Application Technology
Cam-based Mathematics
This is an awesome old-school style video demonstrating how simple cam-based mechanical systems can be implemented to process numbers.
http://www.youtube.com/watch?v=-F7m02XDfvE
Calculating reciprocals, squares, and tangents using rotating disks: it’s amazing stuff! I wish I had seen (and appreciated) something like this as a young student. It might have made me appreciate engineering a little more.
Be sure to check out the barrel cam at the end that is used to compute gun elevation. I imagine something like this is at the heart of the mechanical calculators out there.
Resources
Graph Theory eBook
Here is a complete text on Graph Theory freely available on-line:
http://www.math.jussieu.fr/~jabondy/books/gtwa/gtwa.html
This appears to be a college- or graduate-level text, and it covers the basic ideas from Graphs and Trees to Colorings and Networks.
Each chapter is available as a separate PDF and contains numerous exercises. There are a number of appendices, like this one discussing Some Interesting Graphs, as well as a glossary and index.
I wish my own professor had used this, rather than making us all spend $100 on a flimsy paperback textbook!
Art Teaching
Math Encounters: Craig Kaplan on Math and Art
Craig Kaplan’s Math Encounters talk, “Revolution and Evolution in Math and Design,” was a whirlwind tour of the design space that lies at the intersection of computer science, mathematics, technology, and art. Kaplan, a professor of computer science at Waterloo university, is an innovative software engineer, an accomplished artist, and a passionate and engaging speaker. His talk wove together the mathematical and cultural history of Islamic art, tilings of the plane, non-Euclidean geometries, and the mathematics of aesthetics.
The Math Encounters series, sponsored by the Museum of Mathematics, strives to bring mathematics to the public through dynamic speakers, meaningful topics, and engaging interactivity. In that spirit, after the talk Kaplan and George Hart led a fun, collaborative workshop where the audience teamed up to create a work of art themselves!
Using some tape, some scissors, and some clever mathematics, each group turned their table into a “tile” using the techniques Kaplan covered in his talk.
And as each group finished their “tiles”, we started putting them all together!
It was a fun and fitting end to an inspiring and mind-opening evening! You can learn more about Craig Kaplan and his work at his webpage.
Resources
More on Math Careers
This is a modest, useful assortment of profiles from the Australian Mathematical Sciences Institute that focus on how individuals use mathematics in their jobs.
http://www.mathscareers.org.au/
The profiles range from math-intensive jobs like Sports Statistician and Traffic Engineer to [seemingly] non-math jobs Personal Trainer and Hairdresser.
It’s nice that they make the point that even if your job title isn’t Mathematician, math skills will still give you an edge in whatever you do. For a more specific focus on mathematically-intense careers, check out this site from MathCareers.org.uk.
It’s always good to have one more answer to the recurring question “What can I do with math?”