Program lightens the load on students and strengthens ties with regional high schools

Two years ago, when Doron Levy served as the undergraduate chair of the University of Maryland’s Department of Mathematics, he had a question: Why not let the most advanced high school students take the final exam for second-year college math courses? If they pass and then enroll at UMD, they could earn credits for the course and the grade could be registered on their transcript. 

Advanced Placement exams already enable high school students to earn credits for freshman-level calculus I and II (MATH 140 and MATH 141). But Levy knew that students enrolled in STEM magnet schools, international baccalaureate programs and accelerated math programs often exceed that level before their junior year. Some even take multivariable calculus and linear algebra, both college sophomore-level subjects, before graduating high school. But very few colleges and universities allow students to start as freshmen with such advanced standing.

Levy, who became chair of the department in 2019, thought partnering with schools to allow credit by exam would not only benefit students, but open opportunities for recruitment. He and Mathematics Professor Lawrence Washington reached out to high schools in the region and worked with the college administration to get the ball rolling. Since then, 273 high school students have taken a mathematics exam for UMD course credit and nearly three dozen are now enrolled at UMD.

“The program has been extremely successful on many fronts,” Levy said. “It required the schools to align their curriculum to ours, which has made for a very smooth transition for students, and it has already attracted a remarkable cohort of students to Maryland.”

Of the 148 high school students who took the MATH 241: Calculus III exam in 2019, 120 passed, 35 enrolled at UMD and six are current mathematics majors. In 2020, the department added an exam for MATH 240: Linear Algebra. In total, 125 high school students took one of the two exams offered, and 112 passed. Levy expects many of them will choose to come to UMD when they graduate.

Four schools in Montgomery County, Maryland, currently participate in the “credit by exam” program—Montgomery Blair High School in Silver Spring, Richard Montgomery High School in Rockville, Poolesville High School in Poolesville and Georgetown Preparatory School in Bethesda. Teachers from these schools received mentoring from UMD faculty and access to previous exams through the math department’s test bank. 

The exams students take are selected from previous years’ unused alternate exams, which are held in the department under lock and key for administering to students who are unable to take their finals at the designated time. Using one of these exams ensures that students who earn credit by exam are on an equal footing with their peers.  

“Many students have commented to me afterward that they didn't really believe me when I said they're succeeding in a college course, but their comfort and success with UMD's exam drove it home,” said Jeremy Schwartz, a teacher in the Mathematics and Computer Science Magnet Program at Montgomery Blair High School. “These students are more confident about soon navigating the transition from high school into college.”
Ensuring the alignment of high school curricula with UMD’s math program has multiple benefits.

“There is always this disconnect between what high schools think students need to know and what we think they need to know,” Washington said. "And this helps get everyone on the same page. But also, some of these really advanced students, like physics majors and engineering majors, have so many credits proscribed in advance, anything that eases the course load and frees them up for electives can give them a real advantage. And that’s a great recruiting and marketing tool for us.” 

Schwartz said his students see credit by exam as a way to fit more advanced courses into their schedule when they get to college.

“Many of our students are chomping at the bit to dig into higher- level college courses,” he said. “In effect, these students don't cut a class out of their requirements. They replace Calc 3 with a higher-level course. For those in math, they more quickly get to the real ‘meat’ of their math major. For those in related fields, this allows them an additional space in their schedule for their primary passion.”

According to Levy, colleges across the country have waived their multivariable calculus course requirement for students who passed the UMD exam, and that benefits more than just the students. 

“The program has been very successful in making our department and university visible to the outside world,” Levy said. “Major schools throughout the country have recognized our unique approach to encouraging top talent.”

Levy plans to expand the program in the future by offering it to all Maryland high schools and possibly schools in the District of Columbia that teach advanced math classes. 

Written by Kimbra Cutlip

A pilot calculus course that launched this fall in 10 Prince George’s County Public Schools (PGCPS) is being taught by a University of Maryland mathematics faculty member, coordinated by the College of Education and provided free of charge to students. The online course is underway at geographically and demographically diverse PGCPS high schools, some of which do not routinely offer calculus, a key factor in college admissions.

Fifty students are enrolled in the class, which is offered synchronously and asynchronously to high schoolers who meet prerequisite criteria. A collaboration among PGCPS and UMD’s College of Education and College of Computer, Mathematical, and Natural Sciences (CMNS), the calculus course is fully funded by the President’s Office at UMD.

“The pilot calculus course fulfills two key university goals—preparing a scientific workforce for the state and prioritizing minority enrollment at UMD, particularly from Prince George's County,” said UMD President Darryll J. Pines.

The calculus course is one of several dual enrollment programs available to PGCPS students and is part of a broader effort to support innovative partnerships between PGCPS and the University of Maryland. As a pilot, the course is a learning opportunity on how to best coordinate  curriculum, instruction and academic policies across multiple institutions.

“Building on our longstanding partnership with Prince George’s County Public Schools, this pilot aims to expand access to UMD courses through virtual teaching models,” said College of Education Dean Jennifer King Rice. “We hope this pilot calculus course will lay the foundation for additional virtual course offerings that will prepare high schoolers for college and attract diverse students from local schools to UMD.”

Under the leadership of Mathematics Chair Doron Levy, the department quickly reconfigured its four-credit MATH 140: Calculus I for PGCPS students. This included replacing the traditional textbook with an open-source textbook, redesigning the instructional model and identifying Department of Mathematics Senior Lecturer Nathan Manning to teach the course along with four experienced teaching assistants—all in less than two months. The students’ academic progress is regularly monitored by PGCPS teachers.

"We are very proud of this new program, which expands access to college-level mathematics for talented high-school students in Maryland, and in Prince George's County specifically,” said CMNS Dean Amitabh Varshney. “By bringing our expertise in mathematics education to local area high schools, we hope this program will open these students’ eyes to the world-class college education they can receive at the University of Maryland."

College of Education Professor of Practice Segun Eubanks is organizing the calculus course pilot and serving as the university liaison working to develop a long-term, broad-based agreement to provide UMD college courses to PGCPS students through the PGCPS dual enrollment program.

“This partnership allows our students the opportunity to access rigorous math content while earning college credits," said Dr. Monica Goldson, CEO of PGCPS. "Many of our students are unable to travel to the campus to take courses due to the distance or other priorities. We are hoping to create a replicable model for other courses blending the content provided by the university and support from the school.”

The pilot program allows UMD and PGCPS to use a small-scale project to address the challenges of coordinating curriculum, instruction and academic policies between the institutions. It also allows PGCPS to adjust its internal academic support system as it applies to individual students who are receiving advanced instructional opportunities outside of the school system. The project’s assessment will be used to construct a model for expanding this UMD-PGCPS partnership to more PGCPS schools.

The UMD online calculus course is currently being offered at Bowie, College Park Academy, DuVal, Eleanor Roosevelt, High Point, International High School at Langley Park, Northwestern, Oxon Hill, Parkdale, and Surrattsville High Schools in Prince George’s County.

Written by Audrey Hill

Two professors look back on long, distinguished careers.

Joel Cohen 

Anyone who has been to the Department of Mathematics’ holiday party in the past four decades will know Professor Emeritus Joel Cohen. He was the guy with the microphone challenging revelers to math-related limerick contests and handing out fake prizes, like “a trillion dollars” or the James A. Yorke Rotunda: “Very spacious, fits in most apartments and houses. Keep it inside. Or put it in your yard—just don’t take it home until after the party.”

Cohen is not a shy man. And his enthusiasm for UMD extends way beyond ensuring a good time at a party. Cohen has actively sought to improve the lives of Terps and others in the community since arriving at UMD in 1975. Over the course of his tenure, he led or served on nearly two dozen committees, commissions and task forces, focused on everything from faculty affairs and student conduct to women’s issues and student athlete welfare. 

Cohen was a founding member of the Coalition on Intercollegiate Athletics and the first ombudsperson for the university. He led the University Senate as its chair from 2003 to 2004 and chaired the Council of University System Faculty, which advises the chancellor and reports to the Board of Regents, from 1995 to 1996. In January 2020, Cohen and his wife, Susan Chapin (B.A. ’91, interior design), created the Cohen-Chapin Graduate Student Travel Endowment to help young mathematicians at Maryland attend career-enhancing conferences. 

Outside of work, Cohen has been equally active. He served as the national chair of Americans for Democratic Action and as president of his synagogue. Cohen’s commitment to civic engagement is rooted in his boyhood in Worcester, Massachusetts. 

“I grew up listening to politics with my father,” Cohen remembered. “My parents were members of every anti-discrimination group that was around.” 

He remembers political conversations as a regular feature in his household. He also remembers his parents’ appreciation for academia and education. Cohen’s mother was a teacher, and although his father worked in the clothing industry, he always wanted to be a chemist. Some of their inquiring spirit surely rubbed off.

“I think theoretical mathematics is endlessly fascinating,” Cohen said. “It’s the discovery. What an amazing thing to find something that you know nobody in all of history has ever known, an eternal truth that’s been there but no one has known it.” 

Early in his career, Cohen was intrigued by the idea of applying mathematical methods and concepts to language and linguistic systems. After earning a bachelor’s degree in applied mathematics from Brown University, he went to MIT to earn a Ph.D. in mathematics, and studied with the famed linguist and cognitive scientist, Noam Chomsky. 

He even wrote a paper that Chomsky published in 1967 asserting that two types of grammar were mathematically equivalent. The paper, which solved part of a problem that Cohen said later became known as the Chomsky Conjecture, turned out to be the subject of a decades-long debate that wasn’t fully resolved until the late 1990s. Cohen, was unaware of the controversy, however, because the field of mathematical linguistics turned into a mere side interest, and he quickly moved on to his primary focus.

Cohen began his career studying algebraic topology, which uses abstract algebra to study topological spaces, and teaching at the University of Chicago and the University of Pennsylvania. After arriving at UMD, he found a new path when he met Alessandro Figà Talamanca, a visiting Italian mathematician. Figà Talamanca inspired him to combine harmonic analysis and the study of infinite trees (a form of graph that does not contain a circular path). 

Cohen quickly found himself making frequent trips to Italy to collaborate. He began teaching and giving lectures in Perugia, Milan, Rome and Bari, a city in southeastern Italy. He eventually bought an apartment in Bari. In the 1980s, he divided his time between Maryland and Italy. Since then, he has continued to spend one to two months every year in Bari. Now that he is retiring, he looks forward to spending more time in Italy, indulging his interests in Italian food and art when travel is feasible again. 

John Millson

Professor Emeritus John Millson grew up in Ontario, Canada, but he found his community all over the world through the field of mathematics. 

“I’ve had some 20 collaborators,” Millson recalled. “From France, Germany, India, Russia and the U.S. Some of them I’ve been very close with, and of the 90-some papers I’ve written, at least 70 of them were collaborations.” 

Millson considers it a highlight of his career that he was able to work with people he grew to call friends, like Stephen Kudla from the University of Toronto, William Goldman from UMD and Misha Kapovich from the University of California, Davis. 

As a theoretical mathematician, Millson studies differential geometry with a focus on discrete subgroups of Lie groups, which are fundamental in number theory and algebraic geometry. But he began his journey to math by way of physics. 

After high school, Millson expected to study physics at a Canadian university where he was offered a scholarship. But his father had other ideas. Despite the cost of going to a private school in the U.S., the elder Millson arranged for a friend who had gone to MIT to convince his son that MIT was a better choice. 

“My father’s friend made a very persuasive argument that if I went to MIT instead of a Canadian university, I would end up ahead,” Millson recalled. “It was very generous on the part of my father, and, naturally, it changed the course of my career.”

At MIT, Millson quickly found his calling in mathematics. He remembers being captivated by the n-dimensional version of Stokes’ theorem in his second year. With just four symbols on the left of the equation and four symbols on the right, the theorem encapsulates several different theorems from vector calculus and is fundamental in geometry and physics.

“It’s this really beautiful formula,” Millson said. “Until you study mathematics, you don’t know what an incredibly beautiful world it is, in the way that just a few symbols can explain many seemingly unrelated things.”

After spending his junior year at the University of Paris, Millson received his B.S. in mathematics from MIT and went on to earn his Ph.D. in mathematics from University of California, Berkeley. Millson then took a job at the Institute for Advanced Study in Princeton and a year later became an assistant professor at Yale University in 1974. 

His ease at making friends in the math world paid off when he found himself on sabbatical with a round-the-world ticket and a cadre of colleagues overseas. He had received a Sloan Research Fellowship in 1978 and spent the fall semester at Oxford University. That left the spring open for travel.

“Pan-Am [the now defunct airline] was selling around-the-world-in-80-days tickets for a thousand dollars,” Millson recounted. “You had to keep going in the same direction, but you could stop anywhere along the way for as long as you liked during that 80 days. I had friends all over the world, so I went to Tokyo to work with friends at the University of Tokyo. And I went to Hong Kong and Mumbai to work with his friends at the Tata Institute.”

It’s no surprise that it was a collaboration that brought Millson to UMD as a visiting professor in 1986. Millson was a professor at UCLA at the time. He and Goldman had published a paper that included a conjecture they couldn’t quite prove. In response to the paper, Belgian mathematician Pierre Deligne sent Millson a five-page letter guiding him toward the solution.

“The letter contained a remarkable new idea about deformation theory, and I was stunned at the magnitude of the idea and the extraordinary generosity of Deligne that he had handed this to us,” Millson said. “So, I wrote to Bill [Goldman] and said, ‘Bill, I’m coming to Maryland and we’re going to work this out.’”

Deligne's five-page letter led to a two-year collaboration, a 51-page paper in the prestigious journal Publications Mathématiques de l'IHÉS and an invitation for Millson to speak at the International Congress of Mathematicians in Kyoto in 1990.

During the time he was working with Goldman in Maryland, Millson felt welcomed and appreciated. He also felt right at home on the campus golf course. When he was invited to join the faculty in 1989, he readily made the cross-country move. 

In addition to professional support and friendship, Millson credits the mathematics community with helping him through challenges in his personal life. Twice widowed, Millson said his continuing collaborations with brilliant mathematicians and good friends provided him great comfort through the years. As a reminder of that support, Millson keeps the conference poster from a 2008 birthday celebration the department held in his honor hanging on the wall of his living room. The poster is especially meaningful to him because it was designed by his friend and former UMD mathematics faculty member Richard Schwartz.

When reflecting on his long career, Millson often refers to a quote he heard 37 years ago. In 1983, while Millson was at the Institute for Advanced Study, he was an invited speaker at the 60th birthday conference for the Swiss mathematician Armand Borel. In Borel’s closing speech, he quoted the famous baseball player Willie Mays as saying “getting paid for playing baseball was like getting paid for eating ice cream.”

That quote stuck with Millson, and to this day, it describes how he feels about the career he was fortunate to have in mathematics. And like ice cream, mathematics is something he intends to enjoy for many years to come, even after his retirement.