Since polynomials have been studied extensively for centuries, it is
difficult to find new polynomial problems that are elementary to state,
interesting to study, and do not require elaborate techniques to
prove. In addition, it is difficult to solve those that have been
open for centuries. In this talk we will concern ourselves with
one fairly new conjecture, "The Extreme Curvature Conjecture," posed by
Russell Gordon in 2004, and two very old conjectures: Pólya's
Monotonicity Conjecture" posed by George Pólya in the early
1900s, and "The Hawaii Conjecture" posed by Carl Friedrich Gauss in the
early 1800s. We will show examples supporting these conjectures
and discuss the research and progress that has been made in this area
of function theory. Time permitting, we will also provide a proof
of a special case of a Pólya conjecture.
Join
us for Tea on Thursdays before Colloquia
As part of our colloquium series, the mathematics department
will host a "tea" in the Reading Room (VWF 222) at 3:45 p.m. on
Thursdays before colloquia.
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. We encourage
you to be environmentally friendly by bringing a cup for beverages, but
we'll provide cups if you can't bring your own. Please join us
for tea on Thursdays before colloquia! It's a
great time to chat with the speaker, your professors and other
students!
Today in History
On September 19, 1648, philosopher and mathematician Blaise Pascal
confirmed the existence of a vacuum and the theory of atmospheric
pressure. Ironically, Decartes once wrote of Pascal, rather
cruelly, that "he has too much vacuum in his head." In addition
to his contributions to physics, Pascal made many
important advances in mathematics, including laying the foundations of
probability and determining binomial coefficients with what is now
known as "Pascal's triangle." Given its name, he may also have
invented the computer programming language
"Pascal," although rumors that he invented the Internet are almost
certainly false. To read more about Pascal, please visit:
To mark his place in the algebra book he is reading, Clint always folds
the
page as shown in the figure to the right so that the bottom-right
corner touches the opposite side of the same page. The pages of
the book are eleven inches wide. In terms of theta, what
is the exact length, in inches, of line segment labeled L?
Write your solution on a blank (or almost blank) page from your
favorite book
folded accordingly and drop it on the Problem of the Fortnight slot
outside Dr. Pearson's office (VWF 212) by noon on Friday, September
28. As always, please be sure to include your name, your math
class(es), and your professor(s) (e.g. I. M. Smart, Math 321, Professor
Moore-Smarter) on your solution.
Problem Solvers of the Fortnight
The barber has children ages 1, 6 and 6. Of the sets of three
natural numbers whose product equals 36, two sets have equal sums: {1,
6, 6} and {2, 2, 9}. Since the math professor could not determine
the children's ages by knowing the sum, their ages must have been one
of these two sets. The final clue that the youngest has blond
hair implies that there is a youngest, and hence the barber's children
must have ages 1, 6 and 6.
We were inundated with solutions this fortnight. Congratulations
to our problem solvers of the fortnight: Josh Borycz, Mark Lunderberg,
Josh Hedapohl, Jill Immink, Jeffrey Meyers, Ashley Gruenberg, Ryan
Johnson, Bryan McMahon, Katie Johnson, Devin Bonnie, Lauren Steel, Jeff
Minkus, James Daly, Eddie Helderop, Stephanie Pasek, Allison Pautler,
Brian McClellan, Jack Lepird, Nick Rebhan, Chelsea Miedema, Benjamin
Crumpler, Evan Ormiston, Chris Olds, Tiffany Day, Andrea Eddy, Kelsey
Ensz, Pam Rexius, Laura Schaedig, Dan Halma, Tracy Albus, Lucas
Johnson, Joel Blok, Mallory Chapman, Jake van den Berg, Kelly McGlynn,
Tim Boman, Anna Brandes, Layne Fowler, Ryan Sheets, Nicole Mulder,
Dayna Waters, Austin Castle, Clint Jepkema, Joel Mulder, Rachna
Goswami, Dirk VanBruggen, Wenfei Xue, Jenny Birkenholz, Ben Herrman,
Luc Leavenworth, Benjamin Lewis, Tung Nguyen, Zachary Mitchell, Meghan
Cook, Clare McCullough, Ben Bockstege, and Kelsey Bos! Thanks to
all who submitted, and keep those submissions coming!
Ask Elvis . . .
Dear Friends,
As some of you undoubtedly know, I had my second ACL surgery on Monday,
and I'm happy to report that the surgery went very well. Thanks
to the pain medication my vet prescribed, I seldom notice the
after-effects of the surgery -- except when the wind picks up on a
chilly day! My vet has assured me that I will be able to continue
my column, even while I'm recovering, so please send your math
questions to me at elvis@hope.edu.
Hope to hear from you soon!
I did check up email shortly before I went under the knife. Along
with 557 spam messages that accumulated over the summer, I did have one
real email. That, along with my answer, appears below.
Your pal,
Dear Elvis,
I don't know if you check your
email over the summer, but I have a question for you. My mom is
considering buying a corgi puppy. How do I convince her this is the
right thing to do?
Laura
Dear Laura,
If your mom wants an active and intelligent dog, then a Corgi is for
her. As you probably know, Queen Elizabeth II is often
accompanied by some of my fellow Corgis. If we are good enough
for the queen, we are probably good enough for your mom.
Corgis are also known for their herding ability. So if your mom
has a lot of sheep, goats, cattle, little kids, or cats that need
herding, a Corgi can do the job.
Thanks for you letter Laura!
Elvis Matteson Receives Janet Andersen Award
The first Janet
L. Andersen prize for excellence in mathematical and computational
biology was awarded
at MathFest 2007 to Andrew Matteson of Texas A&M University for his
work on “An Enzyme Kinetic Model
of Tumor Dormancy.”
Andrew is a
native Texan from Amarillo. He reports that he first became
interested in
abstract mathematics in third grade when he was fortunate to have a
mentor who de-emphasized
“practical knowledge” in favor of
questions without answers (the most valuable type) and fostered a
belief that everything should be
possible and knowable. His interest in
in mathematical biology stems from a research methods course he took
during his
freshman year. He says, “I believe there
is something beautiful about pattern formation from a disordered
state.
It is this idea that touches each of my projects and gives me real
pleasure in
this work.”
Outside of
mathematics, Andrew is active in anusara style yoga and lindy hop swing
dancing, and loves spending time outdoors . He has recently taken on
the project
of reading the thirteen volumes of Will
Durant’s Story of Civilization and reports
that he has “about 6000 years to go”. Andrew will
graduate from Texas A&M in 2008 and plans graduate study in
mathematical
biology.
Reverend Fathers, my letters did not
usually follow each other at such
close intervals, nor were they so long.... This one would not be so
long had I but the leisure to make it shorter.
~ Blaise
Pascal,
Lettres provinciales.
