OFF ON A TANGENT
A Fortnightly Electronic Newsletter from the Hope College Department of Mathematics
January 18, 2006 Vol. 4, No. 7
http://www.math.hope.edu/newsletter.html


Hope celebrates undergraduate research next week

The 5th Annual Celebration of Undergraduate Research and Creative Performance will be held next week Friday, January 27. This event showcases student research and creative performance from arts & humanities, natural sciences and social sciences.

The Celebration will be held in the new DeVos Fieldhouse during its dedication activities. From 3:00 to 6:00 p.m. students will be on the fieldhouse concourse to discuss their research with those passing by. 

This is a great opportunity to not only see mathematics research, but all the different types of research that are being done by Hope students.  If you are at all interested or curious about student research at Hope College, this event is a must see.

(The picture above shows Brandon Allemen explaining his research, "Take me out of the Ballgame" that he conducted with Prof. Pennings during the summer of 2004.  This was taken during the 3rd Annual Celebration of Undergraduate Research.)


A summer research opportunity

The mathematics department here at Hope runs a summer research experience for undergraduates (the REU program.)  Under this program, professors Mark Pearson, Airat Bekmetjev, Aaron Cinzori, and Tim Pennings will be working with students this summer on four different projects.  Although students apply from all over the country for this program, Hope students are given special consideration. 

Participating REU students will receive a stipend of $2600 for the eight week program. Free apartment-style housing will be provided. Funds for travel as well as books and supplies are also available.  Visit http://www.math.hope.edu/reu.html for more information about the program.  Application deadline is February 28 this year.

In our last newsletter, we highlighted Prof. Pearson's project.  This time we will look at Prof. Cinzori's project on experimental mathematics.  His project description is as follows.

Suppose that you're working on a problem whose answer is a real number.  You do a calculation on a computer and get a numerical answer which, of course, you only have calculated to a finite number of digits. If the answer that you got was 3.141592, you might suspect that the answer is actually pi, but how would you go about actually proving that? On a more basic level, if your answer was 1.520366, you might not immediately guess that the answer was approximately Zeta(3) + 1/pi. How could you come up with that result and then prove it?

We'll learn some techniques for using high precision calculation, computer algebra systems (like Maple or Mathematica), and tools easily available on the Internet to help point the way to transforming numerical approximations to rigorous proofs. Then we'll use these techniques for tackling some questions that have arisen in earlier REU projects here at Hope or questions that arise while you're here. More information on these techniques is available at www.expmath.info.

To succeed with this project, you should have experience with infinite series and linear algebra and enjoy working on numerical computation. Some programming experience or understanding of how to use a computer algebra system would be helpful as well.


Professor Pennings to speak on chaos

What do the continental divide, the flap of a butterfly's wings and a straw on a camel's back have in common?  Why are tree branches, mountain ranges, and your circulatory system self-similar?  How can simple mathematical formulas command computers to generate incredibly complex and intricate pictures?  The answers to these questions will be given in the mathematics department's first colloquium of the semester. 

The colloquium, titled "Chaos: New Mathematics Reveals the Inner Workings of Nature" will be presented by Prof. Tim Pennings on Thursday, January 24 at 4:00 p.m. VWF 104.  As Prof. Pennings explores the world of chaos and fractals, he will explain how the study of mathematical dynamical systems answers the earlier questions and leads to a better understanding of natural forms and processes.  (If you already have the universe figured out, don't bother coming to this colloquium!)

  Tea at 3:30 in VWF 222 (Reading Room) on Thursdays before colloquia

As part of our colloquium series, the mathematics department will host a "tea time" in the Reading Room (VWF 222) at 3:30.  If tea isn't really your cup of tea, have no fear -- we'll provide some other beverages and snacks, too.  So please join us for a little food and fellowship before you go to the colloquia.  It'll be a great time to chat with the speaker, your professors and other students. 


Modeling competition (the mathematical type) coming soon

The Mathematical Contest in Modeling (MCM) and the Interdisciplinary Contest in Modeling (ICM) will be held here at Hope February 2-6, 2006.  The contests begin at 8:00 p.m. on Thursday (when the problems are released) and run until 8:00 p.m. on Monday.

MCM and ICM are contests where teams of 2-3 undergraduates use mathematical modeling to present their solutions to real world problems.  The problems are open-ended and generally require research and computation.  A team with diverse skills (mathematics, computing, writing, etc.) is usually best.  For the ICM it is advantageous to have a non-mathematician on the team.  The results are usually written up as a paper.

More details and past problems are available at http://www.comap.com/undergraduate/contests/mcm/.

See Prof. Cinzori by January 27 if you are interested in participating.


Prime time in the Show Me State

A Central Missouri State University team using more than 700 on campus computers and a network of thousands world wide has found the largest prime number so far.  The number is 2 to the power of 30,402,457 minus 1 and consists of 9,152,052 digits.  The discovery was made Dec. 15 of last year and confirmed earlier this month.  Cooperative computing groups are on the search for a 10 million digit size prime in a contest called the Great Internet Mersenne Prime Search to win a $100,000 prize from the Electronic Frontier Foundation.

Mersenne prime is a prime number that is 1 less than a power of 2. For several years, the largest primes discovered have been Mersenne primes. They are named after Marin Mersenne, a French monk born in 1588 who investigated the numbers.

For more information about the discovery made at Central Missouri State, visit http://www.cmsu.edu/x85370.xml.  For more information about Mersenne primes visit http://mathworld.wolfram.com/MersennePrime.html.


Problem Solvers of the Fortnight

Congratulations to Carrie Brandis, Devin Bonnie, Benjamin Crumpler, James Daly, Maya Holtrop, Jill Immink, Sara Jongekryg, Gabe Kalmbacher, Becky Lathrop, Nathan Makowski, Jeff Mastin, Nicole Mulder, I.M. Nameless, and Megan Patnott for correctly determining that the minimal area of the 16-gon traced by the bug is 384.


Sudoku

"The sudoku craze has become an epidemic," reports Robin Wilson in the January, 2006 issue of Focus magazine.  Within the past year, the wordless crossword puzzles with the Japanese name -- from Sunji wa dokushin ni kagiru, shortened to sudoku -- have begun to appear routinely in newspapers and magazines throughout the world, capturing the imagination of young and old alike and creating a stir akin to the Rubik's Cube craze of the 1980s. 

A 9 x 9 grid, called a Latin square, is subdivided into nine 3 x 3 grids, and numbers are placed in certain cells of the grid with the remainder of the cells blank.  The object of the puzzle is to fill in the blank cells, subject to only the conditions that the digits 1 through 9 must appear exactly once in every row and column of the 9 x 9 grid and exactly once in each of the smaller 3 x 3 grids.  The Japanese name for the puzzle in fact means 'single number.'  However, sudoku puzzles aren't Japanese; the first known sudoku puzzle appeared in a New York puzzle magazine in 1979, and the puzzles didn't reach Japan until the mid 1980s. 

The number of possible 9 x 9 Latin squares is 5,524,751,496,156,892,842,531,225,600, but fear not -- only 6,670,903,752,021,072,936,960 of these actually produce viable sudoku grids.  And in fact, the number of essentially different grids, after re-labeling the symbols and removing row and column permutations, is substantially smaller: there are only 5,472,730,538 of these.  For more on sudoku puzzles, please consult "The Sudoku Epidemic" by Robin Wilson in the January, 2006 issue of Focus.


Problem of the Fortnight

Prompted by the article on sudoku puzzles in Focus, the problem of the fortnight is the following sudoku puzzle.

 

 

4

 

 

 

 

 

 

 

5

 

2

 

 

 

 

6

 

 

2

3

6

 

 

 

 

 

 

 

 

 

 

 

 

3

 

 

 

 

 

 

 

1

2

2

1

 

7

 

 

 

 

9

 

 

 

9

 

3

 

8

 

 

9

3

8

 

 

7

 

 

 

8

 

 

 

4

 

 

 

Write your solution on the back of two Super Bowl tickets and drop it in the Problem of the Fortnight slot outside Dr. Pearson's office (VWF 212) by 3:00 p.m. on Friday, January 27.



 Got a Math Question?

Ask Elvis ...

... email him at elvis@hope.edu

Dear Friends,

Welcome back to Hope for another semester!  Hopefully I will see many of you around campus this semester.  If you see me, make sure you say hi.

With my short legs and lack of boots and a parka, I was glad to see the snow melt around here.  Hopefully we will have a mild winter.  I also haven't found any nice outdoor winter activity that I really enjoy yet.  I know some dogs like to pull sleds around on the frozen tundra.  (I much prefer herding to pulling.)  I have even seen dogs doing other interesting winter sports.  By clicking here, you can check out a picture of these dogs.  I am not sure that they look like they are having that much fun.

I have one letter to answer this fortnight.  If you have questions for me about mathematics or anything else, drop me an email a elvis@hope.edu.




Dear Elvis,

As I was sitting in my calculus class rubbing my tongue around in my teeth, I notice some calculus deposits.  My question is, why is it that the lovely mathematics course that I am studying right now and that yucky stuff on my teeth have the same name?

Calculusly Confused

Dear Confused,

Our language certainly is an odd one.  You have found an example of a homonym (two or more words spelled and pronounced the same but differ in meaning.)  For example, "If we pool our money, we can buy a pool table or a swimming pool." 

As for calculus, both meanings have the same origin.  In Latin, calculus means a little stone or pebble.  Long before, we had a TI-83, people used to do simple arithmetic on a pebble board.  When calculus was invented in the 1600s, it was named after these early pebbles.  The calculus that your dentist scrapes off your teeth looks and feels like a bunch of tiny pebbles.  So there you go.

Elvis


One person’s constant is another person’s variable.
Susan Gerhart