Department of Mathematics and Statistics
UMKC (University of Missouri - Kansas City)
Expository Talks Series, and
Video/Film Series
Semester: Fall 2008 - 21st Year
Location: Haag Hall, Room 309 (unless otherwise indicated below)
Day & Time: Friday, 4-4:50 pm (talks), 4-5:00 pm (videos)
Campus Map for Talks (PDF Format)
Contact: Richard Delaware,
delawarer@umkc.edu
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Dates, Titles, Speakers (with Abstracts & Posters as available)
Friday Oct. 3
No Talk;
Go to the Kansas City Regional Mathematics Technology EXPO
at Rockhurst University all day today, and tomorrow!
[Preregistration is FREE to all UMKC faculty and adjunct faculty (and just $5.00 for UMKC conference walk-ins); registration is only $15.00 for any student.]
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Friday Oct. 10
Expository Talks Series
Describing the Linear Structure of Space by its Metric (Distance) Structure:
The Mazur-Ulam Theorem
Daniel Fresen, Mathematics, University of Missouri - Columbia
[CLICK on poster image to download poster. Pass it on!]
[Campus Map for Talks (PDF Format)]
Consider three points A, B and C in Euclidean space, with B between A and C.
We can express this as: B = tA + (1 - t)C, where t is in (0, 1), meaning B is a convex combination (weighted average) of A and C. This character-
ization of betweenness is purely linear (algebraic) in nature. However, there is a
second characterization of betweenness based purely on metric structure (involving distances).
Bis between A and C if and only if:
d(A,B) + d(B,C) = d(A,C)
where d(X,Y) denotes the distance between two points X and Y. We take
advantage of this equivalence to show that in the context of Euclidean space (and
more generally, strictly convex Banach spaces), an isometry (a rigid transformation,
one that preserves distances) is affine (preserves convex combinations). This is very
powerful, since an affine transformation is linear if and only if it sends 0 to 0 (and
linear mappings are fundamental to mathematics).
This result (the Mazur-Ulam Theorem) is one of the starting points of nonlinear functional analysis. It tells us that the linear struture of a Banach space is completely determined by its metric structure.
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Friday Oct. 17
Expository Talks Series
From Isosceles Triangles to Pythagorean Triples and Arctangent formulas for Pi:
Some Explorations in Elementary Geometry
Truett Mathis, Mathematics, William Jewell College (retired)
[CLICK on poster image to download poster. Pass it on!]
[Campus Map for Talks (PDF Format)]
This talk begins with the statement of a reed-bending problem that could be as old as time. The solution is easy, but the implications run deep. It speaks to one of life’s persistent questions: What is the value of Pi? The talk will begin with a hands-on approach (the reed), then move to a special geometric case, followed by uses of Euclidean geometry, algebra, trigonometry, a scientific calculator, and finally reference to an inverse trigonometric series from Calculus. We’ll start in a field of reeds and end up on the moon.
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Friday Oct. 24
Expository Talks Series
A Mathematical Look at Elections
Nick Baeth, Mathematics, University of Central Missouri
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[Campus Map for Talks (PDF Format)]
In 1952, Mathematician Kenneth May proved that when there are exactly two candidates there is only one election procedure which satisfies certain reasonable properties. However, as soon as a third candidate is thrown into the mix things become much more complicated. In fact, Economist Kenneth Arrow proved in 1950 that when there are three or more candidates there are no voting procedures which satisfy certain reasonable properties. In this talk we will carefully define these reasonable properties and determine which are satisfied by several voting methods that are used throughout the world. We will conclude with a proof of a weak version of Arrow's Theorem and a list of what we should do in face of this negative result.
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Friday Nov. 7
Expository Talks Series
On the visibility of lattice points
Neil Nicholson, Mathematics, William Jewell College
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[Campus Map for Talks (PDF Format)]
Imagine a military school’s graduation. The graduates march into an open field in perfect formation, forming an r x s lattice. Outside of this rectangular arrangement, parents snap photos of their children. Obviously, to take a picture of their child their straight-line view of their child cannot be interrupted by any other graduates. In particular, there’s a professional photographer who wishes to photograph every member of the graduating class. Is there a position he can stand in order to view each graduate? If so, how close of a point can we find? We will explore this idea more specifically, dealing only with lattice points. We’ll show that there is indeed such a point and put bounds on just how close that point may be.
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Friday Nov. 21
Expository Talks Series
Two (yes two!) Short Talks by Students from Mathematics
[Please come and support our students.]
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[Campus Map for Talks (PDF Format)]
(1)
In Calculus you know that a continuous function
with zero derivative everywhere on [a, b]
must be a constant function.
But, is "everywhere" necessary? Yes!
A Continuous Function with zero derivative "almost everywhere" on [0, 1]
which is nevertheless strictly increasing there!
Dan Krulewich, Mathematics Student, UMKC
[Math 402, Advanced Analysis I]
(2)
Using Combinatorial Games (like Dominoes!)
to prove 1/2 + 1/2 = 1
James Slaughter, Mathematics Student, UMKC
[Math 490, Numbers & Games]
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