Here’s a nice little quiz on plotting points in the Cartesian plane:
http://www.thatquiz.org/tq/practice.html?idpoints-j8-l5-m2kc0-na-p0
After you’ve warmed up, be sure to try plotting complex numbers, or test your knowledge of the Polar plane (in both degrees and radians).
There are a number of simple little quizzes to enjoy at thatquiz.org; just be careful not to let the day slip away!
There is a great set of videos from MathsCareers.org.uk that focus on mathematics in industry. The videos speak to strong math students who have questions about finding careers that utilize their mathematical abilities.
The speakers are employers and recent graduates working in technical fields, and they offer a lot of clear, thoughtful advice.
The “Why are ‘Soft Skills’ Important?” segment is particularly great to see: the speakers all stress how communcation, writing, presenting, and teamwork skills are crucial to success in technical fields. In addition, the “Why are Maths Graduates Sought After?” segment really highlights what is fundamentally important in mathematics: problem solving skills, thinking creatively, and the ability to break complex ideas down into simpler ones. These skills are prized in every field and industry.
The best advice I saw throughout the videos is to start thinking early about what really interests you and explore all the options you can. There’s more to math than just teaching and banking!
This is an engaging, accessible, and surprisingly moving documentary about Andrew Wiles and his lifelong pursuit of Fermat’s Last Theorem:
http://video.google.com/videoplay?docid=8269328330690408516
Although the mathematics of the proof could not possibly be explained to the layperson (there aren’t many people in the world who could really understand it in its entirety), this BBC documentary does a great job of narrating the struggles, setbacks, and triumphs of Wiles’ pursuit.
The story of the hero and the many peripheral characters (including John Conway) opens a wonderful window into the world of advanced mathematics.
This is an amazing resource from the British Columbia Institute of Technology: a cross-referenced list of how various mathematical ideas are used in various technology fields.
http://commons.bcit.ca/math/examples/
Interested in how Linear Algebra can be applied to Nuclear Medicine? Or how Logs and Exponentials can be applied to Forestry and Wildlife? Or how Differential Equations can be applied to Mechanical Engineering?
Well, look no further!
Not only is this visualization of generalized Mobius transformations mesmerizing and beautiful, it is the clearest demonstration of inversion that I have ever seen:
http://www.youtube.com/watch?v=JX3VmDgiFnY
This short movie visually explains all the basic transformations of the plane: translation, rotation, dilation, and inversion. Then it demonstrates how all of these transformations of the plane can really be thought of as simple translations and rotations of the sphere!
If I had seen this video a few decades ago, I might not have given up on topology as quickly as I did.