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!

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.

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?”

The Year in NFL Scoring

football-in-airAs the books close on the 2011 NFL regular season, it’s time to revisit my pre-season prediction that the new kickoff rule would result in a slight decrease in per-game scoring.

The pre-season predictions on the number of touchbacks turned out to be fairly accurate.  In 2011, about 43% of kickoffs (922 out of 2151) resulted in touchbacks; in 2010, only 16% of kickoffs (359 out of 2221) resulted in toucbacks (thanks to NFL.com for the data).

Did the increase in touchbacks reduce overall scoring in 2011, as hypothesized?  No.  In 2011, around 44.4 points were scored per game in the NFL; in 2010, around  44.1 points were scored per game.  Per-game scoring actually increased slightly this year !

One issue worth mentioning, however, is the disproportionate effect the top three scoring teams have on the data.  During the 2010 season, New England was the highest scoring team in the league with 518 points total points; this was nearly 80 points more than the second highest scoring team.  In 2011, the Packers, Saints, and Patriots all scored over 500 points!  If we remove the three highest-scoring teams from each season, scoring for the rest of the league actually drops about 0.7 points per game.

It’s been fun drilling down into the data this year, and many other interesting questions popped up along the way.  And off-season changes always create new opportunities for analysis.

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