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Following up on the discussion at the end of the last meet-up, I wanted to suggest working through the following book on functional data structures:
http://www.amazon.com/Purely-Functional-Structures-Chris-Okasaki/dp/0521663504
(a pdf of the thesis that this book is based on can be found here: http://www.cs.cmu.edu/~rwh/theses/okasaki.pdf).
The books talks about lots of data structures that are set up to be efficient while still being immutable. It might be a fun and challenging exercise to implement some/all of these in Scala. Apart from exercising the language, I think that many of these data structures might be completely new to many of us.