Real Analysis


Interactive Real Analysis is an online, interactive textbook for Real Analysis or Advanced Calculus in one real variable. It deals with sets, sequences, series, continuity, differentiability, integrability (Riemann and Lebesgue), topology, power series, and more. The text is changing constantly, and your comments are very welcome: please sign our guest book.

The text was designed for use by upper level undergraduate math majors, and was modeled after a Real Analysis course (sometimes called Advanced Calculus or Abstract Analysis) given at Seton Hall University in the Fall 1993 and again in 1994. The text has since been used for many additional courses and supplements analysis teaching and learning world-wide.

The project is and will be available for free online but can be downloaded for a small one-time payment, including all future updates. For information on downloading the text, see the section on download.


This hypertext project was developed by Bert G. Wachsmuth and supported by a grant from Seton Hall University. Paul Golba, a former Seton Hall student, assisted in its initial development by compiling the historical references.

You are not allowed to copy, modify, or alter any part of this entire hypertext project without written consent of the author. You can view and print any part of this text for your own use.

The current version is created using a custom-made Java program that creates HTML code based on XML-style code and style sheets. The program also creates an index file to perform full-text searches (currently disabled). As of version 2 the project uses cascading style sheets to define the overall look.

The first versions of IRA, around 1994-98, were written using Microsoft's Word for Windows together with the macro package CU_HTML developed by Kenneth Wong and Anton Lam at the Chinese University of Hong Kong, and later with Microsoft's Internet Assistant. A simple text editor was used to improve the HTML code.

Graphics and Equations were - and still are - created with Microsoft's Equation Editor and are converted to GIF for compatibility with all browsers. Sounds were recorded using a Macintosh Powerbook.

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This text is translated from XML-style code into the HTML (HyperText Markup Language) language. To use it you need an HTML-compatible viewing program (a web browser) that supports:

The recommended web browsers are Firefox or Internet Explorer (latest versions) and you should also have the latest version of the Java plugin installed.

You can view this text offline if you download it - for a one-time fee - to your own computer. For download information, click here.

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Downloading the IRA Project

You will soon be able to download the IRA project and all future updates to your local computer for off-line browsing. There will be a one-time fee of approximately US $17.00 for the current version that includes the rights to all future updates of IRA.

The downloadable version will be available by the end of May, 2007. If you want to be notified when the downloadable version is available, please sign our guest book.

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Navigation and Symbols

Navigating IRA is simple. On the left part of your window you see the chapters and sections of the text. Click on them to jump to that information. Inside the main text you can click on

question mark icons to jump to an answer
Proof to view a proof
Java icon to run a Java applet
Context icon to return to the main text

The non-Java version includes some navigational buttons at the top of your window. Use them to help navigate the text. The Java version includes enhanced navigational control, including full-text search. You can also use the navigational tools that your browser offers to go back and forth between previously viewed pages.

To locate specific information:

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Java and Interactive Real Analysis

IRA includes several Java applets to help illustrate or experiment with concepts introduced in the text. These applets are spread throughout the project but are also available, out of context, in the Java Tools page. All applets have an Options button to bring up a control dialog where parameters can be interactively defined and applied.

In addition to the various applets, an optional navigational program called Java-IRA is available as well. Java-IRA provides an alternate method to access the content, enhanced by additional navigation buttons, quick jumps to specific definitions and theorems in a chapter, as well as full-text search capabilities. Java-IRA provides access to the same content as the regular version of IRA, but offers a more convenient interface.

To use any of the Java tools you must have the Java plugin (version 1.2 or higher) installed (download from

Screen-shot of Java-IRA with "Quick Locator" (search)

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