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Matrices, vectors, vector spaces, transformations. Covers all topics in a first year college linear algebra course. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.
5 important algorithms everyone should know « under a glass moon
1. Merge Sort - O(nlogn) (where n is the input size) Of course we need to include a sorting algorithm in this list, but why Merge Sort? Why not any of the other comparison based sorting algorithms all of which run in O(nlogn)? The reason is that Merge Sort is probably the most simplest implementation of a “divide and conquer” algorithm out there.Given an array of 9 values representing a Tic Tac Toe game (or Noughts and Crosses, depending on where you're from) where the values are -1, 0 or 1, figure out who, if anyone, has won. Yes, I realize these are very simple and we could all knock them off very quickly, but I'm not testing for the end product and I don't want them sitting down for two hours trying to nut out something complicated. I want to see the process followed to arrive at a result (so I get them to white-board the entire thing, explaining as they go). It's more to see if they have problem solving ability. That's far more important than knowing the algorithms off the top of their head. I really don't care if they can code up a bubble sort (it's a crappy sort algorithm for large data sets anyway and, if you need some sort code, you'll be using something built in to the language, pulled out of Wikipedia or found with Google, not writing your own - I'm not going to be happy paying you to re-invent the wheel).
