Real Analysis

About

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 always will be available for free online at the web loation https://www.mathcs.org/analysis/reals/

Credits

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 Paul Golba, a former Seton Hall student, assisted in its initial development by compiling the historical references.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 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.

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 a clickable glossary that can be used at any time to find stuff. As of version 2 the project uses cascading style sheets to define the overall look.

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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RequirementsMozilla's

XML-style code into the HTML (HyperText

  • HTML level 3
  • Cascading Style Sheets (CSS)

    The recommended web browsers are Mozilla's Firefox, Google's Chrome, or Mirosoft's Edge (latest versions).

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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
    Context icon to return to the main text

    To locate specific information:

    • Click on the Glossary button in the top menu bar and use your browser's Back feature to go back. The glossary contains an alphabetical, linked index to all key topics used in the text.

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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 www.javasoft.com).


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

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