Seems to me that this is not only great fodder for a blog but also for a social network like facebook.  While many meme’s that go around annoy me to no end, there have been a few that have allowed me to know a little more about my online friends (mostly friends from days gone by).  That has to be one of my favorite things about Facebook and Twitter, getting to reconnect with old friends and keeping up with all my current ones.

So here it goes, List #1

List the Biggest Turning Points in Your Life

• 1985: In fourth grade, I was recruited to participate in a UIL contest called Number Sense.  This definitely started me down a path toward becoming a mathematician and an educator.
• 1985: Also the year that I accepted Jesus Christ as my personal Lord and Savior.  Life would be totally different without Him.
• 1994: Summer I traveled to Bakersfield, CA, to work as a summer missionary.  Met Si Budagher and made a lot of good friends, a few of whom would eventually come to Wayland.
• 1994: Senior year in high school when I decided to go to Wayland for college.  That was a major life decision considering I met my wife there and now plan on teaching there for as long as they’ll let me.
• 1995: After a year as a Religion major, I missed math too much and decided to add mathematics as a major.
• 1995: Also the year I met the most intriguing, hilarious, intelligent, witty, and beautiful woman that I have ever laid eyes on.  I took only a couple of months to learn that I would have to spend the rest of my life getting to know her.
• 1998: Decided to go to Texas Tech to get my graduate degrees in Mathematics.  I decided very early that I wanted to teach undergraduate mathematics.
• 1998: Marriage.  Almost nothing turns your life around more than this.
• 2000: Children. NOTHING turns your life around more than this.  Emily came in August and being a father has become the most fulfilling and challenging job of my life.
• 2000: Wayland hired me as a Mathematics Instructor. 
• 2003: Along comes Timothy and we now have both a boy and a girl.  The family is seemingly complete.  It is the family that both Lori and I had always planned on.  We’re most likely done having kids at this point.
• 2004: Along comes Zachary and God reminds us that his plans are better than ours.  Life is different and better than we ever imagined.  Our family is just not complete without the life of the party, Mr. Z.
• 2005: Completed the Ph.D.  My formal schooling after 24 years is finally over.  Hard to believe.
• 2007: With all my life goals seemingly met: family, Ph.D., teaching at WBU, I get restless and wonder if I shouldn’t try full-time research for a while.  So I do and after 6 months in a bioinformatics post-doc with Dr. Wilkins in Lubbock, I know that I’m cut out to be an educator.  Research will have to become my hobby.
• 2008: After commuting for a term, we moved back to Plainview for financial reasons.  It’s tough at first but eventually, it becomes clear that this was the right decision.
• 2009: We buy the house of our dreams.  Having saved up and having Lori working full-time (without sending any of the kids to day-care) we are in the perfect place to buy our dream house. 
• 2009: I have been promoted to Associate Dean and begin in August in a new role as an administrator.  Still waiting to see what becomes of this turning point.

That’s a lot of turning points. Not all of them were major changes but most were definitely course corrections in life.

I’m curious, from both the readers of the blog and from my friends on facebook, what are some of your major turning points?

STOCKHOLM (AFP) - A 16-year-old Iraqi immigrant living in Sweden has cracked a maths puzzle that has stumped experts for more than 300 years, Swedish media reported on Thursday.

In just four months, Mohamed Altoumaimi has found a formula to explain and simplify the so-called Bernoulli numbers, a sequence of calculations named after the 17th century Swiss mathematician Jacob Bernoulli, the Dagens Nyheter daily said.

See the rest of the news story here.

Now, I’m no number theorist but I did take a course in Special Functions where the topic of Bernoulli numbers came up.  I was not aware of any 300 year old problem so I did some hunting and couldn’t find out what problem had been solved.  I also couldn’t find any mathematical news source citing the major development.

Thanks to Keith Devlin, we have a little more insight to the story.  In his MAA article this week, he wrote,

So I dug around on the Web for more details. There were a lot of news stories about the topic, but they all said more or less the same as the article I had already seen. Eventually, however, I found a Swedish news Website with an English-language story that was close to the source (Uppsala University).

"Swedish teen tackles centuries-old numbers challenge" was the headline. The story began, "A 16-year-old Iraqi immigrant in central Sweden has single-handedly figured out a formula with Bernoulli numbers that is normally reserved for much more seasoned mathematicians, earning him praise from professors at prestigious Uppsala University." Ah. Much more believable.

The reporter went on to explain that Altoumaimi, the young high school pupil, had developed some equations involving the Bernoulli numbers. When his school math teachers were unable to tell him whether what he had done was correct, the student contacted a professor at Uppsala University, who, after examining his work, declared that it was indeed correct. Not new, however. As the story continued,

"While it’s not the first time that someone has shown such Bernoulli number relationships, it’s highly unusual for a first year high school student to make his way through the complicated calculations, according to Uppsala University senior maths lecturer Lars-ke Lindahl."

I feel better knowing the truth behind the story.  Devlin was able to find the source I couldn’t find in my own digging.  Thanks, Keith.

A) Even
B) Divisible by 3
C) Divisible by 5
D) Divisible by 7
E) Prime

Source: 2002 AMC 10/12B #15

Whenever I would begin recording, the system would slow down enough that the writing on the screen was broken and hard to read.  The sound capture was fine, it just seemed that the CPU was not able to keep up with capturing the video on the screen and allow me to write smoothly.  The laptop, where it works fine, is a faster processor but with the same amount of memory.  I’m not certain how the video adapters compare.

I first discovered the problem several months ago and had been switching back and forth ever since.  However, today I took initiative and attempt to solve the problem one more time and came across a tip I had not considered. 

The Solution that worked for me:  Reduce the color depth from 32 bit to 16 bit.  For the types of videos I am doing, that makes makes no discernible difference and now it is as smooth on my desktop as it is on my laptop.

Some other tips for increasing the capture rate were found here: http://tinyurl.com/arua4b

Here’s a short sample:

Here was the puzzle posted last week:

Mr. Jones has eight children of different ages.  On a family trip his oldest child, who is 9, spots a license plate with 4-digit number in which each of two digits appears two times.

  “Look, daddy!” she exclaims. “That number is evenly divisible by the age of each of us kids!”

  “That’s right,” replies Mr. Jones, “and the last two digits just happen to be my age.”

What is the four digit number in the license plate?

The first thing I noted when I saw the problem is that the solution must be in one of the following forms: aabb, abba, or baba (where a and b are distinct digits).  Also, I noticed that since the oldest child is 9, the sum of digits must be a divisible by 9.  So that 2a + 2b = 9k for some k.  Because 2a+2b is even, k must be even. We know that a and b are distinct digits between 0 and 9, inclusive, the largest 2a+2b could be is 34, so k must be 2.  In other words, a+b=9.

Next thing I noticed is that Mr. Jones will have either 4 year old or an 8 year old or both.  Either way, the 4-digit number is divisible by 4.  This means the last two digits must be divisible by 4.  We thus have the following possibilities: 9900, 5544, 1188, 3636, 6336, 2772, 7272.  I arrived at these by thinking first of numbers of the form bb that are divisible by 4 (00, 44, 88) and providing the appropriate a to get aabb that is divisible by 9.  Then I considered the numbers of the form ba, that are divisible by 9 and 4 (36, 72) and listed both abba and baba.

Notice that in this list only 9900 is divisible by 5 and 00 can’t possibly be the age of Mr. Jones so he must not have a child age 5.  Only 5544 is divisible by the digits 1, 2, 3, 4, 6, 7, 8, and 9.

SOLUTION: 5544

A few folks emailed me their solutions and were all correct, but each had an approach that was not quite the same as mine.  Well done to those!

(From Lifehacker)

For example, if you’re staring in the face of numerous duplicate contacts that should represent the same person, the built-in contact merge feature in Google Contacts is a must. Just find the duplicate contacts, tick their checkboxes, and click "Merge these contacts…." Easy peasy. To manage your contacts, either head to the Contacts page in Gmail or to the unadvertised standalone site.

Gmail just keeps getting better.  I was back to using Outlook for long while until the Tasks feature was launched.  Now, all my email addresses are dumped into Gmail.  I don’t think I’m going back.

Oh, and thanks to the IMAP capabilities in Gmail, I have uploaded all my archived email into my Gmail account.  I can search my work emails dating all the way 2002. 

Oh, and I love the new Multiple Inboxes feature, as well.

Oh, and how about those themes?

You’ll find nothing but love for Google here…

  “Look, daddy!” she exclaims. “That number is evenly divisible by the age of each of us kids!”

  “That’s right,” replies Mr. Jones, “and the last two digits just happen to be my age.”

What is the four digit number in the license plate?

Source: 2006 AMC 10/12B #25 (American Mathematics Contest)

Clearly there are two lines of symmetry in the original problem so by reflection alone we come up with a total of four solutions: where and represent “flips” across the lines of symmetry and represents the identity, or the solution above.  By , I mean the composition of the flipping operations or just consecutive flipping.

There also exists radial symmetry at , but this is equivalent to .  So for this arrangement above, there are four solutions of the same “type”. 

Are any other arrangements possible besides these four?

Problem: Place the digits 1 through 8 in the circles below such that no two adjacent circles contain consecutive digits.

Update: I was missing a couple of lines.  The picture is now correct.

Every semester, I try to remember to convey this idea to my students in each of my classes.  Those that use online social networking tools like Facebook, MySpace, LinkedIn, Twitter, etc., must assume that when they put themselves out there, no matter where it is, anyone can see it.  I understand that most of them require you allowing people to view your page and follow your status updates, but there is very little guarantee that your information is going to be kept confidential.

I tell them to think of it this way: Imagine that you are applying for a position or even a promotion down the road.  Your boss sits down to a computer and “googles” your name.  What will they find about you and how will that affect their decision to hire or promote you?

As for a professor who also uses these tools, I have to be very careful.  I’ve set a policy for my blog that I will NOT discuss details about students in my current classes.  And later on, if I do decide to discuss specific students, I will NOT mention any incriminating information (without their full permission).

I was forwarded an interesting article regarding this very issue this morning (HT: Jay S.).  It is from the current issue of The Chronicle of Higher Education and it is entitled, “How to Not Lose Face On Facebook, for Professors” by Jeffrey R. Young.

He makes some of the same points in this article but goes on say:

But Facebook, like e-mail, yields more pros than cons, so the trick is to learn to master it rather than ignore it. That’s according to Nicole B. Ellison, an assistant professor at Michigan State University, who spent the past three years researching student behavior on Facebook, and who uses it herself. "There’s tremendous potential with these social networks for developing relationships and being exposed to different perspectives," she says. They are particularly well suited to academic work, where researchers need to keep up with a number of far-flung colleagues.

I totally agree with this and have been absolutely blown away by my ability to keep up with our past graduates plus finding alums from years gone by.  It is an amazing tool for connecting with people.  And no, I haven’t begun soliciting donations from them just yet but you never know.

On a related note, I still a little creeped out by the idea of a professor, like me, requesting connection (“Adding as a friend”) from my current students.  If they request it from me, no problem, but the other way around just seems inappropriate.  Plus, the Provost of our University is on Facebook and I have yet to request his friendship on there just because I don’t necessarily want him to know that I’m updating my status 4 or 5 times a day during work hours.

What boundaries have you set or would you set on a professor using social networks like Facebook?