OFF ON A TANGENT
A Fortnightly Electronic Newsletter from the Hope College Department of Mathematics
March 29, 2006 Vol. 4, No. 11
http://www.math.hope.edu/newsletter.html


There are five colloquia scheduled for the next two weeks

If you have waited for warmer weather to take care of your colloquia requirement, then you are in luck for the next two weeks.  Not only do we have warmer weather scheduled, but we also have five colloquia on tap as well.  With is kind of offering, we are sure you will find something to your liking.

Actuary?  What's an Actuary? Are you interested the mathematics or business, but aren't sure what kind of job you'll be looking for when you graduate?  Interested in going to a talk where you can walk out of the door with more money in your pocket than when you walked in?  Then this talk is for you!

At this talk, Prof. Nathan Tintle will explain what actuaries do, why the actuarial profession is rated so highly, and what you should be doing now to prepare yourself to be an actuary.  Since probability is a crucial foundation of actuarial science, we will play a couple of probability games (prizes include Meijer gift cards) and discuss the Topics in Probability course that will be offered next semester.

Come and enjoy some light refreshments before this colloquium at 3:30 p.m. in the Reading Room (VWF 222).
 
Mathematical Ecology
 This Biology Seminar will join with the Mathematics Department to feature Dr. John Vandermeer from the University of Michigan.  He will talk on "Self-organized Spatial Pattern and its Significance for Biological Control in a Coffee Agroecosystem in Mexico."  Refreshments will be served. (I'm not sure if that will include coffee,)

Putting a Spring in Yoda's Step

When the character Yoda first appeared on the silver screen, his movements were due to the efforts of famed muppeteer Frank Oz. In Star Wars Episode II: Attack of the Clones, Yoda returned to the movies but this time the character was not a puppet but a digital image within a computer. In this talk, Prof. Tim Chartier of Davidson College will discuss the role, or more aptly the force, of mathematics behind a few aspects of movie special effects. Armed with differential equations, animators can create a believable flow to Yoda's robe or a convincing digital stunt person.

Come and enjoy some light refreshments before this colloquium at 3:30 p.m. in the Reading Room (VWF 222).

Biostatisics
Dr. Robert Downer will be coming to speak about biostatistics and Grand Valley's new biostatistics program.  Biostatistics is the application and development of statistical techniques for scientific research in disciplines such as clinical medicine, biology, epidemiology, environmental health, wildlife and fisheries, forestry and agriculture. Biostatisticians participate at many levels in the acquisition of knowledge from biological data and they are in demand in industry, research institutions, government and academia.
    
Grand Valley State University is uniquely positioned for launching a new Biostatistics program.   The new biostatistics masters is cross-disciplinary and has close ties to the scientific and business workforce through internship experiences. Come learn more about our masters program in this informational seminar. Plenty of time will be available for questions and interaction.

What will you buy? How much will you spend? How much do you like it?

Three Hope College Graduates, Michael McCune ('99), Andy Kiel ('04) and Jason Mejeur ('04) will share real world applications of mathematics in the field of Marketing Research. After a brief introduction to quantitative marketing research, three distinct methodologies will be explored to understand the analysis tools and basic mathematics skills that are utilized in each. Areas of focus will include everything from basic statistics to linear algebra and regression analysis.

Come and enjoy some light refreshments before this colloquium at 3:30 p.m. in the Reading Room (VWF 222).

GRE preparation help is available tomorrow

The Hope Pew Society and the Office of Career Services are sponsoring an information session on the Graduate Record Examination. Professor Charles Behensky of the Department of Psychology will discuss the mechanics of the GRE, what students might do to prepare for the exam, and answer questions.  The session will be this Thursday, March 30, 5:00-6:00 PM in 1000 Science Center.


From the Margins of My Textbook
A Math Major’s Musings 

By JENNICA SKOUG | Staff Wordsmith

Math – an extension of Reality

When does something become "real?"  When you can see it, or hold it in your hand?  When you can imagine it?   What if you can only imagine imagining it? 

Although such questions are applicable to many different venues in life (and indeed about life itself), I have found them to be particularly apparent in topology, this semester's dose of mathematics.  This class has been a wild ride from the simplest sets to the most abstract and confounded spaces imaginable.  Except that often, they aren’t imaginable!  I think a comment made during class sums it up nicely.  “Well,” Dr. Pearson said pensively, “you’re having difficulty visualizing this…because you can’t.”   We were talking about the projective plane.  You make a projective plane by taking a sphere and “sewing together” each pair of antipodal (opposite) points.  The North Pole and the South Pole, and all other pairs like them, are now the same thing.   The sphere twists in on itself in a way that requires a fourth dimension to see a “real” picture of it.   If you walk from the Pole (since there is now only one) to the Equator, your next step will take you not to higher latitudes, but instead will shift your longitude by 180 degrees – you step out, mirror reversed, on the other side of the world.  But how did you get there?  You certainly didn’t walk the diameter of the earth in one step, nor is this some mathematical form of teletransport.  The opposite points on which you trod are physically connected.  Yet you can’t see this in three dimensions.  A similar venture occurs for the famous Klein bottle, which is essentially a long tube with its ends twisted together in such a way that the whole object has only one side.  Ask any mathematician if such a thing exists and he or she will likely respond “Of course! But only if you have four dimensions.  (Would you like to see my Klein bottle hat?)”

But…is there a fourth dimension?  Are such objects “real” if they can never exist in the only reality we know?   This should be an easy concept for Multivariable students.  They work in n dimensions all the time.  But have you ever tried to draw Rn, or thought about what it really means?  I believe my Calc II professor tried to do this once, but just ended up with a strange looking cube and lot of chalk dust.  We are finite, three-dimensional beings.  We lack the mental and physical capacity to step outside our own reality. 

Yet the amazing thing about the human mind is this: we can push the boundaries; we can tow the line of reality.  We may not be able to imagine what (to us) is unimaginable, but we can imagine imagining the unimaginable.  This is where math – and to its credit, topology – both bewilders and enlightens me.  It bewilders because few other places force me to think about such things.  But math has plenty of concrete, unimaginable examples to spare.   Yet math is also a venue that, as far as possible, provides ways for me to wrap my mind around such strange things, these extensions of conceivable reality.  It is a way to lean out further from the cliff of reality than I ever thought was possible.  It is, in fact, quite thrilling.  Try it sometime.


Problem Solvers of the Fortnight

Most of you who pieced together a solution said that rectangles of the form (2a) x (3b) can be tiled with Ls.  That's certainly true, but this problem was a bit deeper than that.  For instance, given that you can tile a 2 x 3 rectangle by adjoining two Ls to form a block, you can tile a 2 x 6 rectangle with two blocks and a 3 x 6 rectangle with three blocks.  Thus, you can tile a 5 x 6 rectangle as well.  Of the solutions we received, James Daly made the most progress on this problem by devising a way to tile a 9 x 5 rectangle.  (Do you see how?)  Kudos to James for some very fine work!  


Problem of the Fortnight

On the heels of Pi Day (3-14) and the accompanying break you enjoyed celebrating this important number, we offer the following problem about the somewhat more obscure numbers 13,511, 13,903 and 14,589.  (Editor's Note: Whether Hope planned its spring break in honor of Pi Day is unsubstantiated at this point.)

Determine the greatest integer that will divide 13,511, 13,903 and 14,589 and leave the same remainder.

Write your solution in whipped cream on the top of an apple pie (with a cup of coffee, please!) or write it in green ink on the back of a St. Patrick's Day card and drop it in the Problem of the Fortnight slot outside Dr. Pearson's office (VWF 212) by 3:00 on Friday, April 7.  



Got a Math Question?

Ask Elvis ...

... email him at elvis@hope.edu

Dear Friends,

Did you ever have something that you thought was useless, but come to find out was very useful?  For example, in 1970 a scientist at 3M laboratories was trying to develop a strong adhesive, but instead came up with a very weak one.  He never did have any use for the poor quality glue, but never discarded it.  Four years later, another scientist at 3M wanted a way to keep the markers in place in his church hymnal, remembering the weak adhesive that his colleague developed; he invented the Post-it note.

Mathematics is like that. People often study and develop mathematics, not because there is a use it, but because it is interesting. Then years or even centuries later, someone will find a use for it. Number theory is one such branch of mathematics that was long thought to be pure mathematics that had no real world applications. It turns out, however, Internet security makes heavy use of encryption techniques that depend upon results in number theory.

Since 1986, April has been known as Mathematics Awareness Month. Each year a different theme has chosen and this year’s is Mathematics and Internet Security.

When you use your home computer to log on to your bank account and pay a bill, to buy a book from Amazon, or to buy or sell something on eBay, you assume your personal details--your social security number, your bank account access password, or your credit card number--cannot be read by an unauthorized third party. Mathematics, notably number theory, makes this possible. (Now if they can only find a use for a cat.)

For more information about Mathematics Awareness Month, visit http://www.mathaware.org.

I didn’t have any questions the past couple of weeks. It was like you all were on spring break or something. If you have any questions for me, don’t hesitate to send me an email at elvis@hope.edu.




I'm very good at integral and differential calculus, I know the scientific names of beings animalculous; In short, in matters vegetable, animal, and mineral, I am the very model of a modern Major-General.
Gilbert, W. S. (1836 - 1911)
The Pirates of Penzance. Act 1.