**by Massimo Di Pierro**

DescriptionTable of ContentsDetailsHashtagsReport an issue ### Book Description

This book is assembled from lectures given by the author over a period of 10 years at the School of Computing of DePaul University. The lectures cover multiple classes, including Analysis and Design of Algorithms, Scientific Computing, Monte Carlo Simulations, and Parallel Algorithms. These lectures teach the core knowledge required by any scientist interested in numerical algorithms and by students interested in computational finance.

The algorithms you will learn can be applied to different disciplines. Throughout history, it is not uncommon that an algorithm invented by a physicist would find application in, for example, biology or finance. ### Table of Contents

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The algorithms you will learn can be applied to different disciplines. Throughout history, it is not uncommon that an algorithm invented by a physicist would find application in, for example, biology or finance.

This open book is licensed under a Creative Commons License (CC BY-NC-ND). You can download Annotated Algorithms in Python ebook for free in PDF format (4.6 MB).

Chapter 1

Introduction

Main Ideas

About Python

Book Structure

Book Software

Chapter 2

Overview of the Python Language

About Python

Types of variables

Python control flow statements

Classes

File input/output

How to import modules

Chapter 3

Theory of Algorithms

Order of growth of algorithms

Recurrence relations

Types of algorithms

Timing algorithms

Data structures

Tree algorithms

Graph algorithms

Greedy algorithms

Artificial intelligence and machine learning

Long and infinite loops

Chapter 4

Numerical Algorithms

Well-posed and stable problems

Approximations and error analysis

Standard strategies

Linear algebra

Sparse matrix inversion

Solvers for nonlinear equations

Optimization in one dimension

Functions of many variables

Nonlinear fitting

Integration

Fourier transforms

Differential equations

Chapter 5

Probability and Statistics

Probability

Combinatorics and discrete random variables

Chapter 6

Random Numbers and Distributions

Randomness, determinism, chaos and order

Real randomness

Entropy generators

Pseudo-randomness

Parallel generators and independent sequences

Generating random numbers from a given distribution

Probability distributions for continuous random variables

Resampling

Binning

Chapter 7

Monte Carlo Simulations

Introduction

Error analysis and the bootstrap method

A general purpose Monte Carlo engine

Monte Carlo integration

Stochastic, Markov, Wiener, and processes

Option pricing

Markov chain Monte Carlo (MCMC) and Metropolis

Simulated annealing

Chapter 8

Parallel Algorithms

Parallel architectures

Parallel metrics

Message passing

mpi4py

Master-Worker and Map-Reduce

pyOpenCL

Appendix A

Math Review and Notation

Subject

Computer Science

Publisher

Experts4Solutions

Published

2013

Pages

388

Edition

2

Language

English

ISBN13 Digital

9780991160402

ISBN10 Digital

0991160401

PDF Size

4.6 MB

License

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