## Volume 5, Summer 2013

## Chair’s message

At the end of another stimulating academic year at Saint Michael’s, we are recognizing the achievements of twelve graduating mathematics majors.^{1}

Once again, our graduates are formulating a variety of postgraduate plans, from graduate school in statistics and computer science to employment with companies such as Credit Suisse.

Speaking of employment, it is worth noting that once again several of the top rated jobs in 2013 require significant mathematical abilities and skills. In particular, in the Jobs Rated 2013 top 10 list, 4 of their top 5 positions involve proficiency with advanced mathematics.

Check out our alumni spotlights to learn about some of the exciting pursuits of our graduates. We are pleased to hear from our mathematics graduates, whom we encourage to keep in touch!

Other information about and for our current students is available via our departmental webpage. We are pleased that this summer our students are again participating in undergraduate research on campus and at other institutions, including Texas A & M and George Washington University. More information about our students is included at the end of this letter.

This past year, with two Department members on sabbatical, we welcomed a visiting Assistant Professor of Mathematics, Melanie Brown. Prof. Brown, a lively and very busy presence in the Department, taught Linear Algebra, Probability and Statistics, Elements of Calculus, and several sections of Elementary Statistics for us during the year – as well as playing in the Saint Michael’s Wind Ensemble!

In our Departmental Colloquium Series, we have continued to offer talks on relevant mathematical topics. In 2012-2013, we sponsored a diverse array of presentations by our current students and several esteemed visitors. Their talks included:

- In September of 2012, several undergraduates presented results from their summer undergraduate research work. Here are more details:
- Kaitlyn Adams ’15, Jessica George ’14, and Jeffrey Trites ’14, “Signature, Letter, and Word Recognition using Wavelet and Fourier Analysis”
- Alexa Foote ’13, “Explorations in Statistics: San Francisco Bay Area Housing Data”
- Eric Parziale ’13, “Your Imagination is Only Limited by Lack of Software: Investing in a Liberal Arts Education”
- Thomas Dickerson ’13, Mary Falcigno ’15, and Saja Willard ’13 (Katelyn Heath ’14, Tyler Hotte ’14, Miranda LaRocque ’14, Eric Sherman ’14), “DNA Nanostructure Design Strategies”

- Later in September of 2012, Prof. Michael Dorff from BYU, gave the Colloquium talk “Kidney transplants, the Real Iron Man Suit, and the Pixar Movie ‘Incredibles’: What Can you Do with Math?”
- In October of 2012, Prof. Liz McMahon from Lafayette College presented our annual Pi Mu Epsilon Lecture “Mathematics in the Game of SET®.”
- In November of 2012, Prof. Kirsten Stor from Castleton State College gave the Colloquium talk “On the Map Coloring Theorem.” Here is a Tegrity recording link.
- In January of 2013, Prof. Paul Hines from UVM gave the Colloquium talk “Large Blackouts in the Power Grid: Why They Happen and What To Do About It,” and joint Mathematics-Engineering event. Here is a Tegrity recording link.
- In March of 2013, Prof. Ben Baumer from Smith College gave the Colloquium talk “Moneyball Revisited: Assessing the Sabermetric Revolution in Baseball.” Here is a Tegrity recording link.
- In April of 2013, Charles Masenas SMC ’69 gave the Colloquium talk “Balancing the Segway,” jointly sponsored by the Depts. of Physics, Computer Science, Mathematics, and Engineering
- Also, Prof. Jo Ellis-Monaghan has continued to serve as co-organizer/coordinator of the weekly Combinatorics Seminar jointly hosted by Saint Michael’s and the University of Vermont.

## Other Recent Activity

- The Mathematics Department hosted a Northeast Section of the MAA dinner meeting in September of 2012, at which Prof. Michael Dorff from BYU presented “Filling Courses and Recruiting Math Majors,” an abbreviated version of a workshop he has given at several national MAA meetings. Twenty Mathematics faculty members from across Vermont and beyond gathered for the event. Attendees included faculty from UVM, Norwich, all of the VT State Colleges, as well as SUNY Plattsburgh and the University of New England. The session addressed many ways to enhance mathematics programs through a variety of ideas gleaned from successful initiatives at BYU and other institutions, as well as additional ideas generated by the group.
- On campus collaboration in undergraduate research in the area of graph theoretical self-assembly design strategies has continued with undergraduates during the 2012-2013 academic year, under the direction of Profs. Ellis-Monaghan (Mathematics) and Greta Pangborn (Computer Science). Several papers, posters, talks at academic meetings, and a project website have resulted. For example, several students/groups of students presented their research in a wide variety of venues, including the Hudson River Undergraduate Mathematics Conference (Apr. 2013) and the Saint Michael’s Student Research Symposium (Apr. 2013). Six Saint Michaels’ College students will continue the work of the project through the summer of 2013.
- Awarded a major $200,000 three-year National Science Foundation grant running through Aug. 2013, Principal Investigator Prof. Ellis-Monaghan and co-principal investigator Prof. Pangborn continued their collaborative work with undergraduate students and between the mathematics and computer science departments focused on design strategies for nanoconstructs, with potential for wide practical application.
- In 2013, Prof. Ellis-Monaghan continued as Editor-in-Chief of the journal
*PRIMUS: Problems Resources and Issues in Mathematics Undergraduate Studies*. - Under the mentorship of Prof. Phil Yates, Eric Parziale wrote “Keep the Ball! The Value of Ball Possession in Soccer” and submitted it for journal publication review. It has been published in the April 2013 issue of
*Reinvention: an International Journal of Undergraduate Research*. - Under the mentorship of Profs. Pangborn and Ellis-Monaghan, Tyler Hotte and Miranda LaRocque wrote “Design Techniques for the DNA Cubic Lattice”, which has been accepted to appear in the
*American Journal of Undergraduate Research*. - Under the mentorship of Prof. Ellis-Monaghan, Rob Hammond wrote “Graph theory and its importance to conservation”, which has been accepted to appear in the
*Rose-Hulman Undergraduate Mathematics Journal*. - In Fall 2012, Prof. Jim Hefferon was on sabbatical and wrote a Free and Open Source lab manual to accompany his text,
*Linear Algebra*. During the 2012-2013 academic year, Prof. Lloyd Simons was on sabbatical and worked on extending his scholarly focus in algebraic number theory to the areas of algebraic geometry and topology. - Prof. Ellis-Monaghan has a new monograph,
*Graphs on Surfaces: Dualities, Polynomials, and Knots*, now available for preorder through Amazon.com. She will be teaching a workshop on this topic at the Rocky Mountain Mathematics Consortium in June, 2013. - Students and faculty participated in April, 2013 Hudson River Undergraduate Mathematics Conference at Williams College. Nineteen Saint Michael’s students and five faculty members participated in the Conference, celebrating undergraduate mathematics research with students and faculty from across the Northeast. Students presenting included:
- Krista Bird ’13, Thomas Dickerson ’13, and Jessica George ’15: “Techniques for Fractal Terrain Generation”
- Brianne Conlon ’15 and Robert Hammond ’13: “Graph Optimization in Self-Assembling DNA Nanostructures”
- Colin Delaney ’13, Patrick Knapp ’13, Julie Mullowney ’14, and Alison Shappy ’13: “Archimedean Screw”
- Amber Emmell ’15: “Leonhard Euler and the Basel Problem”
- Alexa Foote ’13, Erika Gravelin ’14, Emma Hauser ’13, and Robert Hammond ’13: “Gömböc: An Exception to the Four Vertex Theorem”
- Jessica George ’14: “Search for General Solutions of the Cubic, Quartic, and Quintic Equations”
- Maria Leuci ’13 and Michael Thompson ’13: “Minimal Surfaces”
- Maura O’Riordan ’14: “Evaluating ELL Reform in a Teacher Education Program”
- Eric Sherman ’14 and Saja Willard ’13: “Self-Assembling Objects with Central Vertices”Profs. Ashline, Hefferon, Pangborn, and Yates chaired conference sessions. Also attending was Prof. Ellis-Monaghan.

- Profs. George Ashline and Ellis-Monaghan have continued to give invited talks and workshops at schools in Vermont through the Vermont State Math Coalition’s Expanding Horizons program. For example, in May of 2013, they gave invited presentations at Brattleboro High School and Champlain Valley Union High School, respectively.
- Several mathematics majors are participating in off campus mathematics programs for the summer of 2013.
- Katelyn Heath ’14: Selected to participate in the competitive Summer Program for Women in Mathematics at George Washington University from Jun. 29- Aug. 3, 2013. “SPWM will offer a number of seminars led by active research mathematicians, with the assistance of graduate students. The seminars will be organized to enable the students to obtain a deep understanding of basic concepts in several areas of mathematics, to learn how to do independent work, and to gain experience in expressing mathematical ideas orally and in writing. There will be panel discussions on graduate schools, career opportunities, and the job market. Weekly field trips will be organized to facilities of mathematical interest around the Washington area.”
- Mackenzie Edmondson ’16, Amber Emmell ’15, and Celsey Lumbra ’16: Selected to participate in the competitive summer mathematics pre-REU program on “Signal and Image Analysis” at Texas A & M University during Jun. 23-Jul. 27, 2013. “As technology becomes more sophisticated, the need for efficiently handling vast amounts of data has grown tremendously. In this program, the basic ideas behind the use of Fourier analysis and wavelets in signal and image analysis will be introduced. The material will be appropriate for students who have completed a typical three semester calculus sequence. Initially, in the morning sessions, a faculty member will present ideas, techniques and examples. For the afternoon sessions, faculty and graduate students will be available to provide further guidance to the students while they work on problems over the material presented in the morning sessions. As time goes on, the students will break up into groups and work on projects involving real-world examples.”

^{1} Our 2013 mathematics graduates with their majors and some of their honors are:

Krista Bird |
MA |

Michael Carpenter |
MA |

Colin Delaney^{ b} |
MA |

Thomas Dickerson^{ b, c, d} |
MA/CS/PY |

Alexandra Foote ^{a,c,d,v} |
MA/EC |

Robert Hammond ^{b} |
MA |

Emma Hauser |
MA |

Patrick Knapp |
MA |

Maria Leuci |
MA/BI |

Eric Parziale ^{a, c, d, k} |
MA/EC |

Alison Shappy |
MA |

Michael Thompson |
MA/PY |

a – Pi Mu Epsilon member and co-President of Vermont Alpha chapter of Pi Mu Epsilon

b – Pi Mu Epsilon member

c – Phi Beta Kappa member

d – Delta Epsilon Sigma member

k – Saint Michael’s College Roger Keleher Award, Outstanding Student Athlete of Class of 2013

v – Saint Michael’s College Class of 2013 valedictorian

Finally, here is an interesting recent *Chronicle of Higher Education* article on the importance of mathematics as a foundation to develop the advanced skills required in many fields.

## Chair’s message

At the end of another exciting academic year at Saint Michael’s, we are celebrating the accomplishments and graduation of ten mathematics majors.^{1} They are planning to pursue a variety of endeavors, ranging from mathematics education to graduate school in applied mathematics to employment with insurance and accounting companies.

Speaking of employment, it is worth noting that once again several of the top rated jobs in 2012 require significant mathematical abilities and skills. In particular, in the Jobs Rated 2012 top 10 list, 5 of the top 10 positions involve proficiency with advanced mathematics.

For information on the activities of some of our current students and graduates, please see our alumni profiles and other relevant information available on our departmental webpage. This summer, we once again have students participating in grant-supported undergraduate research on campus and at other institutions. Information about some of them is included at the end of this letter.

This past year, we welcomed a new full time member to the Department, namely Professor Krisan Geary. After completing her Master’s degree in Mathematics at the University of Vermont and teaching there for several years most recently, Prof. Geary has served the College and Department as Instructor and Quantitative Skills Coordinator. She has taught both Elementary Statistics and Elements of Calculus, which have been expanded under the new College curriculum implemented this past year. As part of this curriculum, all undergraduates must now complete at least one Quantitative Reasoning course, and Prof. Geary has provided academic support to students and faculty in quantitative courses and disciplines, such as through coordination of our mathematics peer tutors. Furthermore, she is revising our Calculus Placement Test to provide feedback to incoming and current students about their preparation for introductory Calculus.

In our continuing Departmental Colloquium Series, we have regularly offered talks on a variety of mathematical topics. In 2011-2012, we had an especially rich collection of presentations by our current and former students and well as several distinguished visitors. Their presentations included:

- In September of 2011, several undergraduates presented results from their summer undergraduate research work, including
- James Coolidge ’12 and Kevin O’Brien ’12 “Utilizing the Octet Truss in the Design of Lateral Transfer Retroreflectors”
- Katie Heath ’14 “Signature Recognition using Wavelets and Other Methods”
- Eric Parziale ’13 “Possession is 9/10’s of the Law: Banking, Footie, and how to ‘Excel’ at Multilevel Logistic Regression”
- Jaqui Tuthill ’12 “Rhythmic Clustering of Drum Breaks”

- Later in September of 2011, Prof. Frank Morgan from Williams College presented our annual Pi Mu Epsilon Lecture “Soap Bubbles and Mathematics.”
- In October of 2011, Prof. Emily Proctor from Middlebury College, gave the Colloquium talk “Describing the Orbisurfaces.”
- In November of 2011, Prof. Charles Bergeron from Rensselaer Polytechnic University, gave the Colloquium talk “Least-Squares Curve-Fitting Techniques for Improved Medicine Development.”
- Later in November of 2011, Sarah Hamilton ’07 Ph.D. candidate from Colorado State University, gave the Colloquium talk “Oh the Things You Can Do and the Places You’ll See With a Mathematics Degree from SMC!”
- In January of 2012, Prof. Sheila Weaver from UVM gave the Colloquium talk “Mathematics and the Arts.”
- In February of 2012, Prof. Christine Latulippe from Norwich University gave the Colloquium talk “This is a Test…This is Only a Test…The As Bs and Cs of Assessment in Mathematics.”
- In April of 2012, Prof. Dan Velleman from Amherst College gave the Colloquium talk “Taylor Series by Nonstandard Analysis.”
- Also, Prof. Jo Ellis-Monaghan has continued to serve as co-organizer/coordinator of the weekly Combinatorics Seminar jointly hosted by Saint Michael’s and the University of Vermont.

We enjoy hearing from all of our mathematics graduates. Please keep in touch! And please consider including your post-Saint Michael’s experiences among our alumni spotlights. Thank you for your support!

## Other Recent Activity

- On campus collaboration in undergraduate research in the area of graph theoretical self-assembly design strategies has continued with undergraduates during the 2011-2012 academic year, under the direction of Profs. Ellis-Monaghan and Greta Pangborn from the Computer Science Department. Several papers, posters, and talks at academic meetings resulted. For example, several students/groups of students presented their research in a wide variety of venues, including the Northeastern Section MAA meetings (Jun. 2011), the Saint Lawrence Valley Mathematics Symposium (Jul. 2011), the NASA ATLAS team (Aug. 2011), the Southeastern Section AMS meetings (Mar. 2012), the Vermont Academy of Arts and Sciences Spring Student Symposium (Apr. 2012), the Hudson River Undergraduate Mathematics Conference (Apr. 2012), and the Saint Michael’s Student Research Symposium (Apr. 2012).
- Awarded a major $200,000 three-year National Science Foundation grant running through Aug. 2013, Principal Investigator Prof. Ellis-Monaghan and co-principal investigator Prof. Pangborn continued their collaborative work with undergraduate students and between the mathematics and computer science departments focused on designing nanoconstructs, with potential for wide practical application.
- In 2012, Prof. Ellis-Monaghan continued as Editor-in-Chief of the journal
*PRIMUS: Problems Resources and Issues in Mathematics Undergraduate Studies*. - With Eric Parziale ’13, Prof. Phil Yates wrote “Keep the Ball! The Value of Ball Possession in Soccer” and submitted it to the
*American Statistician*in March, 2012. An earlier version of this paper was presented at the New England Symposium for Statistics in Sports in September at Harvard. - Prof. Yates also presented “Historic Floods and One % Chance Flood Estimation” at a Norwich University Mathematics Colloquium in March, 2012. Focusing on the flood history of the Congaree River in South Carolina, this research was done jointly with Prof. John Grego of the University of South Carolina.
- In July, 2012 at the TeX Users Group Conference in Boston, Prof. Jim Hefferon is presenting with Prof. Michael Doob of the University of Manitoba “Reaching for the Stars with Asymptote.”
- Students and Faculty participated in April, 2012 Hudson River Undergraduate Mathematics Conference at Westfield State College. Five Saint Michael’s students and four faculty members attended the Conference, celebrating undergraduate mathematics research with students and faculty from across the Northeast. Students presenting included: Michaela Burns ’15, “Epidemics and Graph Theory”; Thomas Dickerson ’13, “Computational Generation of Crystal Nets”; Robert Hammond ’13, “Graph Theory and Water Habitat Conservation”; Mary Spuches ’12, “Uniform Polyhedra in the Octet Truss”; Saja Willard ’13, “Self-Assembly Design Strategies”. Profs. Ellis-Monaghan and Yates, and Mary Spuches ’12 chaired sessions. Also attending were Profs. Pangborn and Lloyd Simons.
- Profs. George Ashline and Ellis-Monaghan have continued to give invited talks and workshops at schools in Vermont through the Vermont State Math Coalition’s Expanding Horizons program. For example, Prof. Ashline presented “Correlation Properties and Applications” to three BFA-Fairfax high school classes in May, 2012.
- Several mathematics majors are participating in off campus mathematics programs for the summer of 2012.
- Alexandra Foote ’13: Selected to participate in the competitive Explorations in Statistics Research: An Undergraduate Program at UC Berkeley, California from Jun. 16-24, 2012. “The seven day workshop is designed so that students get a sense of how statisticians approach large, complex problems. During the week, the several different topics that may be presented include text and document analysis, environmental statistics, and earth and space science. Importantly, students will also get a chance to work with data. In the process, students will gain a basic understanding of computing and visualization tools.”
- Kaitlyn Adams ’15, Jessica George ’14, and Jeff Trites ’14: Selected to participate in the competitive summer mathematics pre-REU program on “Signal and Image Analysis” at Texas A & M University during Jun. 24-Jul. 28, 2012. As technology becomes more sophisticated, the need for efficiently handling vast amounts of data has grown tremendously. This program will introduce the basic ideas behind Fourier analysis and wavelets, the two main tools used to analyze signals and images. The students will break into groups and work on projects involving real-world examples.

## Recent Graduates

^{1} Our 2012 mathematics graduates with their majors and some of their honors are:

Laura Backman ^{c,e} |
MA/ED |

Jason DeCoteau ^{c} |
MA/EC |

Brian Goodhue ^{c} |
MA/EC |

Erika Kirslis ^{c,e} |
MA/ED |

Samantha Martell | MA/Secondary Education |

Emily Pratt ^{b, d, e} |
MA/EC |

Daisy Sosa | MA |

Mary Spuches ^{a} |
MA |

Coligny Tataro | MA |

Jacqueline Tuthill ^{c} |
MA/EC |

a – Pi Mu Epsilon member and President of Vermont Alpha chapter of Pi Mu Epsilon

b – Pi Mu Epsilon member and Vice President of Vermont Alpha chapter of Pi Mu Epsilon

c – Pi Mu Epsilon member

d – Phi Beta Kappa member

e – Delta Epsilon Sigma member

## Another Successful Year

After our Commencement exercises in mid-May and the graduation of nine accomplished mathematics majors, we have reached the end of another productive, stimulating academic year. Our graduates are planning to build upon their undergraduate experiences in various ways, ranging from graduate school in mathematics and statistics to employment in the actuarial field.

Speaking of employment, it is worth noting that once again many of the top rated jobs in 2011 require significant mathematical abilities and skills. For example, please visit the Jobs Rated 2011 top 10 list, in which the top 5 positions need advanced education in mathematics.

For information on what some of our current students and graduates are up to, please see some of our student and alumni profiles available on our departmental webpage. This summer, we have students participating in grant-supported undergraduate research both on campus and at other institutions.

This past year, we welcomed a new tenure track member to the department, namely Professor Philip Yates. After completing his Ph.D. in Statistics at the University of South Carolina and teaching at Cal Poly Pomona for several years, Professor Yates taught a range of classes for us last year, including a 400-level Statistical Inference course which we have been unable to offer in a number of years. As the College and Department transitions to a new curriculum in the fall, Professor Yates is designing a new course in Applied Regression which will further enhance our course options for students.

Speaking of our new curriculum, our Mathematics major and minor requirements have been modified. View an outline of what is planned for requirements.

We enjoy hearing from mathematics graduates (both recent and not so recent). Please stay in touch! And please consider sharing your post-Saint Michael’s experiences among our alumni spotlights. Thank you in advance for your support!

## Our 2011 Graduates

Our 2011 mathematics graduates with their majors and some of their honors are:

Brittany Baker^{a, c, d} |
MA |

Andrew Gilbert^{b,c, d, e} |
MA/Classics |

Ed Hakey^{b} |
MA/EC |

Kelly Rose Losi |
MA/Secondary Education |

Marran Ranks |
MA/Secondary Education |

Cody Rock |
MA |

Liz Siracusa |
MA/Elementary Education |

Kaiti Tuthill^{a, c} |
MA/EC |

Amanda Witt |
MA |

a – Pi Mu Epsilon member and co-President of Vermont Alpha chapter of Pi Mu Epsilon

b – Pi Mu Epsilon member

c – Phi Beta Kappa member

d – Delta Epsilon Sigma member

e – Class Valedictorian

## Summer Student Research

Several mathematics majors are participating in off campus mathematics programs for the summer of 2011.

Brittany Baker ’11: Selected to participate in the competitive program for Women and Mathematics at the Institute for Advanced Studies at Princeton University from May 16-27, 2011, followed by the competitive Bridge Program at Texas A & M University from Jun. 26-Jul. 30, 2011. The former intensive 11-day mentoring program for undergraduate and graduate women in mathematics brings together research mathematicians and students to address issues of gender imbalance in mathematics and includes lectures/seminars on mathematical topics and discussions on peer relations and career opportunities. The latter program is intended for 15 students entering graduate school in mathematics in the fall to supplement their knowledge to be better prepared for first year graduate work.

Jaqui Tuthill ’12: Selected to participate in the competitive statistics REU program at Claremont Colleges in California from Jun. 6-Jul. 29, 2011. At this REU, 10 students are funded to work with three faculty members from Claremont McKenna, Harvey Mudd and Pomona Colleges for the eight week clinic. Students work on an exciting research project in mathematics, participate in workshops to inform them about mathematical science careers, and are encouraged to present their findings at a mathematical or statistical professional society meeting.

Jason DeCoteau ’12: Selected to participate in on-campus research during the summer of 2011 with Prof. Patrick Walsh of the Economics Department funding by the Social Science Research Center (SSRC). He is researching per capita Medicare expenditures and trying to find any patterns in why some areas spend more per person than other areas. He is considering both the demographics of these areas and also how the Medicare expenditures are being spent to see if certain demographics can explain some of the variation, such as if an area with a high poverty rate spends more per person on Medicare. Then he is also looking at how the Medicare benefits are being disbursed to see how an area that spends a large amount on Medicare expenditures per capita spends their money, such as on outpatient services, inpatient services, or on laboratory services, etc. Thus, does an area that spends a large amount per person allot a significant percentage of per capita Medicare benefits on outpatient services, or some other type of service, and can the way an area disburses Medicare benefits explain any of the variation in spending? He is focusing on the areas that spend the most, and the least amount of per capita Medicare expenditures, in order to see if he can learn anything about the differences between high and low spending areas, and hopefully determine a pattern that suggests a way to be a low spending area.

Katie Heath ’14: Selected to participate in the competitive summer mathematics pre-REU program on “Signal and Image Analysis” at Texas A & M University during Jun. 26-Jul. 30, 2011. As technology becomes more sophisticated, the need for efficiently handling vast amounts of data has grown tremendously. This pre-REU program will introduce the basic ideas behind Fourier analysis and wavelets, the two main tools used to analyze signals and images. As time goes on, the students will break up into groups and work on projects involving real-world examples.