This appendix gives an overview of the Natural Language Toolkit (NLTK), a useful and widely used module for manipulating natural language data. The topics of corpora, tagging, and tokenizing are all covered.

This is a survey of constructive and computable measure theory with an emphasis on the close connections with algorithmic randomness. We give a brief history of constructive measure theory from Brouwer to the present, emphasizing how Schnorr randomness is the randomness notion implicit in the work of Brouwer, Bishop, Demuth, and others. We survey a number of recent results showing that classical almost everywhere convergence theorems can be used to characterize many of the common randomness notions including Schnorr randomness, computable randomness, and Martin-Löf randomness. Last, we go into more detail about computable measure theory, showing how all the major approaches are basically equivalent (even though the definitions can vary greatly).

In this survey, we lay out the central results in the study of algorithmic randomness with respect to biased probability measures. The first part of the survey covers biased randomness with respect to computable measures. The central technique in this area is the transformation of random sequences via certain randomness-preserving Turing functionals, which can be used to induce non-uniform probability measures. The second part of the survey covers biased randomness with respect to non-computable measures, with an emphasis on the work of Reimann and Slaman on the topic, as well as the contributions of Miller and Day in developing Levin's notion of a neutral measure. We also discuss blind randomness as well as van Lambalgen's theorem for both computable and non-computable measures. As there is no currently-available source covering all of these topics, this survey fills a notable gap in the algorithmic randomness literature.

This chapter introduces object-oriented programming and explains how to make use of it in Python. It covers the basic syntax of defining and using objects. It also introduces the object inheritance system and closes with an extended example of object-oriented syllable structure.

This chapter introduces input and output – how we get data into and out of our programs. The input modes include the command line, file input, pipes, and typed input. (A later chapter treats graphical user interface input.) The output modes include the command line, file output, and pipes.

This chapter treats text manipulation, where we want to do more than find things in our data, but alter it in systematic ways.

This chapter covers graphical user interfaces (GUIs) using the tkinter module. The chapter starts with how to lay out a window and place user interface elements (widgets) in that window. It goes on to explain event-driven programming and how to attach basic functionality to widgets.

This chapter introduces the different data types of Python: integers, characters, strings, lists, dictionaries, tuples, etc. The chapter also treats the concept of mutability.

Ergodic theory is concerned with dynamical systems -- collections of points together with a rule governing how the system changes over time. Much of the theory is concerned with the long term behavior of typical points-- how points behave over time, ignoring anomalous behavior from a small number of exceptional points. Computability theory has a family of precise notions of randomness: a point is "algorithmically random'' if no computable test can demonstrate that it is not random. These notions capture something essential about the informal notion of randomness: algorithmically random points are precisely the ones that have typical orbits in computable dynamical systems. For computable dynamical systems with or without assumptions of ergodicity, the measure 0 set of exceptional points for various theorems (such as Poincaré's Recurrence Theorem or the pointwise ergodic theorem) are precisely the Schnorr or Martin-Löf random points identified in algorithmic randomness.

We discuss the different contexts in which relativization occurs in randomness and the effect that the relativization chosen has on the results we can obtain. We study several characterizations of the K-trivials in terms of concepts ranging from cuppability to density, and we consider a uniform relativization for randomness that gives us more natural results for computable randomness, Schnorr randomness, and Kurtz randomness than the classical relativization does (the relativization for Martin-Löf randomness is unaffected by this change). We then evaluate the relativizations we have considered and suggest some avenues for further work.