DiPierro M. Annotated Algorithms in Python: with Applications in Physics, Biology, and Finance

Massimo Di Pierro, 2013. — 389 p.Main Ideas.
About Python.Book Software.
Overview of the Python Language.
About Python.
Types of variables.
Python control flow statements.
Classes.
File input/output.
How to import modules.
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.
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.
Probability and Statistics.
Probability.
Combinatorics and discrete random variables.
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.
Monte Carlo Simulations.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.
Parallel Algorithms.
Parallel architectures.
Parallel metrics.
Message passing.
mpi4py.
Master-Worker and Map-Reduce.
pyOpenCL.Appendix A: Math Review and Notation.