Mathematics
Contact
Department Chair:
Susan Jane Colley

Department Email:


Phone: (440) 775-8388
Fax: (440) 775-6638

Location:
10 N. Professor St/King 205

Oberlin, OH, 44074

Fall 2012

Fall 2012
 

September 13 -- Student/Faculty Pizza Luncheon
"Water Quality Monitoring In Maryland's Tidal Waterways"
Chris Rackauckas '13
12:15 in Wilder 115

 

The Chesapeake Bay and its surrounding tributaries house over 3,600 species of plants and animals. In order to assess the health of the region, the Maryland Department of Natural Resources (DNR) monitors various parameters such as dissolved oxygen in monitoring stations located throughout the tidal waterways. Utilizing data provided by the DNR, our team assessed the bay for areas of water quality concern. We analyzed the percentage of the readings that failed to meet the threshold values for a given parameter and used the Wilcoxon Signed-Rank test to determine the statuses of the stations. In order to assess the applicability of the Wilcoxon test given the positive skew in the data, a simulation was performed. This simulation demonstrated that log-transforming the data prior to performing the Wilcoxon test helped reduce the Type I Error. Furthermore, our team ranked the stations using a set of different multiple comparison methods (a version of the Tukey’s Test on variance-transformed proportions, the Bonferroni adjustment method, a Bayesian method, and the Benjamini-Hochberg rejection method) and found that the Benjamini-Hochberg method produced the most useful results. Lastly, we conducted a trend analyses for the five stations in the Corsica River. To aid in the presentation of our analyses, we constructed an interactive GUI (Graphical User Interface) for use by the researcher and the general public.

 


October 11 -- Student/Faculty Pizza Luncheon
"Name that Mathematician!"
Jack Calcut
12:15 in Wilder 115

Come enjoy free pizza and play "Name that Mathematician".  Theorems will be stated from several
branches of math.
Candy will be awarded.
Help the students defeat the faculty.


November 8 -- Student/Faculty Pizza Luncheon
"Building good theories of human behavior requires getting the math right"
Joshua Hartshorne '02
12:15 in Wilder 115

  To have a precise scientific theory of any domain, you need a mathematical language capable of
expressing the theory.  It is no accident that calculus and Newtonian physics were discovered at the
same time - and not just because Newton discovered both.  You cannot do Newtonian physics
without calculus.

Over the last 60 years, psychologist, linguists, and computer scientists have struggled to find the
right math for describing human behavior.  This history is punctuated by the periodic arrival of new
mathematical and computational tools; while none have (so far) proved sufficient, each has moved
us closer to our goal.  In this talk, I (briefly) describe (some of) the computational/mathematical approaches
that have been taken, focusing particularly on the recent wave of Bayesian generative models that
have been transforming psychology, and the challenges in creating and using those models.

 

 


 

December 6 -- Student/Faculty Pizza Luncheon
"Pursuit-Evasion in Polygons: When Can Two Cops Win?"
Claire Djang -- Math Major
12:15 in Wilder 115

Motivated by applications in robotics, we study pursuit-evasion in polygonal environments with polygonal holes. In this turn based game, a robber R is pursued by one or more cops C1, C2, C3, etc. The players have full information about the environment and the other players. The cops can coordinate their actions. On the cop turn, each Ci can move to any point within the environment at distance ≤ 1 from his current location. The robber moves similarly on his turn. The cops win if some cop becomes co-located with the robber in finite time. The robber wins if he can evade capture forever.

It is known that one cop can capture the robber in any simply connected environment, and that three cops are sufficient in any environment with holes. We study environments with a winning strategy for two cops. We focus on monotone cop strategies, where the area available to the robber decreases monotonically in each round. Drawing on ideas from both graph theory and computational geometry, we use the polygon dual to give an O(n^2) algorithm to determine whether a given environment has a winning two-cop sweeping strategy. This characterizes a large set of polygonal environments that are winnable by two cops. We also give general conditions for the existence of a monotone 2-cop strategy, and describe how to construct a winning strategy.