A Homework Sampler

This time around, I decided to give all those readers out there an idea of the kind of problems I get for homework.  What follows is one of three problems that I will turn in tomorrow in my Real Analysis class.  However, I think that the question (at least) and most of the solution is pretty accessible to the masses.  I'd love to hear feedback about how well you think the solution was written--keeping in mind that I could have included much more detail.  Mentioning things like the fact that the area of the big square is one because its sides are of length one is unnecessary in the solutions I will hand in.  I'd also love to hear if you have any questions about the problem, the solution, the class, the subject, or anything!  Ok, now to figure out how to include a pdf file...



It seems like that worked.  We'll see! If not, I'll post again and possibly include a link you can go to.  If it worked, you can download the file by right-clicking it if it is too small to read in your browser. 

A bit more information about this problem:  it is approximately the average difficulty (probably a bit easier than normal).  The second problem in this set was twice as long and twice as dense and complex.  However, the third problem was about the same difficulty as this one, but took about half as much space to solve.

I have had analysis before, and I have had algebra before.  However, my statistic background is sorely lacking.  Therefore, I am finding statistics to easily be my hardest class.  We took a test last Monday, and I did not do quite as well as I hoped.  However, I've heard this teacher's first test is always hard.  I am doing well on the homework, though, so overall I feel good about the whole situation.

Hopefully soon I will be able to post an update on the research stuff--and you never know when something funny (like Sting) will come up.  Happy mathing!

Sting is NOT a Mathematician

…as evidenced by his misuse of numbers in quite a few songs by The Police. 

First: From the song “Next To You”: “I’ve had a thousand girls or maybe more…”

                Analysis:  Let’s assume Sting “has a girl” five days out of every week.  That means he has been “having girls” for the past 1000/(52*5) = 3.846 years.  This does not seem so outlandish until one realizes the line after the one mentioned is “But I’ve never felt like this before.”  This is either testament to how amazing this girl is (despite Sting being probably the most diseased person on the planet), or to how little Sting pays attention to all the other girls he has “had.”  (Even if we assume Sting “has a girl” six out of seven days a week, and on the seventh “has” two girls, he has been at it for the past 1000/(52*8) = 2.40 years!)

Second: From the song “Every Little Thing She Does is Magic” : “…a thousand rainy days since we first met…”

                Analysis:  Let’s assume (generously) that it rains one-third of the days in a year.  That means that Sting has known this magic girl for 1000/(365/3) = 8.2192 years.  Considering another line in the song mentions calling her up to propose to her, it shows that Sting has no courage whatsoever:  he’s been trying to propose to this girl for over 8 years?!   (A more conservative and realistic estimate would be that it rains one-fifth of the days in a year, in which case Sting has been wallowing in indecision for 1000/(365/5) = 13.70 years!!)

Finally: From the song “Message in a Bottle”: “A hundred billion bottles washed up on the shore”

                Analysis:  Currently estimates of the worlds population are around 7 billion—that is, 7,000,000,000 people.  So, even if everyone in the world contributes to the cause, each person would have to throw 100,000,000,000/7,000,000,000 = 14.26 bottles into the ocean. 

Since this is not inconceivable, let’s consider the actual physicality of 100 billion bottles on a shore.  Let’s assume (hopefully reasonably) that one bottle takes up half of one square foot.  Let’s also assume that the beach of Sting’s island is 50 feet wide.  100,000,000,000 bottles would then cover 100,000,000,000/(50*2) = 100,000,000 feet = 100,000,000/5280 miles = 18,939.4 miles.  This is equal to 1.7 times the length of the coastline of Great Britain--11,073 miles (courtesy of the Ordnance Survey via Wikipedia).  Sting would need a pretty big island!

So, it is clear that Sting is not a mathematician.  However, I am a tiny bit closer to being one.  With about three weeks of grad school under my belt, things are going pretty well.  My classes in Analysis and Algebra are fairly easy (right now), and my Statistics course is more challenging than I’d like, but I am holding my own—we’ll see how the test on Monday goes!  The recitations that I teach are also going well considering they are full of people who don’t really want to be there.  On the whole, life is pretty good.  I am excited for many things in my future, but  the present is nice too!