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, ago

Who Employs Mathematicians?

Here is a great resource from mathscareers.org:  a collection of links to the Careers pages of various companies that employ mathematicians.

http://goo.gl/m5mIt

It’s easy to envision using math in fields such as Accounting, Education, and Academic Research, but there are also links to Automotive companies, the Food and Drink industry, and Pharmaceuticals.  What a great place for a young mathematics students to get a feel for some of their options!

And here’s another great resource from the same organization:  a set of excellent video interviews about the importance of mathematics skills in industry.

By patrick honner, ago

Street Fighting Mathematics

Sanjay Mahajan’s Street Fighting Mathematics is a short, dense, and engaging book that explores some mathematical problem-solving techniques not typically taught in math class.

These techniques, favored by engineers and scientists who are usually more interested in the answer to a question than in the mathematical theory that gets them there, can turn seemingly intractable problems into simple ones, often just by a change in perspective.

For example, the book offers a short treatment of Feynman’s differentiating-under-the-integral approach, one of the more famous “back of the napkin” techniques.  Mahajan even “guesses” the definite integral that yields the area under the bell curve, using dimensional analysis the likes of which I’ve never seen.

A “Street Fighting Mathematics” course is offered through MIT’s OpenCourseWare, which includes lectures, notes and problem sets.  In addition, Mahajan has made the book available for free in PDF format.

By patrick honner, ago

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!

By patrick honner, ago

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?”

By patrick honner, ago
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