Mathematics Department
Senior Capstone Colloquium
TUESDAY, APRIL 26th
11:30-1:00
Science Center 200
Food service starts at 11:20; talks promptly at 11:30!
Wavelet Methods for Edge Detection
Tessa Thorsen
Edge detection is an integral part of image processing, as it allows us to locate objects and features within an image. While
simple methods of edge detection are computationally fast, they can be very sensitive to noise or orientation of an image
and may not be able to differentiate between different types of edges. More complex methods of edge detection have
therefore been developed to mitigate these problems, many of which utilize wavelet functions. This talk will explore
several different wavelet-based methods of edge detection, and examine the results of applying these methods to different
images.
Analyzing Swimming Records: Are People Getting Faster in the Pool?
Tyler Gould
Since its international debut in the 1896 Olympics, competitive swimming has dramatically
increased in popularity. While more competitors have entered the sport, more talent has been
brought to the pool and world records have been broken multiple times in every event. While
talent plays a large role, it is not exactly a measurable quality. This aside, the question remains:
will humans get faster forever? Will world records always be broken? During
this talk, we will discuss statistical analysis tools such as
Chebyshev’s inequality, as well as a recursively defined function,
that were used in order to calculate probabilities to prove or
disprove our central equation regarding swimming as well as other
applications: If we have data on N attempts on a record, and we know
how many record breaks occurred in those N attempts, how likely is it that
all N attempts were independently drawn from the same distribution?
Why is a Regular 13-gon not Constructible?
Xiaotong Zou
Euclidean Constructions consist of only straightedge and compass. With a straightedge
and compass, constructions like bisecting an angle or a line segment, construct lengths
based on a given length, copying an angle... etc. are easily done. With all these methods
available, one may ask, how do we construct a regular polygon? Which regular
polygons are constructible? We will explore the properties of regular polygons and
prove the famous Gauss Theorem which says that for a regular n-gon to be
constructible, n has to be the product of powers of two and distinct Fermat primes.
Solving Hashiwokakero as a Constraint Satisfaction Problem
Angelica Klosky
Hashiwokakero is a puzzle game where islands in a grid should be connected by
a series of bridges. Though the requirement of creating a connected graph
has previously inspired path-finding focused approaches, Kirchhoff's matrix
allows an algorithmic test for spanning trees. Using constraint satisfaction theory,
the bridges may be modeled as a series of variables in a system of equations that
is easily solvable by row reduction. A Java program will iterate through
these matrices to return all possible solutions for a given Hashiwokakero puzzle.
Chebyshev
in contemplation