EIU Parallelogram

Catherine Kruger Presents at AMS-MAA Conference

2012-01-10T09:39:00.000-08:00

Recent graduate Catherine Kruger gave a presentation at the Joint AMS-MAA-SIAM meeting the past week on Friday January 6, at 9:30 am in the Special Session on Research in Mathematics by Undergraduates and Students in Post-Baccalaureate Program. The presentation was in the
Back Bay Ballroom A, 2nd Floor, Sheraton in Boston Massachusetts.

The title of the talk was On Rosa-type labelings of directed graphs. Collaborators included Saad El-Zanati, Illinois State University and Jessica Klister, University of Wisconsin La Crosse.

Talk By M. Lassak and P. Wiles Today

2011-11-11T05:55:00.000-08:00

ABSTRACT

GeoGebra is a completely free, Java-based tool that gives you the power of Geometer’s Sketchpad, along with sophisticated algebra and spreadsheet packages. Additionally, this tool provides a simplified format for creating web-based applets that one can run with only needing Internet access and Java. You do not even need GeoGebra installed on your computer! We will share some features of the program (including exporting options for LaTeX, including TikZ) along with some applets we have created for classes.

Interpret the Hieroglyph

2011-11-10T09:24:00.000-08:00

Glazebrook to Talk on “La Belle E ́poque of ODEs” Today

2011-10-28T13:08:00.000-07:00

Abstract follows:

Following extensive developments in the theory of differential equations due to Sturm, Liouville, Abel and others, there was a further surge in activity toward the end of the nineteenth century that created substantial breakthroughs into other areas of mathematics. Much of this was inspired by the French school(s) centered around H. Poincare and E. Picard who took the theory of DEs into the realm of algebraic geometry and topology, thus creating an area of mathematics studied to the present day. Prolific contributors at that time included Fuchs, Schlesinger, Garnier, and Painleve (the latter was the French Prime Minister 1917, 1925).

In much of this work one discovers the ubiquitous ‘tau-function’, most notably in Painleve’s theory of transcendents’ which I will briefly discuss in the context of second order nonlinear ODEs. This is a topic that continues to have far-reaching consequences in mathematical physics (wave equations and ‘integrable systems’), algebraic geometry and representation theory. There is also a remarkable geometric-functional analysis slant to this theory which can be studied within the framework of ‘Convenient Geometry’, about which I will provide some background and some explanation, and reveal that ‘tau’ actually possesses a startling geometric property.

Galperin Talk Today: Billiards bouncing in gravitational field.

2011-10-21T10:46:00.000-07:00

Assume that there is a collection of semi-circles of diameter 1 in the upper half plane centered at the integer points (n,0) on the x-axis. A released billiard ball falls down under the vertical constant gravitational force g. The ball bounces off the semi-circles according to the billiard law and describes a trajectory γ. Record the indices of the semi-circles the ball hits as a sequence

ω = (ω1, ω2, ...),

which we call the one-sided itinerary of the trajectory γ. We will investigate this dynamical system.

A Proof By Any Other Name ...

2011-10-19T12:48:00.000-07:00

there once was a lady logician
whose trade was still liquor production
as her batch made its rounds
thru vast coil surrounds
she claimed it a "proof by induction"

More graffiti

2011-10-13T08:41:00.000-07:00

Where there is number there is beauty

2011-10-12T10:42:00.000-07:00

So said Proclus, a Greek geometer who wrote a commentary on
geometry and lived from about 412 to 485 AD.

Escher and Bach

2011-10-07T10:11:00.001-07:00

William Green to Talk in Colloquium Today

2011-10-07T05:05:00.000-07:00

Title: Schroedinger Equation in Dimension Two ...

In this talk we will discuss some recent research on mapping
properties of the Schroedinger operator in dimension two. The
majority of the talk will be discussing background issues
needed to understand these new results. See also

Math Talks

Fermat's Last Thing on the To Do List

2011-10-06T12:36:00.000-07:00

Should I write the whole proof in the margin or what? ...
It's clear isn't it? ...
Oh well, I'll do it tomorrow...
Que sera sera.

Job Fair Today

2011-09-21T08:09:00.001-07:00

Career Services is hosting several employers today so put on your best and hustle over and attend the job fair from 10 am to 2 pm in the Grand Ballroom. See

Job Fair

More Sad News

2011-09-20T08:51:00.000-07:00

Ferrel Atkins long time coordinator of the Computational Mathematics program at EIU died this last week. Ferrel received his Bachelor of Science degree from EIU in 1945 and his doctorate from the University of Kentucky in 1950. He was an active and ardent member of the Democratic Party. Ferrel was also devoted to nature and worked each summer as Ranger Naturalist at Rocky Mountain National Park in Estes Park, Colorado, where he became the Park Historian. Ferrel was 87 years young. See

Ferrel Atkins

Woalf

2011-09-15T09:36:00.000-07:00

Wolfram Alpha is a great tool for teachers and students.

1. it is free and available through any internet/web connection

2. it attempts to parse input rather than require computer language-like syntax
(this can be a + or a - but if you use Mathematica syntax you can usually get what you want).

Check it out at

woalf

Click on the ABOUT link for a tour of woalf

September 16, 4:00 pm: If This is Alpha – What is Beta?

2011-09-12T08:14:00.000-07:00

Speakers: Peter Andrews, Patrick Coulton and Marshall Lassak
Old Main 2231

Over the centuries, tools such as slide rules, calculators, computer algebra systems and dynamic geometry software have provided new ways for us to make computations or view mathematical results. They have also forced us, at times, to think long and hard about how and what we teach. While it can address much more than computational or symbolic mathematics, Wolfram Alpha is another such tool. This is a web based technical answer/search engine accessible to everyone (and that includes students!) with an internet connection. Often the results from Alpha are superior to graphing calculators or computer algebra systems. Alpha is a computer algebra/calculus/statistics system and solves a variety of mathematical problems. It is relatively easy to use and has very good online help. We will demonstrate some of Alpha’s capabilities and hope to provoke a discussion of its usefulness and/or pitfalls for how our students might do their homework, how they can best learn mathematics, and how we might need to rethink our teaching and testing.

College of Sciences Meeting

2011-09-08T09:15:00.001-07:00

College of Sciences Faculty and Staff College Meeting to be held Thursday, Sept. 8, 2011, from 3:30 p.m. - 4:30 p.m. in the Phipps Lecture Hall (Room 1205, Physical Science Building).

On Facebook

2011-08-29T09:15:00.000-07:00

The department is developing a site on facebook to make it easier for students and others to connect with the department. The facebook url is

http://www.facebook.com/pages/EIU-Math/270256819652847

More Sad News

2011-08-29T07:58:00.000-07:00

It seems that each new semester makes us the bearer of bad news. This summer former department Chair Clare Krukenberg passed away at his home in Charleston. Clare was an avid Bridge player and competed in tournaments throughout the Midwest. He was a soccer referee at the high school and youth levels for many years.

He was generous with his time with students and faculty and was very popular as a teacher and academic adviser. He loved to go fishing in the North Country each summer with a close group of friends. He was a supporter of local drama and enjoyed sponsoring trips to The Little Theater on the Square in Sullivan.

Professor Wesley Calvert of SIU speaks on Proofs

2011-04-13T12:59:00.000-07:00

Professor Wesley Calvert spoke on the topic 'How is a Proof Like a Function' at the Department Colloquium on April 1. No really he did! The abstract follows:

Mathematics seems to have quite a lot to do with functions; see how many mathematics courses are, implicitly, or explicitly, about functions. We mathematicians are also rather fond of proofs.

Proofs are the gold standard of what it means to have conclusively solved a mathematical problem. More recently, mathematicians have also been very interested in computers.

These three things (just a few of our favorite things) — functions, proofs, and computer programs — are related in very deep ways. In a sense, we can think of them as different forms of the same objects. I’ll tell you how this is so.

Gordon Discusses The Continuum Hypothesis.

2011-04-13T12:52:00.000-07:00

Professor Evgeny Gordon spoke in the department colloquium on February 18th and 25-th the abstract of the talk follows:

L.V. Kantorovich, who is mostly known for the discovery of Linear Programming, was also an outstanding expert in functional analysis. He introduced and investigated conditionally order
complete vector lattices that are known in Russian mathematical literature as Kantorovich's spaces (K-spaces).

He came to these spaces in early 30's guided by the idea to find vector spaces that have as many properties of the field of real numbers as possible. At that time this problem couldn't be written in formal mathematical terms.

In the middle of 60's P. Cohen proved the independence of CH. The method of forcing that he developed for this problem was later rewritten in terms of Boolean-valued models of set theory by D. Scott and R. Solovay. In the middle of 70's I proved that Boolean-valued models of the field of real numbers are exactly the universal K-spaces. This fact did not only give a rigorous mathematical formulation to the problem of Kantorovich, but also allowed to transfer many properties of real numbers to K-spaces. In particular, it allowed generalizing a lot of theorems about linear functionals on operators with the values in Kantorovich spaces.

Many results in this area were obtained by functional analysts from Novosibirsk.

Galperin Talks on the Dynamics of Continued fractions

2011-04-13T10:57:00.000-07:00

Professor Gregory Galperin spoke on the dynamics of continued fractions in the departmental colloquium on March 4th. Professor Galperin discussed various results due to Gauss, Kuzman, Bykovskij and Arnold.

Galperin's Talk on Invisible Objects

2011-02-24T08:52:00.000-08:00

Gregory Galperin recently gave a talk in the colloquium series about invisible objects. These objects are typically invisible in one direction in the sense that light flows around the object and not through it. We give here an example of such an invisible object.

Can you show that light from infinity (parallel rays) flow around the object as shown if the base angles of each isosceles triangle is 30 degrees?

Gordon to Speak on the Continuum Hypothesis

2011-02-18T08:33:00.000-08:00

From the abstract:

In the middle of 60's P. Cohen proved the independence of CH. The method of forcing that he developed for this problem was later rewritten in terms of Boolean-valued models of set theory by D. Scott and R. Solovay. In the middle of 70's I proved that Boolean-valued models of the field of real numbers are exactly the universal K-spaces. This fact did not only give a rigorous mathematical formulation to the problem of Kantorovich, but also allowed to transfer many properties of real numbers to K-spaces. In particular, it allowed generalizing a lot of theorems about linear functionals on operators with the values in Kantorovich spaces.

Many results in this area were obtained by functional analysts from Novosibirsk. However, this method did not become popular among specialists in analysis, since it requires a deep knowledge of mathematical logic, especially of the axiomatic set theory.

Recently, I found an exposition of this method that seems to me quite accessible for non- specialists in mathematical logic. I will try to explain the basic ideas of this method (including the idea of the independence proof of CH) in two consecutive talks.

Galperin to Give Feb 4 Colloquium

2011-02-04T08:14:00.000-08:00

Gregory Galperin is slated to give the Friday colloquium this week. His topic is

A Geometric Problem That Leads to the Billiard Law of Reflection

Abstract:I will show some examples of "invisible geometric objects." This means that light bends around an object, causing it to become as it were invisible. The Billiard Law of Reflection, which states that the angle of reflection equals the angle of incidence, will play a crucial role. The main examples will concern billiard reflection for ellipses and hyperbolas.

Maxwell's House

2011-01-28T07:58:00.000-08:00

There once was the physicist Maxwell
whose theories of light didn't wax well
lo, equations he found
with a d little round
by checking his E & M facts well

Newton's Fall

2011-01-26T12:06:00.000-08:00

There once was a fellow named Newton
who sat neath a pear tree bout noon-time
his head was then hit
by the fruit not the pit
which forced him to gravitate sublime

More grafitti

2011-01-26T08:45:00.001-08:00

A Supertask Puzzle

2011-01-21T08:36:00.000-08:00

A supertask is a countably infinite sequence of tasks to be performed in order, say

{T₁,T₂,T₃,...}

such that we first perform task T₁ and then task T₂ and so forth.

As an example one might consider the case of Zeno's Paradox where an arrow is shot at some target. The arrows first task is to complete the journey half way to the target. The second task is to complete the remaining journey half way to the target and so on.

Now consider the case of Jon Perez Laraudogoitia's beautiful supertask: There are a sequence of unit point mass balls stationary at x=1/2,x=1/4,x=1/8 and so on. A unit point mass at x=1 and time t=0 is moving with a velocity of 1 unit per second to the left (i.e. toward x=1/2).

We assume that there is an elastic collision at x=1/2 and so the moving ball is left stationary at x=1/2 and the ball at x=1/2 moves with velocity 1 unit per second in the direction of the ball at x=1/4. It is clear that at t=1 all the balls have been hit by the preceding ball.

Assuming that all the collisions are elastic and behave in exactly the same manner as the first collision, is there a ball that passes through x=0?

Sage Advice to be Given Jan. 14th

2011-01-12T08:20:00.000-08:00

Patrick Coulton will give the first colloquium talk of the spring semester Friday January 14th. The topic will be "An introduction to using Sage".

Sage is a computer algebra system which is free and open source.
The talk will center on applications to the college classroom.

See the department website for more details.

A Philosophical Conudrum

2011-01-12T08:12:00.000-08:00

If a tree falls into a black hole does it make a sound?

News from the Mathematics Castle

2011-01-12T07:52:00.000-08:00

The new semester (spring) has begun. Classes started January 10th.
Andrew Mertz and family provided treats in the department lounge
to help start us off on the right foot.

Peter Andrews, Sylvia Carlisle and William Green attended the
joint AMS/MAA conference in New Orleans.

Peter was particularly disappointed in the beautiful weather
since the weather afforded no opportunity to play hockey.

The department will host a low dimensional topology conference on
March 26th. See the department website for more details.

Semester Update (News from Old Main)

2010-12-13T06:50:00.000-08:00

The semester has flown by and like the proverbial bee we have been busy.
The Department has been sadden with the loss of our one time Chair
Alphonso (a.k.a Dr. D) DiPietro and Llyod Koontz.

We are now in the midst of Final Exams and we look forward to a
little break from the classroom routine.

The department held its holiday party on Friday December 10th after classes. Some 7 loaves of bread were consummed as well as a variety of treats.

The Comerford's hosted a holiday party for the math majors this past Saturday
December 11th. The highlight of the party was a game of departmental trivial pursuit.

The colloquium committee hosted several talks this semester including two lectures from outside the department ending with a delightful talk on boids and other animation curiousities by Professors Van Cleave and Mertz.

Once again the departments majors participated in the Putnam Exam December 4th. The exam preparation is headed by Keith Walcott.

Fall Semester

2010-08-31T07:22:00.000-07:00

Well, the fall semester is upon us which leaves us wondering what happened to all those lovely 100 degree August days with 90 per cent humidity. The temperatures are down and the humidity too and classes have begun. Some old faces are missing and that makes us a little sadder, but there are new faces and new challenges. Good luck to all and have a good semester.

Phil Huling of SLU to Give April 23rd Talk

2010-04-23T13:06:00.000-07:00

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

2010-04-16T12:44:00.000-07:00

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

2010-04-14T11:16:00.000-07:00

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

2010-04-02T08:51:00.000-07:00

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

2010-03-26T08:11:00.000-07:00

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:

2010-03-26T06:48:00.000-07:00

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:

2010-03-26T06:45:00.000-07:00

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

2010-03-24T11:33:00.000-07:00

Svetlana Butler to Give March 12th Colloquium

2010-03-10T08:20:00.000-08:00

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

2010-03-05T13:36:00.000-08:00

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

2010-02-26T05:49:00.000-08:00

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

2010-02-15T08:57:00.001-08:00

Who am i?

2010-02-11T10:50:00.000-08:00

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

2010-02-05T06:25:00.000-08:00

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

2010-01-28T07:01:00.000-08:00

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

2010-01-22T11:13:00.000-08:00

Gregory Galperin to Give January 22nd Talk

2010-01-22T09:40:00.000-08:00

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!

2010-01-17T14:21:00.001-08:00

A Tall Tale?

2010-01-16T12:52:00.000-08:00

Can you decipher this tall tale?

Keith Wolcott to Give Jan. 15th Talk

2010-01-14T07:17:00.000-08:00

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

2010-01-13T07:57:00.000-08:00

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

From the Desk of Peter Andrews

2010-01-11T08:35:00.000-08:00

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

2010-01-02T10:40:00.000-08:00

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:

2009-12-11T10:56:00.000-08:00

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

2009-12-08T09:03:00.001-08:00

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

2009-12-04T10:58:00.000-08:00

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

2009-11-12T07:31:00.000-08:00

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

2009-11-05T11:26:00.000-08:00

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

2009-11-04T14:08:00.000-08:00

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

2009-11-02T08:06:00.000-08:00

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.

Professor Galperin to give October 30th Colloquium

2009-10-30T12:40:00.000-07:00

Gregory Galperin will give the Friday afternoon colloquium this week.

He will discuss the dissection of polgons. In particular, if you dissect a polgon using the diagonals and the triangular pieces have rational area, what can be said of the inner piece?

Darin Johnson Gives Lecture on Rook Polynomials

2009-10-26T09:08:00.000-07:00

The rook problem is related to the number of nonattacking rooks that can be placed on a Ferrers Board. A Ferrers board is a board in which the number of cells in a column is always nondecreasing from left to right until it terminates. A rectangular board is a simple example of a Ferrers board.

Dr. Johnson showed how the Rook problem on the Ferrers board generates various polynomial coefficients which are in turn related to several examples of well known number sequences in mathematics and combinatorial number theory.

It's How One Sees The World

2009-10-23T09:20:00.000-07:00

An Area Restaurant?

2009-10-22T07:39:00.001-07:00

Gina's Pies Are Square Restaurant in Wilton, Wisconsin. Does this mean that cornbread are round?

The reference is to the old joke about the hayseed helping his son with his homework. He asks his son for the area of a circle and his son responds with Pi R squared to which his father replies,
No, no, son, pie are rounded, cornbread are squared.

Dr. Darin Johnson to Talk at October 23rd Colloquium

2009-10-20T09:28:00.000-07:00

Darin Johnson (EIU B.S. Comp. Sci. and M.A. Mathematics graduate) will give the October 23rd colloquium talk. He will discuss the Generalized Rook Problem.

Newtonian Mechanics?

2009-10-19T14:13:00.000-07:00

Despite the image of Issac in overalls, Newtonian mechanics is not so much about fixing automobiles as it is about how automobiles move in space. Issac Newton laid down the basic principles of motion. Namely, 1) a body in motion tends to stay in motion unless acted upon by an outside force, 2) the applied force is equal to the mass times the acceleration, 3) for every action there is an equal and opposite reaction.

..and when the teacher told Tommy to write a sentence about Issac Newton, Tommy wrote I sack a new ton of potatoes every day.

Professor Delman's Friday Colloquium

2009-10-19T14:04:00.000-07:00

Professor Delman gave the department colloquium talk on October 16th. The talk concerned some recent work by Lenhard Ng. Professor Ng uses the connected paths between pairs of points on a knot to construct formal polynomial rings. Equivalence classes for certain topological operations are introduced which produce the so-called Cord Ring. Professor Delman indicated how one could compute the Cord Ring for certain kinds of knots such as those that can be constructed on the surface of a torus

Charles Delman to Talk on Knots at October 16th Colloquium

2009-10-15T10:04:00.000-07:00

Lenhard Ng introduced a knot invariant in 2005 called the cord ring invariant. Professor Delman will discuss the properties of this invariant and some work in progress.

October 2nd Colloquium by Peter Andrews

2009-10-15T07:05:00.000-07:00

Peter Andrews gave the colloquium talk on Friday October 2nd at 4 p.m.

The purpose of the talk was to introduce the faculty to a new package of free software called Geogebra which can be used for geometric demostrations.

An example of its use was given by showing that every conic section could be defined as the set of points equidistant from a fixed point and a moving point on a circle (including the circle at infinity, i.e. a straight line).

Professor Andrews also discussed Archimedes' measurement of the ellipse and parabola using Geogebra to demonstrate certain relations not easily obtained.

We're Off Like a Herd of Turtles

2009-10-15T07:00:00.000-07:00

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