I have been experimenting with using Wolfram CDF files to introduce and illustrate certain concepts in my linear algebra classes. I send out the CDF files to students along with a brief set of questions to guide their exploration at home. In class the next day, students break into groups to explain what they observed, along with any insights they had. The CDF demonstration files were created using Wolfram Mathematica , while the students used the freely available Wolfram CDF Player to view and experiment with the files.
I gave a talk on this at the Joint Mathematics Meetings in Seattle in January 2016, where I demonstrated the use of some of these files. The slides from my talk can be found here. Most of the talk involved going through the demonstrations and worksheets, so the slide portion was somewhat brief.
Demonstrations and Worksheets
Below are some of the more successful demonstrations and worksheets. Any of the 3D plots can be rotated by dragging with the cursor to view from different angles.
- Solutions to System of Equations in 3 Variables (CDF)
- Solutions to System of Equations in 3 Variables Worksheet (PDF)
- Span of Vectors Demonstration (CDF)
- Span of Vectors Worksheet (PDF)
- Linear Independence Demonstration (CDF)
- Linear Independence Worksheet (PDF)
- Determinants and Area Demonstration (CDF)
- Determinants and Area Worksheet (PDF)
- Coordinates in R2 Demonstration (CDF)
- Coordinates in R2 Worksheet (PDF)
- Eigenvectors Demonstration (CDF)
- Eigenvectors Worksheet (PDF)
I have several more demonstrations in development (involving topics like orthogonal projections, coordinate vectors, Gram-Schmidt, etc.). I plan to post them once they are stable and ready for wider use.