book giveaway is in the OO, Patterns, UML and Refactoring forum. We're giving away four copies of Refactoring for Software Design Smells: Managing Technical Debt and have Girish Suryanarayana, Ganesh Samarthyam & Tushar Sharma on-line! See this thread for details.
I don't know what the "unicode library" is, but the String and Character classes have toUpperCase() methods that you can use.
As for the arithmetic your prof is talking about, every character has a corresponding number (actually is a number, just interpreted a special way), and you can do math on those numerical values. And the numbers go in the same order as the letters, and increase by one with eacn subsequent letter, which is convenient sometimes, but shouldn't be relied on in an OO context, or when we might have to deal with more than just A-Z and a-z.
So, for instance, since 'G' comes 3 positions after 'D', we get 'G' - 'D' == 3. 'D' is 68 and G is 71, but those specific values don't matter here.
So, given that we have numbers for 'A'..'Z' and numbers for 'a'..'z', and even without knowing anything about what those numbers are or where the lowercase ones are in relation to the uppercase ones, it's just simple arithmetic to turn any lowercase to its corresponding uppercase, or vice-versa. I'll leave you to work out that last bit for yourself.