Visualizing Vectors

From the Math Values blog of the Mathematical Association of America:

Anyone who has taught linear algebra knows how easy it is for students to get absorbed in performing matrix computations and memorizing theorems, losing the beauty of the structures in this foundational subject. James Factor and Susan Pustejovsky of Alverno College in Milwaukee, WI, bring back the visual beauty of linear algebra through their NSF-funded project Transforming Linear Algebra Education with GeoGebra Applets.

The applets are freely available in the GeoGebra book Transforming Linear Algebra Education https://www.geogebra.org/m/XnfUWvvp. Each topic is packaged with a video to show how the applets work, the applet, and learning activities.

Read more about it here: https://www.mathvalues.org/masterblog/visualizing-vectors

Goodbye Aberration: Physicist Solves 2,000-Year-Old Optical Problem

This was a nice write-up (with some entertaining interspersed snark) of the solution of the the Wasserman-Wolf problem concerning the construction of a perfect lens (like a camera lens). Some quotes:

[L]enses are made from spherical surfaces. The problem arises when light rays outside the center of the lens or hitting at an angle can’t be focused at the desired distance in a point because of differences in refraction.

Which makes the center of the image sharper than the corners…

In a 1949 article published in the Royal Society Proceedings, Wasserman and Wolf formulated the problem—how to design a lens without spherical aberration—in an analytical way, and it has since been known as the Wasserman-Wolf problem…

The problem was solved in 2018 by doctoral students in Mexico. For those fluent in Spanish, the university press release can be found here. As an added bonus, here’s the answer: