Resources

Career Advice for the Mathematics Student

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!

By patrick honner, 14 yearsFebruary 10, 2012 ago

Fermat’s Last Theorem Documentary

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.

By patrick honner, 14 yearsFebruary 4, 2012 ago

Application Resources

Applications of 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!

By patrick honner, 14 yearsJanuary 28, 2012 ago

Geometry Resources

Mobius Transformation Video

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.

By patrick honner, 14 yearsJanuary 27, 2012 ago

Application Resources

The Other Line Always Moves Faster

This is a nice introductory video on elementary queuing theory from Bill Hammack, the engineer guy.

http://www.youtube.com/watch?v=F5Ri_HhziI0

Hammack poses a classic queuing theory conundrum: people in a town use phone lines at an average rate of two per hour; how many phone lines should the town have? The naive answer of two lines is far from optimal, because of bunching.

In addition to exploring this basic idea, Hammack also discusses the efficiency of the single-line system (everyone waits in one line for the next available cashier) versus the multiple-line system (each cashier has a separate line). Assuming that delays are distributed randomly among the cashiers, the single-line system minimizes the overall impact of a delay at any one cashier, and so, is more efficient.

And if every individual line has an equal chance of experiencing a delay, it stands to reason that every line has an equal chance of being the fastest. This explains why the other line always seems to move faster: if there are ten lines, you’ve got a 1 in 10 chance of choosing the fastest one, which means 9 times out of 10 a different line is moving faster!

By patrick honner, 14 yearsJanuary 19, 2012 ago