Main Features of the Interactive Linear Algebra
with Maple V
- The navigation among the various components (Lessons, Labs, Projects, Proofs, Animations, and Help Demos for the Automated Linear Algebra Functions) are supported by a user friendly graphical user interface (GUI).
- Geometrical display and demos of Linear Algebra concepts include: Transformation of images via matrix multiplication and its effects (rotation, reflection, dilation); Algebra of vectors; Subspaces; Least square; change of basis; eigenvectors and many more animations in the interface.
- Independent computer interactive lessons that may be used by instructors for explaining the main concepts of the course. The lessons include a collection of well-selected exercises that encourage exploration. Solutions to the exercises are provided. Also included at the end of each lesson a short quiz. This is intended to give the students immediate feedback on their progress.
- In addition, to the computer interactive lessons, we have two other components: Labs and Projects. Instructors may request students, after learning the lessons and going over the exercises and the quiz at the end of each lesson, to either choose Labs, Projects or a combination of these. Each serves a different purpose. Labs are intended to enforce the concepts. Projects are intended to emphasize the utility of the concepts and viable applications. Labs and projects are two additional components and can be integrated in a variety of ways depending upon the students' level and the choices of the instructor.
- A library of Automated Linear Algebra Functions. Unlike the built-in functions of a CAS (Computer Algebra System) where the output for a given input is readily displayed, our functions display the intermediate steps. Thus students can use the functions to learn in a self-paced manner an underlying concept or algorithm and experiment with as many examples as needed. Our functions act to some extent as an "intelligent electronic tutor".
- All units tie together with a single unifying theme namely: Solvability of Linear Systems. Students can relate to this concrete theme. All concepts are studied and presented within this framework. Students can then learn the abstract notions from this perspective. Our experience indicates that this unifying theme has a great impact on their retention of concepts.
- Besides the short quiz at the end of each lesson, the Adpative Testing System (ATS) with over 300 multiple choice questions provides the instructor with an apparatus for testing students on the units of the course. Instructor, using the ATS, may add, modify the existing questions and their level of difficulty to suit the needs of their students. Also, instructors may use the ATS to keep records of the students.
