Dan McQuillan, PhD patiently walks a visitor through his area of expertise— topological graph theory—with a collegial tone signaling his confidence that even an abecedarian can grasp its complexities.
McQuillan’s work utilizes sophisticated mathematics to calculate the crossing numbers of complete graphs embedded on a surface—but McQuillan doesn’t explain it this way. Instead, he invokes common geometrical shapes to illustrate the precise area of his inquiry.
“Imagine the vertices of a square as people, and the lines between those vertices as relationships,” he begins, conjuring a simplified version of a graph Facebook might use to represent its subscriber base. “Now, imagine drawing the two diagonal lines between opposite corners; this symbolizes the full complement of possible relationships among the people.”
He continues, “It’s my job to figure out, in any given graph, how many edge crossings there are—the point where those diagonal lines meet in this example— and whether there’s a way to reduce them. Why? Because there are concrete instances where such crossings are undesirable: when you’re designing an electrical circuit, for example.”
Aha: his visitor understood. This pleases McQuillan.
“If you can view math as a language, and you know what the words and sentences mean, then it becomes much more fun and meaningful!” he says.
Indeed. In conversing with McQuillan in English, his knack for teaching math as a second language becomes immediately clear, and for good reason: he has been speaking mathematics fluently since 1989. That year, as an undergraduate student at Carleton University in Ottawa, Canada, he co-authored his first paper with mathematics professor R. Bruce Richter titled On the Crossing Numbers of Certain Generalized Petersen Graphs. This seminal event launched a career of inquiry into a topic McQuillan remains immersed in today.
A pure Mathematician
McQuillan is a pure mathematician: a scholar involved in basic research for which there may be no immediate, or even future, application. As such, he feels fortunate to be at Norwich.
“A lot of the best research has no grander intent than to ask questions simply for the sake of asking them,” he explains. “Yet many decision-makers don’t understand this. At Norwich, I don’t have to justify everything that I do. The leadership here supports the value of investigation, regardless of outcome.”
One of McQuillan’s current queries is, “How many edge crossings are possible for a complete graph with 15 points?”
“We literally do not know the answer,” McQuillan says. “It becomes mathematically impossible to avoid edge crossings in complete graphs with as few as five points; with 15, no one can conceptualize what’s going on. Even a computer can’t. That’s what I’m working on right now.”
McQuillan can’t say whether the results of this work will be useful in his lifetime. But the fact that it might—even a century from now—is precisely the reason he perseveres.
“The way most difficult problems are solved, in any field, are by using things that people didn’t originally think would be part of the answer,” he says. “Yet the ‘publish or perish’ culture of academia often pressures researchers to seek straightforward projects. I am extremely grateful to Norwich for encouraging me to take significant risks. That’s when truly special work emerges.” A genuine collaborator
“Since Dan first arrived at Norwich 15 years ago, he has raised the collective level of scholarship within the mathematics department,” says Dave Westerman, Charles A. Dana Professor of Geology and Vice President for Research at Norwich.
McQuillan, as humble as he is brilliant, demurs.
“There’s this misconception that some people are good at math, and some aren’t. But it’s a continuum. There are many, many skill sets required to be a really good mathematician; I just happen to have some of them.”
If McQuillan is missing a particular skill set, it’s hard to identify. A prolific author, he has published several impactful papers in topological graph theory, as well as in the diverse areas of discrete mathematics, linear algebra, and calculus. His article On the Crossing Number of K13, also co-authored with B. Richter and S. Pan, has ranked number one on Science Direct’s list of “hottest papers.”
Adept at identifying his colleagues’ complementary competencies—and regularly seeking their counsel on particularly difficult questions—McQuillan has co-authored several articles with Norwich faculty as well, including department chair Rob Poodiak, Darlene Olsen, and Jeremy Hansen. He also has a paper in progress with Joe Latulippe.
“When you see mathematics everywhere, then it’s easy to engage with your colleagues in creative ways. Sometimes, those conversations lead to a publication. But it’s important to note that this is not particular to me. Our entire department is very receptive to starting interesting discussions to see where they lead.”
An inspiration in the classroom
A passionate teacher and mentor, McQuillan regularly brings his research into the classroom—using it to catalyze students’ understanding of complex concepts, and to spark investigations of their own.
Recalling his own experience as an undergraduate, when he often didn’t fully grasp the material until years later, he strives “to be aware of what sorts of things take time to sink in, and what will be helpful to students a decade from now.”
By equipping students to solve problems through real-world examples, as opposed to memorizing equations just to get through the course, McQuillan hopes his approach to teaching will have a lasting impact.
This is another area in which he believes Norwich shines.
“Small class sizes offer the opportunity to experiment,” he says. “When I use my work to illustrate the application of a particular topic, I know right away whether or not it ‘clicks’ with the students,” he says. “That level of interaction doesn’t exist in 500-person lecture halls.”
Nor, perhaps, would the opportunity to publish as an undergraduate—something McQuillan actively encourages. To date, he has co-authored four peer-reviewed publications with Norwich students.
“I challenge students to reach beyond their comfort zones,” he says. “Because truthfully, there are unsolved questions in mathematics where undergraduates know enough to contribute to their solutions,” he says.
McQuillan also believes that Norwich undergraduates are fully capable of considering problems at the highest level, and signals this through his oversight of the university’s participation in the annual Putnam Competition—considered one of the most prestigious mathematics tests in the world.
Raised in Ottawa, McQuillan earned his master’s and PhD degrees in mathematics from the University of Western Ontario. He joined the Norwich faculty in 2002 after serving as a visiting assistant professor at Lakehead University in Ontario, and a lecturer at Southern Illinois University at Carbondale.
Since his arrival, McQuillan has taught 17 different mathematics courses, often carrying a full load. He has mentored 20 students in their summer research and independent study projects.
Noting the importance of long-term research goals, he is excited to be developing the concept for a textbook on the process of mathematical problem-solving with Norwich colleague (and former student) Addie Armstrong. In the more immediate future, he anticipates (within two years) the publication of “by far the best” paper he’s ever done with international collaborators B. Richter, Alan Arroyo and G. Salazar.
In recognition for his outstanding research, scholarship and teaching, President Richard M. Schneider named McQuillan as a Charles A. Dana Professor—the first in Mathematics since the award’s inception in 1974—during Commencement on May 14, 2016.
“My best work has occurred since joining the Norwich University community,” McQuillan says. “And I believe that—thanks to the support I receive here— even better work lies ahead.”
Norwich University officials announced top positions filled:
Provost and dean of faculty: Norwich has named Sandra G. Affenito, Ph.D., as new provost and dean of faculty beginning August 1, 2017. Affenito holds a doctorate in nutritional sciences from the University of Connecticut and she completed postdoctoral training in biomedical and behavioral sciences at Wesleyan University through the National Institutes of Health, Office of Women’s Health.
As a 2012 alumna of the HERS (Higher Education Resource Services) Institute for Women in Higher Education Administration, Wellesley College and a 2015 graduate of the Institute for Management and Leadership in Education at Harvard University, Affenito has extensive background experiences in higher education leadership and management. Collectively, she has more than 35 years of leadership and administrative experience in higher education, health care, and the corporate sector; this background has provided for diverse leadership experiences across a variety of functions and units.
Chief information officer: Norwich has named Francis (Frank) Moore, of Spanaway, Washington, as chief information officer at Norwich University beginning July 5, 2017. Since 2000, Moore has served as the chief information officer at two universities: Longwood University, Virginia. and Pacific Lutheran University, Washington. At both institutions, he handled information technology services budgeting and strategic planning. Besides performing the traditional chief information officer duties at Norwich University, Moore will teach several computer science and computer security and information assurance classes.
These two positions are newly created.
“With the addition of these two positions to our university leadership team, we are well positioned as an institution to deliver a world-class education to our future leaders as we usher in our bicentennial in 2019 and envision the next phase of Norwich University,” President Richard W. Schneider said.
College of National Services dean: Norwich named Air Force Col. Andrew Hird (pictured) as dean of the College of National Services, which oversees Reserve Officer Training Corps (ROTC) programs at Norwich through the departments of Army Military Science, Aerospace Studies and Naval Science.
Hird is Commander of U.S. Air Force ROTC Detachment 867, Northfield, Vermont., where he leads and manages the administration of the Air Force officer training program at Norwich University. Detachment 867’s nine authorized personnel guide and mentor approximately 150 officer candidates, active and special cadet students through training and professional leadership development as well as instruction in Air Force structure, history and national security affairs.
He has commanded aircrew in the C-141B and C-17A, and is a former C-17A schoolhouse instructor. He has served on the Air Staff, the Central Command Combined Air Operations Center staff and the United States Transportation Command Staff. Besides his current command, Hird commanded the 62nd Operations Group, 517th Firebird Airlift Squadron and the 385th Air Expeditionary Group. He is a Command Pilot with over 5,000 flying hours and has flown combat missions in Operations Deliberate Force, Allied Force and Enduring Freedom and Iraqi Freedom.
About Norwich University
Norwich University is a diversified academic institution that educates traditional-age students and adults in a Corps of Cadets and as civilians. Norwich offers a broad selection of traditional and distance-learning programs culminating in Baccalaureate and Graduate Degrees. Norwich University was founded in 1819 by Captain Alden Partridge of the U.S. Army and is the oldest private military college in the United States of America. Norwich is one of our nation's six senior military colleges and the birthplace of the Reserve Officers’ Training Corps (ROTC).
Norwich will celebrate its bicentennial in 2019. In fulfillment of Norwich’s mission to train and educate today’s students to be tomorrow’s global leaders, Norwich launched the Forging the Future campaign in 2014. The five-year campaign, which is timed to culminate in 2019, is committed to creating the best possible learning environment through state-of-the-art academics and world-class facilities and is designed to enhance the university’s strong position as it steps into its third century of service to the nation.
Daphne E. Larkin M’17
Director of Media Relations & Community Affairs
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Thy Yang has been named assistant vice president for international education at Norwich University beginning July 11, 2016.
As the Assistant Vice President for International Education, Yang will lead Norwich’s efforts at internationalizing the community with oversight of the International Center. The International Center acts as the clearinghouse and enabler for faculty and staff to create programs and relationships that increase the affordability and applicability for both incoming and outgoing study abroad and exchange students. One example of their work is CityLAB:Berlin, Norwich’s micro-campus in the German capital, offering academics in architecture, visual and liberal arts.
Yang is an experienced international educator with more than 15 years of serving students and scholars at various universities in the Midwest. Most recently, Yang served as the associate vice president for international studies at St. Cloud State University, Minnesota. Prior to that, Yang directed international and multicultural programs in Michigan, North Dakota and Kansas.
“I look forward to meeting and getting to know our students and the many stakeholders at Norwich to create a comprehensive internationalization plan,” Yang said. “I intend to focus my work to support and retain our increasing number of international students and scholars, doubling the number students going abroad, and making valuable contributions to a campus climate which welcomes and encourages global voices and perspectives.”
Yang is most noted for her work establishing 2+2 dual degree programs, joint partnerships, and articulation agreements. Through this work, incoming and outgoing students are able to enroll in programs with every confidence that their academic credits will be recognized when they return to their home university, greatly increasing the number of participants in international programs. Yang is active in NAFSA: The National Association of International Student Advisors. She has presented at conferences regionally, nationally, and internationally, and has contributed to publications on dual degrees and strategic partnerships. Yang is an expert in SEVIS and F-1/J-1 visa compliance and international health, safety, and risk-management issues.
Yang earned an EMBA from Benedictine College and a BA in English from Ottawa University. She studied abroad at Nottingham Trent University in England where she found her passion for international travel. She also speaks Hmong.
Norwich University’s tradition of welcoming international students is nearly as old as the institution. Norwich’s first international students began attending classes in 1827 and came from Greece, the United Kingdom, Cuba and the Bahamas, making Norwich the second school in the country to offer an international program.
Over the past academic year, 69 Norwich students studied abroad and Norwich welcomed 69 students from 23 different countries.
Beginning fall 2016 Norwich University will offer a new major, a Bachelor of Science in Exercise Science.
The new program adds to the previously announced new Bachelor of Science in Neuroscience and is part of an administrative restructure of the College of Science and Mathematics.
The new major will roll out this fall under the leadership of Assistant Professor Thomas Roberge, who also oversees Physical Education. Norwich University pioneered the academic study of physical education when in 1822 it was the first school to incorporate PE into the curriculum. Norwich’s founder, Captain Alden Partridge, was known in the early 19th century for his long distance hiking as described in this article.
Founded two years ago by Ben Fertich '16 and fellow senior AJ Johnson ’16, the Norwich University Student Investment Club (NUIC) steadily expands membership as driven individuals look to join. Although not a requirement, the majority of our six members study business, or have strong business backgrounds.
The idea for the club was first conceived when Ben and AJ were discussing the Norwich University School of Business with professor Alex Chung after a trip to New York City. Chung, who was new to the university then, noticed the lack of clubs within the business school and spoke highly of finance clubs from his prior university experiences. AJ and Ben took the idea and ran with it, holding our first Investment Club meeting just three months later.