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First year computer science students are mainly focused on learning how to program. MIT's first algorithms course, 6.006, is therefore a pretty gentle introduction. It covers
* core concepts of runtime and asymptotic analysis
* divide and conquer
* sorting (merge sort, quicksort)
* searching (balanced binary search trees, hash tables)
* graphs (breadth and depth first search, topological sorting)
* dynamic programming (shortest paths, text justification)
That's really enough for a first year. Our next course, 6.046, dives much deeper.

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