Phil Huling of SLU to Give April 23rd Talk

Homeomorphic topological spaces have isomorphic fundamental groups. An obvious questionc is then: when must spaces with isomorphic fundamental groups be homeomorphic? That is, when is the fundamental group a complete invariant? Flat conformal deformation theory investigates this question in the case of hyperbolic orbifolds and further asks if we can describe what happens when the fundamental group fails to be a complete invariant. We will look at what is known about these questions and then we will discuss my recent work with cofinite Coxeter groups and the lattices that contain them. In particular, we are able to develop tools which give the deformation spaces of the reflective Bianchi groups.

Sylvia Carlisle to give April 16th Colloquium

A metric space X is a real tree if between any two points in X there is a unique arc, and that arc is a geodesic segment. An isometry on a real tree is hyperbolic if it has no fixed points. In this talk, I will discuss the continuous theory of real trees with hyperbolic isometries, and discuss the model companion for that theory. As time allows I will talk about some properties of this model companion.

Colloquium April 9th by Martz and Parwani

Andrew Mertz and Kamlesh Parwani showed how lottery number distribution could be analyzed using Mathematica. Frequency distributions showed definite anamolies regarding the random nature of the numbers selected in lotteries. But it is generally the case that the odds of winnning are so low that these anomalies can not lead to effective strategies for winning money.

On the other hand, using Mathematica to analyze stock market data, Mertz and Parwani showed that there are low risk stategies that can work.

Andrew Schultz of UIUC to Give Colloquium April 2nd

Linear algebra is often thought of as a gateway to the abstraction of modern mathematics, but it is also a discipline with a number of terrific real-world applications. In this talk we'll discuss some applications of linear algebra which we encounter in our day-to-day digital lives. Topics include Google's PageRank algorithm, image compression, noise filtering and - if time allows - mp3 compression.

53rd EIU Math. Ed. Conference set April 5th, 2010

Using Billiards in the classroom?

Using the equinox to find latitudes?

Social Justice and Dark Matter: What do they have in commmon?

Just how big is a trillion?

Interested? Attend the EIU Mathematics Education Conference and find out more

see

http://www.eiu.edu/~adulted/10MathConf.pdf

for more details.

Department to Host Geometry/Topology Day March 27:

The Eastern Illinois University Department of Mathematics and Computer Science will host a day of hour long talks in geometry and toplopogy on Saturday March 27th. The schedule follows:

9 am coffee

9:30 am Bruce Kitchens - IUPUI

The Dynamics of the Nash Map for 2 by 2 Games

11 am Kamlesh Parwani, EIU

Quasi-isometric foliations for partially hyperbolic diffeomorphisms

12 pm Lunch

2 pm Hong Kun Zhang U-Mass-Amherst

Spectral gap for the Markov operator of certain random billiards


3:30 pm Serge Tabachnikov, Penn St. U.

Pentagrama Myrificum, Old wine into new wineskins

Peter Andrews to Give March 26th Colloquium:

Peter Andrews will speak today on 'Well Behaved Matrices and Knotty Diagrams'. In particular, he will discuss how to compute the Khovanov invariant for various knots or not.

More Nerd Graffiti

Svetlana Butler to Give March 12th Colloquium

Abstract:

We would like to analyze what can be said about the large deviation behavior of martingales,approximate identities, and related operators. Given some sequence m_n of positive integers, and some sequence w_n of positive real numbers, and let the linear operators

T_n : L1(R) \to L1(R)

be either the dyadic Lebesgue derivatives or the dyadic martingale. We will prove positive and negative results concerning certain convergences related to these sequences and operators

Rick Anderson to Give March 5th Talk: Abstract follows

Mathematics educators have an ongoing concern with students' achievement and participation in mathematics courses. It is recognized that all groups of students do not have comparable access to mathematical opportunities or success in mathematics courses. Students in rural areas and small towns approximately one-fifth of US school-aged children are one such group whose mathematics achievement and participation have been tracked in recent decades. In this talk I will summarize the mathematics achievement of rural high school students in the US as it compares to students in non-rural areas. Then I will present results of rural high school students' mathematics course-taking drawn from data collected for the 2005 NAEP High School Transcript Study. I will conclude with a discussion of the implications of the results for mathematics teachers in rural areas.

Patrick Coulton to Give Feb 26th Talk on Colorings

Historians trace the origins of the map coloring problem to Francis Guthrie, a nineteenth century cartographer. Francis' brother, Fredrick, was a student of mathematics and so he naturally asked his brother whether it was known that only four colors were sufficient to color a geographic map of distinct regions. Fredrick passed the problem onto Augustus De Morgan who wondered whether a necessity for five colors could not be contrived.

It occurs that such a necessity and more exists on the torus as well as other well known surfaces such as the Klein bottle. We will investigate the coloring of maps on various surfaces and show that the topology of the surface plays an important role.

The colloquium will begin at around 4 pm in Old Main 2231.

Nerd Graffiti

Who am i?

a complex ol creature am i
O this negative radical guy
as i travel in fours
all out thru my pores
will flow my idenitie

Challenge of the Week

The Department sponsors a problem solving competition for undergraduates at the university with a new challenge each week or so. We will feature some of the old problems on this blog, but changed slightly. Here is an example

Suppose that we have two rational numbers whose sum is negative 9 times their product and the sum is also negative 16 times their quotient. Find the two numbers.

x+ y = -9(xy)

x+y = -16(x/y)

Find x and y.

Galperin to Continue with Talk on January 28th

Gregory Galperin will give a second lecture on the foundations of hyperbolic geometry today at 4 pm. This talk will concentrate on certain geometric constructions of Gauss, Lobachevsky and Bolya.

Nikolai Lobechevsky

Gregory Galperin to Give January 22nd Talk

In my talk, I will tell you how the three great mathematicians: the Russian N. I. Lobachevsky ( who first offcially published the whole concept of non-Euclidean geometry); the German Carl F. Gauss (The Prince of Mathematicians, who wrote about this modern geometry only in his letters); and the Hungarian J. Bolyai (whose new concept was published as an Appendix to his father's book on geometry) were simulatenously and independently creating a modern geometry quite different from Euclidean Geometry. See full abstract

Analyze This!

A Tall Tale?

Can you decipher this tall tale?

Keith Wolcott to Give Jan. 15th Talk

ABSTRACT: When you rinse out a container, you add a bit of water, shake it around, and then dump it out. Then you repeat this process until you are satisfied that it is rinsed well enough. There are many ways to do this. For example, you could use a lot of water and very few rinses or little water and many rinses. Or you could use more water for the first rinse (since it is dirtier at the start) and then use less water for subsequent rinses. What method is best? My calculus class and I enjoyed working out what is the most efficient way to achieve the optimum results for this problem. We will share the results in this talk.

A Simple Toothpick Puzzle

The object of this puzzle is to move exactly one toothpick to obtain a square.

From the Desk of Peter Andrews

Welcome to another term - the economy may be sputtering, but Mathematics and Computer Science motors on. It is hard for a Canadian not to be delighted by a cold snowy day like we had on Thursday. I trust a harbinger for good things to come this term! Unfortunately, there are a few worries to occupy our minds, but I will get to them in a bit.

First, we will have our usual opening day faculty meeting, but this time we really do have some business to take care of.

We have hired Allen Bryant, who many of you may know from one of his earlier incarnations as a graduate student, ACF, or undergraduate (second BS in Computer Science), to teach the courses Bert Reed had on her schedule before she made her retirement decision. He will be in the center tower with Karim, Chad, and Clay for the spring.

I am sure most of you read the President's email about the budget situation and many of you will have been following the discussions on the UPI listserve. This is clearly a fluid process. I will give you the best update I can on Monday (today).

There are new classroom computers in the OM 3110, 3010, and 3030. Let me know if you need a hand getting used to them or if they don't have software you need. If you plan on using them, you might check them out before your first class.

Happy New Year to all.

Happy New Year

Happy New Year to all of the EIU family and friends from eiumath.

To start the new year we propose a little riddle.

Two friends, both fond of disputes, are walking down the street arguing about who has the most money in their wallet, though out of sheer stubbornness neither is willing to divulge the amount of money they are carrying. They meet a friend along the way who agrees to check each wallet to see if the amounts are different.

After checking, the friend announces that one wallet has twice as much as the other. He then hands the wallets back and disappears. The two disputants realize that the wallets are identical and they are not sure whether they have the right wallets.

Then it occurs to them that by switching wallets the amount of money that each of the two friends expect to have would increase. Is this right? How is this possible? This is sometimes called the wallet game and is attributed to Maurice Kraitchik.

A note from our fearless leader Peter Andrews:

If you have been in the lounge this morning you will have seen the bread
laid out on the table as a reminder that our end-of-term party is coming
up this afternoon. I hope you will all be able to come by for at least
a short while and preferably a long while!

As you probably know, Bert Reed and Greg Ronsse are both retiring at the
end of this term. Greg has stated publicly that he will be back a few times
in the spring and that he would rather we held any formal recognition until
sometime in the spring. I'll keep you posted.

If there are any others of you planning to retire in the next 3 weeks,
please let me know!!

Take a whiff of the bread and come by the center tower at 4:00 to sample
each loaf -- and then some!!

Thanks for another term -- furlough free!! Happy Finals, Happy Grading,
and finally Happy Holidays.

Anyone within the sound of this message is invited to attend.

James Garfield's Proof of the Pythagorean Theorem

James Garfield, the 20th President of the United States, gave the following simple proof of the Pythagorean theorem



It begins by constructing the trapezoid with parallel sides of height a and b and with base a + b. The area is given by the base times the average height or

A = (1/2)(a+b)².

On the other hand, we may compute the area of the three nonintersecting interior (and necessarily right) triangles

A = (1/2)(ab + ab + c²),

where c is the hypotenuse.
Setting up the equation for the two equal area calculations we have


(1/2)(a² + 2 a b + b²) = (1/2)(2 a b + c²),

or
a² + b² = c².

Yevgenia Movshovich to Give December 4th Colloquium

Yevgenia Movshovich will give the final coloquium of the semester today.

A pdf abstract can be found on the department website
The talk will concern positive harmonic functions on Dirichlet domains.

Suhrit Dey to Give Friday November 13th Colloquium

Professor emeritus Surhit Dey will talk at 4 pm. Friday November 13th about stiff systems. The talk will attempt to explain certain natural phenomena of perception.

There Once was a Fellow Named Gauss

There once was a fellow named Gauss
whose scholarly peers could not grouse
of his genius elan
on which he had drawn
for his manifold curvature blouse

Scott Tichenor of the University of Illinois to Give November 6th Colloquium

Scott will give a short introduction concerning curves of constant width and provide examples. He will also show how to construct these curves.

Gregory Galperin Discusses Rational Dissection of Polygons

Professor Galperin discussed the problem of dissecting a pentagon using the diagonals as shown.


The first question is whether the areas a1,a2,...,a10 taking rational values implies that the area a11 is a rational number. The answer is that it does. But more surprisingly, we need only a1,a2,...,a9 to take rational values in order to imply that the areas a10 and a11 take rational values.

Professor Galperin was able to show that it is only necessary that 5 consecutive triangles have rational areas in order to show that all of the dissected areas are rational for the pentagon. In addition, he indicated how the result generalizes.