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Graphics, Animation, and 3D-printed Education Resource

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GA3DER

Graphics, Animation, and 3D-printed Education Resource

I would like to increase access to and ease of use of visual aids in classroom teaching of introductory math courses, especially calculus and linear algebra. I have in mind some manageable subset of the following:

  • Math 15/25 (Intro calculus): graphics and animations to illustrate various topics, including limits, Riemann sums, solids of revolution, Taylor polynomial approx’s, etc.
  • Math 33/34/35 (Multivariable calculus): graphics and animations to illustrate topics such as graphs of surfaces, limits, differentiability, level curves, gradient properties, vector fields, etc.
  • Math 25/33/34/35: 3D-printed solids to illustrate solids of revolution and finding volumes thereof, or mass; or solids to illustrate various multivariable concepts.
  • Math 27/28 (Linear Algebra): graphics and animations to illustrate topics such as spanning sets, linear combinations, subspaces, linear transformations, projections, etc; interactive applets to allow students to explore techniques, such as Gaussian elimination or determinant
  • Math 43/44 (Differential Equations): graphics and animations to illustrate or allow students to draw phase planes or solutions to differential equations.

Various members of my department have used software packages such as Mathematica, SAGE, Graphing Calculator, or CalcPlot3D to create graphic displays for use in class or for students to use outside of class. But some systems are difficult to use (Mathematica) or are no longer easily available (Graphing Calculator). In addition, it’s hard for us to keep track of what everyone else is doing. Finally, there are likely many great applications out in the broader community that we don’t know about or do not have the knowledge to bring into use at Swarthmore. With the help of tech-savvy Swarthmore students, we could gather what has already been created here at Swarthmore, explore what has been created elsewhere that we can use, determine what would be most valuable to create in-house, and then determine if there is an efficient way to make the resulting resources easily available to all members of the department who might want to use them. This is a rather large project (!). A more manageable version would just be to gather information/apps/visualizations/etc already created by department members and put them into some organized and accessible format, perhaps all in SAGE. I will be teaching linear algebra next year and would use relevant graphics in that course. My colleagues Cheryl Grood and Aimee Johnson are also interested in using visual materials in their single and multivariable calculus courses.

Besides my own ideas, there are several department members who have already shared some information (such as info on CalcPlot3D, which is free), who have written apps in SAGE they are willing to share, or who know of applets or other tools already available online.

I am available most of the summer. My summer travel plans are not yet set, but I expect to be be away for short trips in late June and mid August. These are likely to be about 5-6 days each.

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