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Colloquium: Discovering the missing piece: 4-connected, 4-regular, claw-free graphs of odd order

On Tuesday, February 22 at 4:45 in Napier 201, mathematics majors Trevor Gionet '12 and Yixiao Sha '12 will speak about their summer research experience last summer. In 1995, Plummer published a paper in which he gave a characterization of the 4-regular, 4-connected, claw-free graphs. Based on that work, he and Hartnell published a paper on 4-connected, claw-free, well-covered graphs a year later. However, in his 1995 paper, Plummer inadvertently omitted some of the graphs with odd order. Last summer Trevor and Yixiao were working on a related question under the direction of Prof. Erika King when they discovered this omission. Together they completed Plummer's characterization of all 4-connected, 4-regular, claw-free graphs, and then showed the implications this has on the well-covered graphs he and Hartnell determined. In addition, they characterized the 4-connected, 4-regular, claw-free, well-dominated graphs. The talk will be exploring the route they took to these findings. In addition, Yixiao will share her experiences presenting their work at the Nebraska Conference for Undergraduate Women in Mathematics in January. (Refreshments will be served beforehand.)

Posted 1 March 2011

Colloquium: The Wide World of Mathematical Biology

The first departmental colloquium of the Spring 2011 semester will be Prof. Jonathan Forde speaking about his research. He will present a talk on Wednesday, February 9 at 4:00pm in Gulick 206A. After a brief introduction to what mathematical biology is and why it is a growing area of active research, Forde will present preliminary results from some of his current research projects: immune therapy for HIV, treatment of hepatitis delta virus and the ecology of plant-herbivore-carnivore systems. He will also give a preview of the upcoming summer research program on modeling infectious disease. (Refreshments will be served beforehand.)

Posted 1 March 2011

Putnam Exam 2010

Four HWS students participated in the 2010 Putnam Competition. Math majors Justin Dotzman '11, Yaoxin Liu '12, Shaun Viguerie '12, and Zhiyou Cao '12 took the six-hour Putnam exam on Saturday, December 4.

The results from the exam will be published in March.

Posted 1 March 2011

Math in the News: Four Are Awarded Medal in Mathematics

The Fields Medals, often considered the most prestigious awards in mathematics, have been given to four mathematicians in diverse areas of research. See this article that appeared in the New York Times.

Posted 1 March 2011

Department Prizes

Each Spring, the Department of Mathematics and Computer Science awards several prizes to recognize students for their academic achievements. The prizes for 2010 went to the following students:
  • The Robert L. Beinert Prize, awarded to a graduating Senior to recognize excellence in Mathematics, to Christine Luongo '10 and Katelyn Tyson '10.
  • The John S. Klein Prize, awarded to a graduating Senior to recognize excellence in Computer Science, to Joshua Davis '10, Robert Hendry '10, and Sara Young.
  • The Abigail Mosey Prize, awarded to a graduating Senior or generosity in helping others to learn and appreciate mathematical ideas, to Lisa Maticic '10.
  • The Catharine Adele Rippey '35 Prize, awarded to a William Smith student to recognize excellence in Mathematics, to Katelyn Tyson '10 and Christine Luongo '10.
  • The William Ross Proctor Prize, awarded to the William Smith students who have achieved the highest rank in mathematics in their first two years at the Colleges, to Jing Luo '12 and Marcela Melara '12.
  • The Irving Bentsen Prize, awarded to the second year student at Hobart College who has the most outstanding record in mathematics and computer science, to Yaoxin Liu '12.

The Department also nominated six seniors for student membership in the Sigma Xi Scientific Research Society: Joshua Davis, Robert Hendry, Alexander Kridler, Christine Luongo, Katelyn Tyson, and Sara Young.

We also note that the following Mathematics and Computer Science majors were inducted into the Phi Beta Kappa honor society in Spring 2010: Daisy Bird, Joshua Davis, Robert Hendry, Christine Luongo, and Sara Young. In addition, two Mathematics minors were inducted into ΦΒΚ as Juniors in Spring 2009: Emma Daley and Desislava Byanova.

For more information about departmental prizes and lists of past recipients, see the departent's prize page.

Posted 1 March 2011

Honors Projects 2010

Two students, Joshua Davis '10 and Robert Hendry '10, have completed Honors in Computer Science in Spring 2010. The Honors program allows a student to work closely with a faculty member for a full year on a substantial research project. About midway through the the project, the Honors candidate takes a written Honors exam which covers their major field of study. At the end of the project, the candidate submits an Honors thesis covering the work that they have done. An Honors project in computer science typically also includes a major programming project. The last step in the process is a one-hour oral examination, which is conducted by an Honors Examination Committee consisting of a specialist in the field from outside of the Colleges, a faculty member from the candidate's department, and a member of the Colleges' faculty from outside of the candidate's division.

Joshua Davis completed an Honors Project entitled "MathOML: An XML Language for Visualization of Mathematical Objects." Abstract: Understanding of abstract mathematical objects can be greatly enhanced by visualizations of those objects. For example, the graph of a mathematical function makes visible properties of the function that are not obvious just from looking at its definition. Computers have made it possible to create visual representations of complex mathematical objects. However, existing computer visualization programs are tied to particular programming languages, and much of the meaningful mathematical content is lost in the code. The MathOML project aims to create a language that can be used to describe mathematical objects and their visualizations in a way that is human-readable and is independent of any particular programming language. Descriptions written in MathOML can be processed in many ways by many different programs. Part of the project is a sample program, written in Java, that can read a MathOML file and display the visualization that it describes.

Joshua's advisor for the project was Prof. David Eck. His examination committee consisted of Prof. Iva Deutchman of the Political Science Department, Prof. Carol Critchlow of the Department of Mathematics and Computer Science, and Dr. Gregg Vesonder, Executive Directory, Communications Software Research Department, AT&T Research and Adjunct Professor at the University of Pennsylvania.

Robert Hendry's project was entitled "COGS: A Comprehensive Compiler Generation System." Abstract: In academic and research environments, new programming languages often need to be developed. However, developing a new programming language requires software which converts programs written in the desired language into executable machine code. These pieces of software are called compilers, and can be very large and complex. As a result, there are many existing tools that assist in compiler development by generating pieces of compilers from abstract specifications. Hendry's honors project offers a tool that combines different generation techniques to facilitate compiler development as much as possible, without sacrificing too much flexibility.

Rob's advisor was Prof. Marc Corliss. His examination committee consisted of Prof. Eric Barnes of the Department of Philosopy, Prof. Stina Bridgeman of the Department of Mathematics and Computer Science, and Prof. Doug Lea from the State University of New York, Oswego.

For a complete list of honors projects in the Department of Mathematics and Computer Science since 1956, see the department's prizes page.

Posted 1 March 2011