Annotated Algorithms in Python: with applications in physics, biology, and finance

Abstract

This book is assembled from lectures given by the author over a period of10years at the School of Computing of DePaul University. The lecturescover multiple classes, including Analysis and Design of Algorithms, Sci-entific Computing, Monte Carlo Simulations, and Parallel Algorithms.These lectures teach the core knowledge required by any scientist inter-ested in numerical algorithms and by students interested in computa-tional finance. Even if we cover many different algorithms and examples, there are a fewcentral ideas in this book that we try to emphasize over and over.The first idea is that we can simplify the solution of a problem by usingan approximation and then systematically improve our approximation byiterating and computing corrections. The divide-and-conquer methodology can be seen as an example of thisapproach. We do this with the insertion sort when we sort the first twonumbers, then we sort the first three, then we sort the first four, and soon. We do it with merge sort when we sort each set of two numbers,then each set of four, then each set of eight, and so on. We do it with thePrim, Kruskal, and Dijkstra algorithms when we iterate over the nodes ofa graph, and as we acquire knowledge about them, we use it to updatethe information about the shortest paths.