Description: Mathematical analysis of a variety of computer algorithms including searching, sorting, matrix multiplication, fast Fourier transform, and graph algorithms. Time and space complexity. Upper-bound, lower- bound, and average-case analysis. Introduction to NP completeness. Some machine computation is required for the implementation and comparison of algorithms.

Preliminaries: Algorithm Correctness, Asymptotic (big-Oh) Notation, Problem Modeling

Data Structures: Review of Elementary Data Structures (stacks/queues), Dictionary Data Structures Such As Binary Search Trees, Priority Queues Such As Heaps

Sorting: Algorithmic Applications of Sorting, Analysis of Quicksort, Mergesort, and Heapsort, Distribution/radix Sorting, Lower Bounds

Problem Decomposition Algorithms: Dynamic Programming (edit Distance, Chain Matrix Multiplication), Divide-and-conquer Algorithms (binary Search and Ariants)

Combinatorial Search: Backtracking, Exhaustive Search, Permutations/subsets

Graph Algorithms: Graph Data Structures (adjacency Lists/arrays), BFS/DFS, Topological Sorting, Connectivity Testing, Minimum Spanning Trees, Shortest Paths (Dijkstra's and Floyd's Algorithms)

Intractability: Problem Reductions, NP-completeness, Approximation Algorithms