OFF ON A TANGENT
A Fortnightly Electronic Newsletter from the Hope College Department of Mathematics
September 24, 2003 Vol. 2, No. 2


Information session about the GRE is scheduled for tomorrow

Taking the Graduate Record Exam (GRE) is a requirement for entrance into many graduate schools.  The Hope Pew Society and the Office of Career Services are sponsoring an information session on the GRE. Professor Kim Risley of the Department of Biology will discuss the mechanics of the GRE, what students might do to prepare for the exam, and answer questions.  The session will be tomorrow night, September 25, from 7:00 to 8:00 p.m., in VWF 102.

For more information, go to the Career Service’s GRE web page: http://www.hope.edu/student/career/GRE.html. The site provides more information on the GRE, including subject test dates, and announces the availability of some practice test software.


Problem Solvers of the Fortnight

Congratulations to Michael Banducci, Robert Dody, Peter Holden, Mackenzie Smith, Sarah Story, Nick Sumner and Sara Tatge, all of whom correctly determined that the four weights allowing any integral weight from 1 to 40 pounds to be weighed are 1, 3, 9 and 27 pounds. The "blue ribbon" prize this fortnight goes to Nick Sumner, and he, along with all other authors of correct solutions, may claim their prizes from Dr. Catalano (VWF 209).

Last fortnight's problem about the merchant's weights is a famous one, first posed in 1624 by Bachet de Meziriac, whose books on mathematical puzzles and games became the classical ones of that genre. Bachet is probably most famous, though, for his Latin translation of Diophantus's Greek text Arithmetica, for it was in the margins of a copy of that translation that Fermat wrote his famous "Last Theorem," claiming, "I have discovered a truly remarkable proof which this margin is too small to contain." Had Bachet's margins been larger, Fermat might have been able to provide his "remarkable proof" himself; instead Fermat's Last Theorem was the subject of intense scrutiny for the next 350 years, drawing the attention of some of the world's greatest mathematicians, and was proved in 1994 by Andrew Wiles. To read more about this interesting chapter in the history of mathematics, beginning with Bachet, see http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Bachet.html and follow the links to Fermat and Wiles.


Surf's Up. . . A Useful Web Resource

What is Fermat's Last Theorem? Check out http://www.wikipedia.org/ for a description. Wikipedia is a free web encyclopedia containing articles on just about anything in many different languages -- including some in Esperanto, for those of you who have made the transition. It has an extensive mathematics section, where you can read about hypercomplex numbers, bone up on the Fundamental Theorem of Calculus, or do a search to find out what Penrose tilings are (they're really cool!).


The Problem of the Fortnight

It’s that time of year again.  Time for naïve hopefulness to rise up against brutal realism and decades of despair.   Time for fatalistic skepticism to wrestle with the vestiges of optimism that remain hidden deep within the hearts of many among us.  Time for long-suffering fans of the North Siders to agonize once again over happenings at the Friendly Confines.  Yes, we are nearing the end of the baseball season and the Cubs are still in the hunt! 

In fact, as we write, the Cubs are ½ game behind division leading Houston.  The Cubs have six games to play and Houston has seven.  The current records are:


CENTRAL W
 L
 PCT
Houston
 84
 71
 .542
Chicago Cubs
 84
 72
 .538

What are the chances that the Cubbies win their division?  The Cubs must finish with more wins than Houston, or, should they tie after finishing the 162 game schedule, the Cubs would have to beat Houston in a single elimination game. 

Let’s assume that the current percentages given above represent each team’s probability of winning any particular game, and assume this remains constant for the rest of the regular season.  Should the teams tie, assume the probability of either team winning the single elimination game is 50%.   Under these assumptions, what is the probability that the Cubs will win the division? (Note: the Cubs are not scheduled to play Houston during their remaining six games.)

Solve the problem and pin the hopes of thousands of Cubs fans on a single, unforgiving number.  Drop your solution in the Problem of the Fortnight slot outside Dr. Pearson’s office (VWF 212) by 3:00 p.m. on Friday, October 3.


Famous Nonmathematians

What can you do with a degree in mathematics?  How about being a president of a country.  Or a song writer.  Or perhaps a professional athlete.  Check out the list of famous nonmathematians at http://www.loyola.edu/mathsci/resources/famousnonmathematicians.htm.


The Annual Undergraduate Research Celebration is coming

Hope's 3rd Annual Undergraduate Research Celebration is being held this year on Friday, October 17 (4 - 7:00pm) in the new Science Center.  A preview of the poster session will be held for the Board of Trustees on the evening of October 16.  For both events to run smoothly it is requested that all posters be displayed by 6 pm on Thursday, October 16.  If you have done research or completed an independent study in the past year, you should display your results at this event.  Abstracts are due by September 29.  Therefore, it is important for you to get together with your faculty mentor as soon as possible to get this done.


The Michigan Autumn Take Home Challenge will be held soon

As mentioned in the last newsletter, the 2003 Michigan Autumn Take Home Challenge (or MATH Challenge) will take place on the morning of Saturday, November 1 this year.  Teams of two or three students take a three-hour exam consisting of ten interesting problems dealing with topics and concepts found in the undergraduate mathematics curriculum.  Each team takes the exam at their home campus under the supervision of a faculty advisor.  Each year 20-30 teams compete in this competition with teams from Hope regularly placing in the top three.  Last year, two of our teams tied for third behind Alma and Tri-State University.   Contact Prof. Cinzori for more details.


Three undergraduate mathematics conferences are slated for this fall

There are three opportunities this fall for students to participate in conferences.  

The Pew Undergraduate Research Symposium for the Physical Sciences and Mathematics is scheduled for Friday to Sunday, November 12 to 14 at the University of Chicago.  This conference is for students who want to give 15 minute talks or poster presentation.  This is a great opportunity for you to present your work from summer research or independent studies.  The deadline is for completed pre-registration forms, housing reservation forms, and abstracts is Friday October 3, 2003.  Please contact Prof. Kenneth Brown (chemistry department), Representative of the Local PEW Consortium, at brownk@hope.edu for more information, and to obtain all necessary forms. You can also visit the PEW 2003 Symposium website at http://www.college.uchicago.edu/pewsym/ to obtain all forms.

The Pi Mu Epsilon Regional Undergraduate Math Conference will be held at St. Norbert College in DePere, Wisconsin on November 7 and 8.  Students are welcomed to give short talks.  The deadline for registration for this conference is November 3.  For more information, visit http://www.snc.edu/mathclub/pme.htm.

Finally, closer to home, the Michigan Undergraduate Mathematics Conference will be held on Saturday, October 25 at the Grand Rapids campus of GVSU (the deadline for registration is October 17).  This is another great opportunity for students to give 15 minute talks about their summer research or independent studies.  In addition, this is an excellent venue for students to obtain information about graduate schools and career opportunities.  The keynote speaker is Dr. Suzanne Lenhart (Univ. of Tennessee).  For more details contact Prof. Andersen or go to http://www.gvsu.edu/math/mumc.html .