Random is a website devoted to probability, mathematical statistics, and stochastic processes, and is intended for teachers and students of these subjects. Many of the elements are designed so that they can be modified and reused to fit the needs of students at various levels. The project has two basic types of resources:
Ancillary materials open in small pop-up windows on laptop and desktop computers, and in separate tabs on tablets and phones. Thus, these materials can remain open and accessible while you browse the expository material in the main window. The expository material has extensive links to the ancillary materials, but some of these materials are also designed to stand alone so that they can be used in other projects. The ancillary materials are of the following types:
This project uses standard web technologies, including HTML5 and JavaScript. Almost all of these tecnologies are based on open, published standards endorsed by various standards groups, including the World Wide Web Consortium. One of our goals is for this site to be fully standards compliant and to implement best practices for web-based expository mathematics. To use this project properly, you will need a modern browser that supports these technologies.
Display of mathematical notation is handled by the open source MathJax project. Mathematical expressions rendered by MathJax scale appropriately with the surrounding text, and can be copied and pasted into other applications.
The expository material is divided into chapters, similar to chapters in a conventional book. The chapters explore the basic theory and applications of probability, mathematical statistics, and certain special models and stochastic processes. Each chapter in turn is divided into web pages
, similar to sections in a conventional book. Each section explores a particular topic, mostly through a series of exercises that guide the student through the development of the mathematical theory and the development of probabilistic intuition.
The expository text assumes knowledge of calculus, at the standard undergraduate level. A few sections require knowledge of linear algebra, at the standard undergraduate level. No prior knowledge of probability or statistics is assumed. Some of the chapters are divided into basic topics that are essential to all students, and advanced and special topics that can be omitted for new students. The chapter on foundations has sections on other branches of mathematics that have significant interplay with probability, statistics, and stochastic processes. These sections can studied as needed.
The basic exposition on a page is organized into mathematical units
that are numbered consecutively on the page. A unit could be a definition, an assumption, a theorem, a lemma, a corollary, a computational exercise, or an exercise involving an app or a data set. Most units have details that are initially hidden but that can be expanded or contracted. The details for a unit could variously be a proof, multiple proofs, a sketch of a proof, an heuristic argument, the soloution or simply the answer to a computational problem. Having the details initially hidden provides several benefits:
Buttons at the top and bottom of each page allow all details to be expanded or contracted. In addition to the numbering, the units are denoted with a small die icon (the basic symbol of our project). A unit that gives a definition or an assumption has a green die; a unit that involves an ancillary web app or data set has a red die; all other units (representing mathematical statements or exercises) have a blue die.
A you are here
navigational map is given on each page. The contents page of a chapter has links to the Random home page and to the contents pages of the other chapters. Each section in a chapter has links to the Random home page, to the contents page of the chapter and to the other sections in the chapter.
Links to units on a page are by number and are colored blue. Links to other pages (sections) are by the name of the section and also are colored blue. You may want to open these links in a separate tab in order to keep you place in the exposition and to avoid the delay in rendering the mathematical notation. Links to ancillary materials (apps, data sets, biographical sketches) are colored red. Links to external resources are colored brown and always open in a separate tab.