## Math Minutes: A Mathematics Department E-Newsletter for Students and Alumni

# Math Minutes:

**A Mathematics Department E-Newsletter for Students and Alumni**

**Chair’s Message – Prof. Joanna Ellis-Monaghan**

2015-2016 was another exciting and eventful year for both faculty and students in the math department. The big news was At the end of another exciting year, we celebrate a strong class of nine graduating mathematics majors.

Our graduates are embarking on a variety of postgraduate plans, ranging from continuing education in fields such as teaching, geological sciences, and biostatistics to working at Pricewaterhouse Coopers in Transfer Pricing. Long-term goals include working in academia and secondary education, data and statistical analysis, and environmental research.

Please visit our alumni spotlights for more information about what our graduates are up to. Also, check out our departmental webpage

**In This Issue:**

**Our 2016 Graduates and their Majors and Honors****Mathematics Department Colloquium Series****Hudson River Undergraduate Mathematics Conference (HRUMC XXIII)****New Faculty****Prof. George Ashline – Northeastern Section Award for Distinguished College or University Teaching****DataFest****Math Department Professors’ Sabbatical Work****Math Leadership Conference****New Tutoring Model****Simons Institute at Berkeley****Student Research in Self-assembling DNA Nanostructures****Academic Symposium**

** Upcoming Events – (Alumni are always welcome!)**s for further details about our Department and programs.

**Our 2016 Graduates and their Majors and Honors:**

**Katelyn Bania **– Mathematics

**Logan David** – Mathematics *Who’s Who Among Students in American Universities and Colleges*

**Mackenzie Edmondson** – Mathematics *President of Vermont Alpha chapter of Pi Mu Epsilon, Phi Beta Kappa, Delta Epsilon Sigma, Who’s Who Among Students in American Universities and Colleges*

**Brianna Healy** – Mathematics/Economics *Pi Mu Epsilon, Phi Beta Kappa, Delta Epsilon Sigma, Who’s Who Among Students in American Universities and Colleges*

**Nathan Hodge** – Mathematics/Economics *Pi Mu Epsilon, Phi Beta Kappa, Delta Epsilon Sigma, Omicron Delta Epsilon, Who’s Who Among Students in American Universities and Colleges, Outstanding Graduate for the Saint Michael’s Mathematics Department *

**Celsey Lumbra** – Mathematics *Pi Mu Epsilon, Phi Beta Kappa, Delta Epsilon Sigma, Who’s Who Among Students in American Universities and Colleges*

**Kristen McCarthy **– Mathematics/Environmental Studies, Who’s Who Among Students in American Universities and Colleges

**Logan Tracy** – Mathematics/Elementary Education

**Melissa Westland** – Mathematics *Pi Mu Epsilon, Who’s Who Among Students in American Universities and Colleges*

**Mathematics Department Colloquium Series**

Our 2015-2016 Departmental Colloquium Series again spanned a wide range of topics shared by various experts. The talks included:

- In September 2015, several undergraduates presented results from their summer undergraduate research work, including:
- Mackenzie Edmondson ’16, “Pathway Analysis and iMRMs: A Summer Research Experience in Statistical Genetics”
- Brianna Healy ’16 and Melissa Westland ’16, “Using the Matching Algorithm to Improve DNA Nano-structure Design Strategies”
- Alexandra Brown ’17, “Mathematical Blueprints for DNA Nanostructures”
- Kristen McCarthy ’16, “Using Rhodamine dye to Quantify Incoming Solar Radiation Along Streams with Heterogeneous Canopy Cover”
- Celsey Lumbra ’16 and Nathan Hodge ’16, “From Boston to Orlando: The Transfer Pricing Internship Experience at PwC”
- In October 2015, SMC’s Mathematics Department’s Craig Jensen gave the colloquium talk “Battle of the Dice”

- In November 2015, Prof. George Ashline from Saint Michael’s presented our annual Pi Mu Epsilon Lecture “Exploring the Famous Problems from Antiquity: Angle Trisection, Cube Duplication, and Squaring the Circle”
- In January 2016, Eric Hernandez from UVM gave the Math-Engineering Colloquium Talk “Mathematical Modeling of Smart Structural Systems”
- In March 2016, Samuel Scarpino from UVM gave the talk “Modeling Infectious Disease Outbreaks on Social Networks”
- In January-March 2016, we also had three presentations from Statistics candidates, including:
- Brooke Alhanti, “Bivariate Quantile-Based Calibration of Numberical Model Outputs with Application to Climate Projections”
- Junshu Bao, “Bayesian Nonparametric Multivariate Ordinal Regression”

Brian Powers, “An Analysis of Multivariate Final-Offer Arbitration”

**Hudson River Undergraduate Mathematics Conference (HRUMC XXIII)**

On Saturday, April 2, the Saint Michael’s College Mathematics Department hosted the 23rd annual Hudson River Undergraduate Mathematics Conference (HRUMC XXIII), with an estimated 300 students and faculty from 34 colleges and universities in New York and New England in attendance. HRUMC provides a venue for undergraduates to present the results of their research projects to their peers, and this year’s conference featured 110 talks from a wide variety of areas of mathematics.

This year’s keynote speaker was Scott Aaronson (MIT and U T Austin), who discussed the status of the Millennial Problem P vs. NP and its implications in computing and beyond. Dr. Aaronson’s talk was both entertaining and enlightening for all who attended, explaining why many experts think that P!= NP is true and but why it is necessarily difficult to prove.

We had 13 Saint Michael’s students and faculty members give talks at HRUMC:

- George Ashline, Mathematics: “The Pythagorean Theorem: Some History, Derivations, and Extensions”
- Katelyn Bania ’16: “Generating Spirographs and the Mathematical Rose”
- Marcella Daley ’17: “Non-Orientable Surfaces”
- Rachel Field ’17: “Gyroid Surface”
- Brianna Healy ’16: “Fractal Landscape Generation”
- Nate Hodge and Logan David ’16: “Spinning Tops: Physics That Will Make You Dizzy”
- Zsusanna Kadas, Mathematics: “Population Models and the Logistic Equation: The Importance of Being Discrete”
- Boris Li ’17: “Fibonacci Pineapples”
- Celsey Lumbra ’16, Mackenzie Edmondson ’16: “Archimedean Solids”
- Kristen McCarthy ’16: “Stereographic Projections of Loxodromes on a Sphere”
- Bethany Ramrath ’16: “Hyperbolic Crocheting”
- Samantha Tremblay and Conor Disher ’17: “The Prison Epidemic: Using Graph Theory to Model Contagion”
- John Trono, Computer Science: “Predicting the NCAA Men’s Postseason Basketball Poll More Accurately”

Melissa Westland ’16: “Using Weierstrass Elliptic Functions to Look at Motion in an Asymmetric Double Well Potential” and “Topics in Knot Theory”

**New Faculty**

In the Fall of 2015 Dr. Craig Jensen joined the Math Department. Dr. Jensen graduated with a Ph.D. in Mathematics from Cornell University in 1998 under Karen Vogtmann. He spent three years as a Zassenhaus Assistant Professor at the Ohio State University. Following this, he was first an Assistant Professor and then an Associate Professor at the University of New Orleans from 2001 until 2015. In the fall of 2015 for family reasons, he moved to Vermont and became an instructor in the mathematics department at St. Michael’s College.

His research areas and interests include algebra, mathematics education, and topology. Copies of his papers can be downloaded from his web page at:

http://knightsite.smcvt.edu/cjensen/

Craig is excited to be at St. Michael’s College. His teaching strategy is to pursue a launch-explore-summarize framework. Classes begin with a “launch”, which is a fun—often applied—topic which grabs the interest of the students. Students then explore this topic and related topics for most of the class, and things are concluded with a summary of what was learned.

Calculus I topics this past year included a trip to a stream to measure stream flow using Google Earth to estimate the area of Lake Champlain, using lasers and mirrors to find the speed of light in different substances, growing duckweed in different environments and plotting the growth of it, and studying consumer and producer surplus.

**Prof. George Ashline – Northeastern Section Award for Distinguished College or University Teaching**

We are pleased to announce that SMC’s own George Ashline is the 2016 winner of the Northeastern Section Award for Distinguished College or University Teaching! Professor Ashline’s work in teaching has extended far beyond the classroom, inspiring students at St. Mike’s and in the greater Vermont area. A reception formally announcing George’s award will take place at the NES/MAA Meeting at University of New England on June 3-4, 2016.

Professor Ashline is pictured below with his former professor, Patti Frazer Lock (St. Lawrence University), who coincidentally was the 2016 winner of the Seaway Section Award for Distinguished Teaching.

**DataFest**

On April 8 through April 10, Saint Michael’s College and Middlebury College jointly held the first ever DataFest Vermont at Saint Michael’s College organized by mathematics professor Phil Yates and his Middlebury counterpart Albert Kim. The American Statistical Association (ASA) DataFest is a celebration of data in which teams of undergraduates work around the clock to find and share meaning in a large, rich, and complex data set. The first ever DataFest was held at UCLA in 2011. Six teams of students, five teams from Middlebury and one from Saint Michael’s College, were exposed to the joys and difficulties of working with “big data” provided by Ticketmaster. The Saint Michael’s College team was made up of three mathematics majors: junior **Abigail Hotaling**, sophomore **Rebecca Rouleau**, and first year student **Jess Barlow**. They presented on ways Ticketmaster can geographically optimize the advertising of events to potential customers.

**Math Department Professors’ Sabbatical Work**

On sabbatical in 2015-2016, **George Ashline** is working with the Vermont Mathematics Initiative, a three-year Master’s Degree Program at the University of Vermont, to enhance courses for K-12 teachers with Mathematics History components. This project also involves developing more advanced materials, as the program is incorporating more secondary education teachers.

George has also been reaching out to math alumni going back several decades and enhancing the Alumni Spotlights on the SMC Mathematics homepage. He published the article “Career Arcs and Advice: Voices from the Field” in the April 2016 issue of Math Horizons featuring the experiences and advice from SMC alumni **Andrea Austin** ’08, **Claudette Foisy Fowler** ’09, **Andrew Gilbert** ’11, **Gordon Hines** ’05, **Michele Williams Hudson** ’95, and **Dan Lewis** ’10.

**Zsu Kadas** is on sabbatical through the Fall semester. She is writing a collection of course materials focused mainly on mathematical models in Population Dynamics. These are intended for use either as a complete text for a Topics course (such as the Population Dynamics course that ran in Fall 2013) or as labs and projects to enhance courses in Calculus or Differential Equations.

**Math Leadership Conference**

On March 18, 2016, Saint Michael’s College hosted a Math Leadership Conference. The conference was organized by SMC’s George Ashline; Mary Fitzgerald, president of the Vermont Math Leadership Council (VMLC); and Lara White, math content specialist at the Vermont Agency of Education (AOE). The keynote, entitled “What Coaches Do: Myths and Realities”, was delivered by Patty Kelly and Christine Pereira, Springfield Supervisory District coaches and the VMLC Board Members, pictured below.

The conference provided time and space for nearly 70 Vermont math professionals to network, share successes, and problem-solve challenges. Sessions included topics on mathematical mindsets, fluid intervention models, coaching teachers, structures that sustain professional learning, performance tasks, co-planning, and proficiency in the classroom.

The conference was organized in honor of Professor Timothy Whiteford, who recently retired from his position in the Saint Michael’s College Education Department, recognizing his many years of dedicated service to the educational community in Vermont, particularly the VMLC, and beyond.

**New Tutoring Model**

**Krisan Geary** has led the implementation of a new model for peer tutoring at Saint Michael’s. In this new model, tutors are embedded in a particular section of a course and attend class alongside students at least once a week. Each week these embedded tutors offer a couple of hours each of small group and drop-in tutoring sessions. Feedback from all constituents has been overwhelmingly positive and we look forward to continuing the program next year.

In addition, Krisan has developed a new course, Mathematics for Teachers, which is designed for education majors to develop both a deep conceptual understanding of pre-K to 8+ mathematics along with the mathematical knowledge necessary to teach these topics.

**Simons Institute at Berkeley**

Jo Ellis-Monaghan was a Visiting Scientist in the Counting Complexity and Phase Transitions program at the Simons Institute at Berkeley during March, 2016, with particular interest in quantum analogs of classical problems. She presented a tutorial on the quantum Ising model and met with several of the authors and reviewers of the CRC Handbook on the Tutte Polynomial and Related Topic she is editing with Iain Moffatt at Royal Hollow Univeristy of London. She continues as Editor-in-Chief, together with Matt Boelkins at GVSU, of the journal PRIMUS: Problems Resources and Issues in Mathematics Undergraduate Studies.

**Student Research in Self-assembling DNA Nanostructures**

Prof. Ellis-Monaghan is co-PI on a $2 million dollar NSF grant in collaboration with Caltech, NYU, and City of Hope to develop origami-based DNA self-assembly processes. The project includes Prof. Greta Pangborn in the CS department and involves SMC students in undergraduate research experiences. The research group this year included SMC students Anna Cook, lana Houlihan, David Perry, Rebecca Rouleau, and Brenna Smith. Collaborators William Atkinson, and undergraduate from the University of Chicago), Ada Morse, a graduate student at UVM, and Margherita Ferrari, a graduate student at Politecnico di Milano, completed the group. Further information on the project may be found at: https://sites.google.com/site/nanoselfassembly/

**Academic Symposium**

In April 2016, a number of students participated in Saint Michael’s College Academic Symposium, celebrating undergraduate mathematics research. Student talks included:

- Ahmed Albluwi ’18: “Graph Isomorphism”
- Mariah Boudreau ’19: “Neural Networks in Autism”
- Will Kitterman ’17: “The Traveling Salesman Problem”
- Tyler Malone ’18: “Random Graphs”
- Lucas Margenot ’17: “Neural Networks and Schizophrenia”
- Tyler Tolisano ’19: “A Graph Theoretical Approach to Fingerprint Matching”
- Samantha Tremblay ’17; Conor Disher ’17: “The Prison Epidemic: Using Graph Theory to Model Contagion”
- Melissa Westland ’16: “An Exciting Application of the Weierstrass Elliptic Function”

There were also a number of poster presentations given by mathematics students, including:

- Katelyn Bania ’16: “Generating Spirographs and the Mathematical Rose”
- Marcella Daley ’17: “Non-Orientable Surfaces”
- Rachel Field ’17: “Gyroid Surface”
- Brianna Healy ’16: “Fractal Landscape Generation”
- Nathan Hodge ’16; Logan David, ’16: “Spinning Tops: Physics That Will Make You dizzy”
- Celsey Lumbra ’16; Mackenzie Edmondson, ’16: “Archimedean Solids”
- Kristen McCarthy ’16: “Stereographic Projections of Loxodromes”
- Bethany Ramrath ’17: “Hyperbolic Crocheting”
- Melissa Westland ’16: “Topics in Knot Theory”

**Upcoming Events – (Alumni are always welcome!)**

Mathematics Department Colloquium Series, Fall 2016-Spring 2017 (tentative schedule to date):

Friday, Sept. 9th: students will share results from their undergraduate mathematics research and other summer investigations. We will also present Calculus Awards recognizing outstanding students from the calculus sequence.

Friday, Sept. 30: The Pi Mu Epsilon Mathematics Honor Society Annual Lecture and Induction. The plenary speaker this year will be David Bressoud, the DeWitt Wallace Professor of Mathematics at Macalester College and a former president of the Mathematical Association of America, giving a talk titled Proofs and Confirmations: The Story of the Alternating Sign Matrix Conjecture.

Saturday, Oct. 1. David Bressoud will be giving a workshop hosted at SMC and open to all calculus instructors throughout the Northeast, on Teaching Calculus Now—Current Trends and Best Practices.

Friday, Oct. 28: Alumni Panel—Reflections on a Mathematics Liberal Arts Education: Experiences of our Graduates:

**Eric Caputo ’92 ** Partner, Transfer Pricing PricewaterhouseCoopers

**Lisa Martin Eriksson ’90** Optometrist New England Vision Correction

**Ed Hakey ’11 ** Quality Assurance Lead National Life Group

**Cody Rock ’11 ** Public Health Analyst State of Vermont

**Ali Shappy ’13 ** Distribution Analyst Boston Beer Company

**Rob Troy ’97** Pilot Air National Guard and United Airlines

**Please submit comments or spotlight information to Jo Ellis-Monaghan or George Ashline. It’s great hearing from you!**

On Saturday April 2, 2016, nearly three hundred mathematics students and faculty from 34 colleges in New England and beyond converged on Saint Michael’s College for the 23^{rd} annual **Hudson River Undergraduate Mathematics Conference**, a celebration of student-faculty research and exploration in the mathematical sciences. One hundred and twenty papers were presented by students and faculty members during concurrent topic-oriented sessions, and Scott Aronson, MIT professor and expert in Computation and Complexity Theory, gave the plenary address to a packed Recital Hall in the McCarthy Arts Center.

*History and Overview*

The Hudson River Undergraduate Mathematics Conference (HRUMC) was founded in 1994 by a consortium of colleges located mostly in the Albany, NY area, hence the title “Hudson River”. Originally, the conference rotated among the founding institutions: Union, Skidmore, Williams, and Siena Colleges, but gradually other colleges were added, and HRUMC travelled to Massachusetts, New Hampshire, and New York. This year marks a milestone as the “Hudson” flowed north, and was held for the first time ever in Vermont, with Saint Michael’s joining the list of prestigious institutions as host. Despite the more remote location, conference participation increased, with attendees from the New England states and New York.

The purpose of the HRUMC is to provide students with an opportunity to present their own research and to experience a professional mathematics meeting aimed especially at undergraduates. Although HRUMC always features an hour-long plenary address by a prominent speaker, the majority of the day is taken up with short talks (15 minutes) by students and faculty members. There are talks for specialists as well as talks aimed at a broader audience and accessible to first- and second-year students. The presentations may describe independent study projects or collaborative student-faculty research. Some talks present original research; others are more expository in nature; some faculty talks feature highlights of new courses or curricular innovations. The papers are organized by topic — such as Geometry, Number Theory, Applied Math, Statistics, Computer Science — into three sets of parallel sessions. This year there were 38 sessions in all, with 3 or 4 papers presented in each session – a total of 120 talks. Students as well as faculty served as session chairs.

Overall the Conference aims to create an atmosphere that conveys the message “** welcome to the mathematics community!** “ – and encourages students to continue their pursuit of mathematics, whether they are math majors or minors or are pursuing another field of study.

*Saint Michael’s College Participation- A Tradition*

Saint Michael’s participation in HRUMC dates back to 1998, when four SMC students presented talks at Union College. These pioneers were: Jim Donegan ’98, Wendy Shepard ’99, Beth White ’99, and Joe Kudrle ’99 (who is now a Senior Lecturer in Mathematics at the University of Vermont). Sarah Menard ’99 and Angie Lavoie ’01 also attended – and gave talks in a subsequent year. One or two van-loads of Mathematics and Computer Science students and faculty have gone to nearly every HRUMC since then, with more than 150 Math and Computer Science alumni participating over the years.

Papers presented by SMC students typically stem from their Senior Seminar, an Honors Thesis, a Summer Research Experience, or one of their courses. In recent years, Prof. Jo Ellis-Monaghan’s Senior Seminar students have created attractive props for their presentations: mathematical surfaces or solids, many printed on 3-D printers in SMC’s own Maker Space. This year’s collection included a fractal landscape, spinning tops, wood-burned images of “Spirograph” curves, crocheted coral reefs illustrating hyperbolic geometry, and a particularly beautiful rendering of “Stereographic Projections of Loxodromes on a Sphere” (see photo). Students who participated in a Summer Research Experience, either at SMC or elsewhere frequently describe the results of their explorations: in particular, members of Jo and Greta Pangborn’s summer research team on Graph Theory and DNA Self-Assembly have presented at many past meetings. Students who have done particularly good work on class projects are also encouraged to present at HRUMC. For instance, students in Prof. George Ashline’s History of Mathematics course (given in the Fall semester in alternate years) are always assigned a term paper on a historically significant mathematical development, and these are easily turned into HRUMC presentations.

This year, 14 Saint Michael’s students were among the presenters:

- Katelyn Bania ’16: “Generating Spirographs and the Mathematical Rose”
- Marcella Daley ’17: “Non-Orientable Surfaces”
- Rachel Field ’17: “Gyroid Surface”
- Brianna Healy ’16: “Fractal Landscape Generation”
- Nate Hodge and Logan David ’16: “Spinning Tops: Physics That Will Make You Dizzy”
- Boris Li ’16: “Fibonacci Pineapples”
- Celsey Lumbra and Mackenzie Edmondson ’16: “Archimedean Solids”
- Kristen McCarthy, ’16: “Stereographic Projections of Loxodromes on a Sphere”
- Bethany Ramrath, ’16: “Hyperbolic Crocheting”
- Samantha Tremblay and Conor Disher, ’17: “The Prison Epidemic: Using Graph Theory to Model Contagion”
- Melissa Westland, ’16: “Using Weierstrass Elliptic Functions to Look at Motion in an Asymmetric Double Well Potential” and “Topics in Knot Theory”

Three Faculty members also gave talks:

- George Ashline, Mathematics: “The Pythagorean Theorem: Some History, Derivations, and Extensions”

- Zsuzsanna Kádas, Mathematics: “Population Models and the Logistic Equation: the Importance of Being Discrete”
- John Trono, Computer Science: “Predicting the NCAA Men’s Postseason Basketball Poll More Accurately”

** Main Speaker**:

*Entertaining and Accessible*In his plenary address titled “P ?= NP” Professor Scott Aronson provided an overview of deep questions about computability that was both lighthearted and insightful. Currently on the faculty at MIT and newly appointed as David J. Bruton Jr. Centennial Professor of Computer Science at the University of Texas at Austin, Aronson has an international reputation for his expertise in the Theory of Computation. He studies the fundamental limits on what can be efficiently computed in the physical world, including quantum computing, the most powerful model of computation currently known. After the talk, Professor Aronson joined attendees for lunch in the Roy Room of the Dion Center and was seen engaged in lively discussions of computational theory with students.

*Organization and Funding *

The daunting task of organizing HRUMC was spearheaded by local organizers Professors Jim Hefferon and Lloyd Simons, with other Math Department members pitching in as needed. A team of students, outfitted in bright yellow and purple HRUMC T-shirts, designed by the students, welcomed attendees at the Registration desk and were stationed around the campus to provide directions. Funding HRUMC proved particularly challenging this year since the national funding previously available had expired. The Office of the Vice President for Academic Affairs at Saint Michael’s has consistently supported this event, providing funds for student and faculty travel each year. The Vice President for Academic Affairs again provided the critical initial commitment of support that allowed the event to be held at SMC, with the conference made possible by a combination of funds provided by the Departments of Mathematics and Computer Science together with generous grants from the NASA-VT Space Grant Consortium and from Pi Mu Epsilon, the national Mathematics honor society.

__Footnote: Although the focus of HRUMC is the accomplishment of students, it also provides an opportunity for faculty at participating colleges to renew their friendships and share ideas. This year we had a particularly happy reunion of two long-time HRUMC mentors who had both been named winners of the 2016 Award for Excellence in Teaching by their respective Sections of the Mathematical Association of America: Patti Frazer Lock from St. Lawrence University for the Seaway Section, and our own George Ashline for the Northeast Section.__

**Math Minutes: **

** **

**An E-Newsletter for Students and Alumni of the Saint Michael’s Mathematics Department**

** **Volume 7 Summer 2015

*Chair’s message*

At the end of another exciting year in the Saint Michael’s Mathematics Department, we have applauded the achievements of a strong class of twelve graduating mathematics majors.^{1}

Our graduates are embarking on a variety of postgraduate plans, ranging from secondary teaching positions at Enosburgh High School (VT) and Oak Hill High School (ME) to an analyst position with a local healthcare company to graduate studies in finance.

As in previous years, several of the top rated jobs in 2015 require significant mathematical abilities and skills. For example, in the Career Cast 2015 top 10 list, 4 of their top 6 positions involve proficiency with advanced mathematics and statistics.

This summer, some of our students are participating in scholarly and internship programs at other institutions, including the Summer REU in Statistical Genetics and Biostatistics at Dordt College, University of Vermont NSF-REU in Interdisciplinary Research on Human Impacts in the Lake Champlain Ecosystem, the Northeast Water Resource Network, Price Waterhouse Coopers, and National Life of Vermont. More information about these student explorations is included at the end of this letter.

Our 2014-2015 Departmental Colloquium Series again spanned a wide range of topics shared by various experts. The talks included:

- In September of 2014, several undergraduates presented results from their summer undergraduate research work, including
- Brianna Healy ’16 and Celsey Lumbra ’16, “Mathematics in the Business World: A New York City Experience”
- Mackenzie Edmondson ’16, “Predicting Pathogenicity in Human Genetic Variants: A Summer Research Experience in Biostatistics”
- Kaitlyn Adams ’15, “Exploring the World of Actuaries”
- Samuel Blakely ’15 “Making Use of Quantum Computing”
- Later in September of 2014, Eric Sandberg, Chief Actuary of National Life Group, gave the Careers talk “Introduction to the Actuarial Profession and Actuaries at the National Life Group.”
- Later in September of 2014, Julian Voss-Andreae, physicist and sculptor, gave the Colloquium talk “Sculpture Inspired by Proteins, Physics, and People.”
- In October of 2014, Prof. Phil Yates from Saint Michael’s presented our annual Pi Mu Epsilon Lecture “&#%!@? — Censoring and the Analysis of Partially Known Data.”
- Later in October of 2014, Prof. Nat Lew from Saint Michael’s gave the talk “Counterpoint, Canon, and Fugue: The Algorithms and the Art of Constructing Simultaneous Melodies.”
- In November of 2014, Prof. Sheila Weaver from UVM gave the Colloquium talk “Social Justice and Decision Making with Bayes’ Rule.”
- In January of 2015, Prof. Donna Rizzo from UVM gave the Colloquium talk “Using Machine Learning to Better Understand Complex Systems.”
- In March of 2015, Prof. Michael Schuckers from Saint Lawrence University gave the Colloquium talk “A Peek at Statistical Analysis of the National Hockey League (NHL).”

Please visit our alumni spotlights for more information about what our graduates are up to. Also, check out our departmental webpages for further details about our Department and programs.

*Other Recent Activity*

- In 2015, Prof. Jo Ellis-Monaghan continued as Editor-in-Chief of the journal
*PRIMUS: Problems Resources and Issues in Mathematics Undergraduate Studies*. Ellis-Monaghan is also co-PI on a $2 million dollar NSF grant in collaboration with Caltech, NYU, and City of Hope to develop origami-based DNA self-assembly processes. The project includes Prof. Greta Pangborn in the Computer Science Department and involves several SMC students in undergraduate research experiences. (See below for further information.) - Students and faculty participated in April, 2015 Saint Michael’s Symposium, celebrating undergraduate mathematics research at the College. Students presentations included:
- Catherine Corrigan ’17: “Graphing the World: Stereographic Projection” (MA 315-Complex Analysis Final Project)
- Brianna Healy ’16: “Complex Newton’s Method” (MA 315-Complex Analysis Final Project)
- Melissa Westland ’16: “Bessel Functions: Derivation, Types, and Specific Applications to Optics” (MA 315-Complex Analysis Final Project)
- Rebecca Rouleau ’18: “A Chapter from the History of Statistics: The Origins of the Normal Distribution and the Mathematicians Behind It” (MA 304-History of Mathematics Final Project)
- Samuel Blakely ’15 and Michaela Burns ’15: “The Interlace Polynomial in Graph Theory” (MA 410-Mathematics Seminar Capstone Project)
- Stephanie Nadow ’15: “A Look at Basic Cryptosystems” (MA 407-Abstract Algebra II Honors Project)
- 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, this past year, they gave invited presentations at high schools in Canaan and Brattleboro.
- Several mathematics majors are participating in summer 2015 enrichment programs:
- Mackenzie Edmondson ’16: Selected to participate in the competitive eight-week Dordt College summer REU in Statistical Genetics and Biostatistics, Jun 1–Jul 24, 2015. “Every summer 5-6 top undergraduate students join (the) nationally recognized research team…to investigate current research problems in statistical genetics… Critical components of (the) program are to bring research results forward to
**publication in leading peer-reviewed journals**and to present our work at**national and international conferences**of statistics and genetics. Most students participating in (the) program use it as a stepping stone to Ph.D. programs in statistics, biostatistics, statistical genetics, bioinformatics and other related disciplines.” - Erin Keough ’17: Selected to participate in the competitive ten-week University of Vermont NSF-REU in Interdisciplinary Research on Human Impacts in the Lake Champlain Ecosystem, May 31–Aug 7, 2015. The program provides “…ten undergraduate students the opportunity to conduct research on the ecological and socioeconomic impacts of humans in the Lake Champlain ecosystem…REU students will participate in an interdisciplinary cooperative model that promotes integrated thinking across disciplines within and between the natural and social sciences…
**” (Erin is researching****‘**Habitat Fragmentation and Walleye Movement in Lake Champlain.’) - Kristen McCarthy ’16: Selected to participate in the competitive paid ten-week Northeast Water Resource Network undergraduate research internship on Continuous Water Quality Monitoring in the Lake Champlain Basin at the University of Vermont, Jun 2 – Aug 11, 2015. This is “second field season of deploying chemical sensors in waterways entering Lake Champlain…Students will work in both field and lab settings throughout the summer.”
- Celsey Lumbra ’16 and Nathan Hodge ’16: Selected to participate in the competitive paid ten-week Pricewaterhouse Coopers summer internship program in Boston, Jun 15–Aug 17, 2015; their internships are on the Transfer Pricing team, on which math graduate Erika Kirslis ’12 is a member and math graduate Eric Caputo ’92 is a Partner.
- Colby Ajoku ’16: Selected to participate in the competitive paid ten-week National Life summer internship program in Montpelier, Jun 1–Aug 7, 2015; the internship is part of the new Business Delivery Office and on the Quality Assurance Team, supervised by math graduate Ed Hakey ’11.
- Current mathematics majors Brianna Healy ’16, Samantha Tremblay ’17, and Melissa Westland ’16 and mathematics minors Bharti Singh ’16 and Alexandra Brown ’17 are participating this summer in the Saint Michael’s NSF-funded on campus collaboration in undergraduate research in the area of graph theoretical self-assembly design strategies under the direction of Prof. Jo Ellis-Monaghan and Prof. Greta Pangborn. (Bharti and Melissa are supported by the
*NASA-VT Space Grant Mentored Undergraduate Research at Saint Michael’s College*)

*Upcoming Events*

Mathematics Department Colloquium Series, Fall 2015-Spring 2016:

- 2015: Students will share results from their undergraduate mathematics research and other summer experiences.
- Fall 2015: Pi Mu Epsilon Annual Lecture and Induction.

^{1} Our 2015 mathematics graduates with their majors and some of their honors are:

Kaitlyn Adams^{ b, p } |
MA |

Julia Bianconi | MA/ED |

Samuel Blakely David Bouthillier Michaela Burns |
MA MA MA |

Amber Emmell | MA/ED |

Mary Falcigno^{ a} |
MA |

Olivia Gregory | MA/ED |

Maya Lopez | MA |

Stephanie Nadow Zhendong Shang |
MA/ED MA |

Jeremy Wong | MA |

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

b – Pi Mu Epsilon member

p – Saint Michael’s College Mathematics Department Program Honors graduate

** **For example, find out more about Saint Michael’s alumni that have gone on to careers in mathematics education! Thank you for sharing those details!

Please submit comments or spotlight information to George Ashline. It’s great hearing from you!

** **

*Chair’s message *

*Dr. George Ashline*

We have reached the end of another rich academic year in the Mathematics Department at Saint Michael’s! We are thrilled to celebrate the accomplishments of a large class of fifteen graduating mathematics majors.^{1}

As usual, our graduates are planning to pursue various postgraduate plans, ranging from Ph.D. graduate school in Economics to an analyst position with Verizon to teaching positions at such schools as Hartford High School and the Canterbury School.

Once again this year, several of the top rated jobs in 2014 require significant mathematical abilities and skills. For example, in the Career Cast 2014 top 10 list, 4 of their top 5 positions could involve proficiency with advanced mathematics and statistics.

This summer, some of our students are participating in scholarly and internship programs at other institutions, including Columbia University’s Summer Institute for Training in Biostatistics, the Fullbridge Program, and National Life of Vermont. More information about our student activity is included at the end of this letter.

Our 2013-2014 Departmental Colloquium Series featured many interesting, wide-ranging topics and various visiting experts. The talks included:

- In September of 2013, several undergraduates presented results from their summer undergraduate research work, including
- Mackenzie Edmondson ’16, Amber Emmell ’15, and Celsey Lumbra ’16, “Chord and Word Recognition using Fourier and Wavelet Analysis”
- Katelyn Heath ’14, “From Bernoulli Shifts to Fish Schooling: A Summer Program for Women in Mathematics”
- Maura O’Riordan ’14, “Curricular Changes in a Teacher Education Program: How Successful Are They?”
- Samuel Blakely ’15, Mary Falcigno ’15, Nathan Hodge ’15, and David Robbins ’15 (Eric Sherman ’14), “DNA Nanostructure Design Strategies”
- Later in September of 2013, Prof. Bonnie Shulman from Bates College, gave the Colloquium talk “Social Justice: What’s Math Got To Do With It?”
- In October of 2013, Prof. Rick Cleary from Babson College presented our annual Pi Mu Epsilon Lecture “Some Non-Standard Applications of Mathematics to Sports.”
- In November of 2013, Prof. Jim Hefferon from Saint Michael’s gave the Colloquium talk “Developing a Math Book that is Free.”
- In January of 2014, Prof. Rachael Oldinsky from UVM gave the Colloquium talk “Orchestrating Complex Tissue Regeneration.”
- In March of 2014, Dr. Shelbi Cole from the Smarter Balanced Assessment Consortium gave the Colloquium talk “A Smarter Balanced System for Supporting Mathematics Teaching and Learning.”
- In April of 2014, Prof. Joe Latulippe from Norwich University gave the Colloquium talk “Modeling Wrist Oscillations Using Differential Equations.”
- Also in April of 2014, Prof. Raina Robeva from Sweet Briar College gave the Colloquium talk “Creating and Using Mathematical Models in Biology: Why, When, and How.”
- During her visit, Prof. Robeva also led a Bio-Math faculty workshop on “The Mathematical Training of Undergraduate Biology Majors.”

Please visit our alumni spotlights for more information about what our graduates are up to. Also, check out our departmental webpages for further details about our Department and programs.

*Other Recent Activity*

- In 2014, Prof. Jo Ellis-Monaghan continued as Editor-in-Chief of the journal
*PRIMUS: Problems Resources and Issues in Mathematics Undergraduate Studies*. Prof. Ellis-Monaghan has embarked on a new project, co-editing, with Iain Moffatt of the Royal University of London, a CRC Handbook on the Tutte Polynomial and Related Topics.

- On sabbatical in 2013-2014, Prof. Ellis-Monaghan is co-PI on a $2 million dollar NSF grant in collaboration with Caltech, NYU, and City of Hope to develop origami-based DNA self-assembly processes. The project includes Prof. Greta Pangborn in the CS department and involves SMC students in undergraduate research experiences. At the Joint Math Meetings in Baltimore in January, she presented “Polynomials of Graphs in Surfaces” at the MAA Invited paper session on Graphs Don’t Have to Lie Flat: The Shape of Topological Graph Theory and was a panelist for the Project NExT panel on The Nuts and Bolts of Undergraduate Research.

- On campus collaboration in undergraduate research in the area of graph theoretical self-assembly design strategies has continued with undergraduates during the 2013-2014 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 Saint Michael’s Student Research Symposium (Apr. 2014).

- Prof. Phil Yates recently published two jointly written articles, including one entitled “A Behavioural Dynamic Model of the Relative Age Effect” in the
*Journal of Sports Sciences*and another entitled “How Predictible is the Overall Pattern in the NCAA Men’s Basketball Post Tournament Poll?” in*CHANCE*.

- At the Joint Math Meetings in Baltimore in January, Prof. Jim Hefferon presented “Groups and Fields in Open Text Authoring” as part of the MAA Session on Open Source Mathematics Textbooks.

- Students and faculty participated in April, 2014 Saint Michael’s Symposium, celebrating undergraduate mathematics research at the College. Students presenting included:
- Katherine Garaffa ’14: “The $150,000 Formula: History, Derivations, and Applications of Mersenne Primes” (MA 410-Mathematics Seminar Capstone Project)
- Michael Gilbert ’14: “Fourier Transforms and their Applications to Music” (MA 417-Applied Mathematics Honors Project)
- Michael Gilbert ’14: “The Fibonacci Sequence and Applications to Music” (MA 410-Mathematics Seminar Capstone Project)
- Ryota Ishisaka ’14: “PageRank: Mathematics As A Tool To Provide Best Search Results” (MA 410-Mathematics Seminar Capstone Project)
- Janelle Lavery ’14: “Berlekamp’s Algorithm to Factor Polynomials” (MA 407-Abstract Algebra II Honors Project)

- 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, this past year, they gave invited presentations at high schools in Canaan, Danville, Milton, Montpelier (U-32), and South Burlington.

- Several mathematics majors are participating in off campus enrichment programs for the summer of 2014.
- Mackenzie Edmondson ’16: Selected to participate in the competitive Summer Institute for Biostatistics (SIBS) at Columbia University from May 27 – July 18, 2014. “ In the CSIBS 8-week training module, a small number of well-qualified participants will experience:

• an entertaining yet rigorous walk through the fundamentals of probability and statistical inference

• the development of an analytic “tool box”, including exposure to state-of-the-art design and analytic methods and training in the use of statistical software

• the synthesis and application of these tools via immersion in a mentored data analysis project using NHLBI datasets

• exposure to public health case studies illustrating the power and influence of biostatistics in biomedical research

*Biostatistics In Action*field trips to labs throughout the campus and around New York City to understand the breadth of the impact biostatistics has on research

• seminars on advanced methods and current challenges in biostatistics and research

• project preparation and presentation

• preparation for graduate school including GRE training (Kaplan), application and resume writing training, and interview skill development

• training in the responsible conduct of research.”

- Celsey Lumbra ’16 and Brianna Healy ’16: Selected to represent Saint Michael’s College along with several other students as initial participants in the Fullbridge Program this summer. According to the program website, “We provide ambitious students the tools to succeed in the 21st century global workplace. The Fullbridge Program delivers a hands-on, full immersion into business fundamentals—integrated with personalized coaching, world-class content, and team collaboration. It’s intense, it will challenge you, and it will change you. Get ready to take the workplace by storm.”

*Upcoming Events *

Mathematics Department Colloquium Series, Fall 2014-Spring 2015, tentative schedule so far

- Friday, Sep. 12
^{th}: students will share results from their undergraduate mathematics research and other summer investigations.

Pi Mu Epsilon Annual Lecture and Induction, Fall 2014.

^{1} Our 2014 mathematics graduates with their majors and some of their honors are:

Maeve Carroll, MA

Katherine Garaffa, MA

Jessica George, MA/ED^{ b}

Michael Gilbert, MA ^{b,c,d}

Erika Gravelin, MA/ED

Katelyn Heath, MA/EC ^{ a,c,d}

Ryota Ishisaka, MA/CS

Miranda LaRocque, MA ^{b}

Janelle Lavery, MA ^{b}

Meaghan Leong, MA

Julie Mullowney, MA ^{n}

Maura O’Riodan, MA/ED

Eric Sherman, MA

Jeffrey Trites, MA/ED^{ a}

Amy Winter, MA/ED ^{b}

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

n – Saint Michael’s College NCAA Woman of the Year for 2014

** **For example, check out the endeavors of some Saint Michael’s alumni that have gone on to careers in business, finance, and investment banking. Thank you for sharing those details!

Please submit comments or profile information to George Ashline. It’s great hearing from you!

## 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.

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!

- 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.

^{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

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 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