Technical Requirements

These learning objects consists of Flash-based diagrams, both static and interactive, embedded in HTML pages. To view and interact with them, you will need:

• An installed copy of the Flash player, version 8 or later. You can download the Flash player here.
• A modern browser which displays CSS stylesheets correctly. Please do NOT use Microsoft Internet Explorer, as it may not display the size of boxes like this one correctly. You can use Safari (Mac) or Firefox (Mac and PC). Safari comes included with the Mac OSX operating system, or you can download Firefox (Mac or PC) here.
• Whichever browser you use, do not change the fontsize set for the text of the learning objects. The text is sized to fit correctly inside the boxes and may not display properly if it is resized. Also, some of the mathematical formulas are actually pictures and will not resize appropriately if you resize the font.

   What this is

This is a collection of fifteen learning objects on selected topics in elementary linear algebra. The learning objects are intended to be used either concurrently with a first course in linear algebra, or before such a course, as a "prequel".

The idea is to present an informal, interactive approach to some of the foundational topics in linear algebra and to build intuition and visualization for those topics. Specifically, the objects are meant to be:

• Informal: Rather than present a string of definitions and theorems couched in formal mathematical terminology, the language and concept structure used to convey the ideas is kept as simple as possible.
• Interactive: Many of the diagrams in these learning objects are interactive - for example, vectors can be dragged to different positions and the consequences examined and experimented with. Several of the numerical algorithms are also interactive - different portions of the calculation may become visible when clicked on, for example. (Interactive diagrams are enclosed in red boxes.)
• Intuitive: The intent is to build a "gut level" understanding of linear algebraic concepts (particularly those involving vectors) as a motivation and preview of the definitions and theorems students will encounter either concurrently or later as part of a formal linear algebra course.
• Visual: At its origins, linear algebra is a highly visual, geometric subject. To help students understand just where many of the apparently algebraic concepts come from, the learning objects contain numerous diagrams, both static and interactive, to provide a visual interpretation of those concepts.

Also included is an experimental version of one of the learning objects done with voiceovers instead of written text. This objects was created to illustrate the positive effect on understandability of using voice instead of text in learning objects. For details of the theory behind this idea, see J. Sweller, Instructional Design in Technical Areas.