Sophomore math major Marie Brodsky finds a different way to teach children math.

Marie Brodsky found her passion for mathematics by going in circles—math circles. Originating in Eastern Europe, math circles spread to the United States in the 1990s, where they found Brodsky in 2006. From the age of 4, Brodsky participated in these extracurricular math learning experiences and her love for problem-solving grew from there. 

By the time Brodsky was 11 years old, she was leading a math circle of her own—teaching younger children foundational math and problem-solving skills through something she calls “recreational math.”

“I still can’t believe that all these parents allowed this little girl with pigtails and polka-dot clothing to teach their kids,” the sophomore math major at the University of Maryland recalled with a laugh. “But I think they recognized that their kids would have a lot more fun learning from someone just slightly older than them rather than a serious adult.”

Brodsky came to UMD as a Banneker/Key Scholar in the Honors College’s Advanced Cybersecurity Experience for Students (ACES) program—and she was looking for an opportunity to continue teaching when she found the Student Initiated Courses (STICs) program. 

STICs help students design, develop and teach their own courses under the guidance of faculty advisors. This year, Brodsky is the executive director of the program, and this fall she taught MATH299Y: Teaching Math to a Young Audience. The course curriculum is inspired by Brodsky’s experience tutoring through her platform Conversations in Math during the pandemic, when she taught math virtually to dozens of children around the world. 

“I took a lot of notes on what worked well and how to explain certain resources I’d found on all those topics,” Brodsky said. “To put together the curriculum for MATH299Y, I went through my lesson notes, picked out the topics I thought were most interesting and put them in logical order for the semester.”

MATH299Y makes connections between seemingly disparate mathematical concepts and introduces topics typically not covered in elementary school curricula—helping college students take advanced topics and simplify them to understand their core ideas. Brodsky anticipates that students will come away with a stronger foundation in math and greater confidence in their abilities to break down these concepts for a young audience.

“I want my students to feel why math can be exciting,” Brodsky said. “Then, when they go on to teach, they remember that these connections between concepts are exciting and see how they can frame them in a more interesting way.”

In each class, Brodsky diagrams problems on the blackboard and guides her students to solutions. She poses math problems geared toward children ages 4, 8 and 12 and asks her students how they would break them down for younger audiences. Brodsky frequently asks, “But why?” to help the students dig deeper into these core mathematical concepts.

For example—a frog is jumping back and forth over a stream. It jumped 101 times. Which side did it end up on? 

“It’s not obvious. What’s your first reaction?” Brodsky said to her class. “In the end, it’s equivalent to having done one jump. If you are teaching 4-year-olds, I would totally act this out by having students jump back and forth in the classroom.”

“I think Marie has done an excellent job understanding what skill sets the various age groups have and how her examples apply or don't apply to those various age groups,” said Mathematics Principal Lecturer Justin Wyss-Gallifent, Brodsky’s faculty advisor for MATH299Y. “In teaching, knowing how to structure the material is probably more than half the battle. In Marie’s case, she is not just teaching problems but also understanding how those age groups would approach the problems.”

Wyss-Gallifent explained that learning to break down problems for others and developing public speaking skills are just some of the benefits of teaching a STIC. Additionally, undergraduate students connect with content differently when another undergrad is teaching the course.

“It’s definitely different having an undergrad student in a professor role. Marie really knows what she’s doing,” said Shiraz Robinson, a plant biology major and one of Brodsky’s students. “This class has given me a different way to look at numbers and it’s helping me understand math better. You can scale these ideas to very deep ideas that require all your computational power.”

In her role as executive director of the STICs program, Brodsky wants to give the students teaching STICs creative license to teach the topics they’re passionate about while also holding them accountable as teachers.

“We’re planning to do workshops where the facilitators give each other feedback on their course planning, content, syllabus, maybe teach a little bit to each other and get feedback,” Brodsky said. “Most people who are teaching a STIC are really committed to this idea of students teaching courses, so we want to support them and give them even more resources to become even better teachers.”

When it comes to her future career plans, Brodsky is still figuring that out. For now, she’s interested in learning more about education policy and curriculum development. One thing she’s certain of: She wants to make education better.

“I want to help improve the education system,” Brodsky said, “and revamp how teachers get incentivized to teach in better ways, how they decide the material and curriculum, and how to make the experience better on a larger scale.”

Written by Katie Bemb

Musician Sheyda Peyman to release her debut album while conducting research for her doctoral dissertation.

Scales, intervals, patterns, symbols—to Sheyda Peyman, all music is math. Though to some it may seem an unlikely connection, Peyman, a Ph.D. candidate in the Applied Mathematics & Statistics, and Scientific Computation program at the University of Maryland, says the link between mathematics and music is undeniable. 

“The arts and sciences all describe the same reality from different perspectives,” Peyman explained. “I’m attracted to the beauty of math and music in a truly philosophical way.”

Peyman, a vocalist, guitarist and pianist who goes by Sheyda Do’a on stage, will release her debut album in 2022. She was inspired to work on the album while an artist in residence at Strathmore, where she forged connections in the D.C. music scene.

“My music has influences from jazz and Latin music, as well as my Albanian culture,” said Peyman, who was raised in Albania. “When I’m writing my music, I don’t really have a formal process—I just get inspired in the moment, the music comes to me and I play it.”

Peyman has learned from experience that her music isn’t quite as meaningful without math in her life. After completing her bachelor’s degree in mathematics at the University of Edinburgh in 2016, Peyman attended Berklee College of Music. She spent a semester studying only music and quickly realized that she missed math—so she quit the program. 

  When she moved to the D.C. area in 2018, Peyman decided it was time to resume her math studies. The University of Maryland Department of Mathematics offered exactly what she was looking for. 

“I’m so happy with where I’m at in my career, in both my music and in my studies at UMD,” Peyman said. “I’ve realized I need both math and music in my life.”

In her first few years at UMD, Peyman took graduate-level courses while also teaching undergraduates—earning the 2020 A. Kadir Aziz-John Osborn Graduate Student Award for her teaching skills. Now, with her qualifying exams behind her, Peyman’s research is ramping up. Her focus is network theory, which Peyman notes is a “hot topic” nowadays. 

“Simply put, a network can be thought of as a set of objects and the interactions between them. The objects can be anything from people to proteins to neurons, and the interactions can be anything from emails sent to connections on social media to synapses between neurons,” Peyman explained. “Though I started at UMD doing a lot of abstract algebra, I found myself leaning more and more toward this kind of applied math. The possibilities are fascinating to me.”

Peyman is preparing to submit a paper on adversarial data contamination, which happens when data is either maliciously or accidentally altered. Consider, for example, a Facebook network of 156 vertices representing 156 people—if two of them are friends on Facebook, then there is an edge connecting the two corresponding vertices. If an adversary hacks one of the 156 accounts in the network and deletes that account’s friendships, how can that information be recovered?

“This adversary could, for example, delete a number of edges from the graph,” Peyman said. “If we have a second network that is related, we can use this information to retrieve at least part of the original network, implementing regularization techniques to help mitigate the effect of an adversary.”  

In a paper written with her advisor, Mathematics Associate Professor Vince Lyzinski, Peyman proposes that network trimming should be simulated to make networks faster, smaller and more efficient—without risking network function or data loss.

With her paper wrapping up, Peyman is embarking on a new project with Lyzinski: programming an algorithm to optimize recommendations based on user inputs.

“Let’s say you’re watching Netflix. On Netflix, you can ‘like’ something you watched, and then the computer algorithm sends you recommendations based on that. Sometimes those recommendations might be wrong because the algorithm is not perfect,” Peyman explained. “We’re trying to see how we can use the information that the user inputs to give a better recommendation.”

Now in the initial exploratory phase of this new project, Peyman spends most of her time reading relevant papers and preparing to write code to apply and test her theories. 

When she’s not deep in her doctoral studies, Peyman performs around the metro D.C. area and prepares for her upcoming album release. Longer term, she plans to continue pursuing her career in music while also working in applied math and programming.

“Similar to how music inspires and moves me, it’s very empowering to see a math problem, try to solve it, and then actually apply it myself to see if the results work,” Peyman said. “I’m really getting to appreciate and pursue these two passions of mine, which is why I love where I’m at right now.”

Written by Katie Bemb

Sarah Brown (M.A. ’03) connects the dots from mathematics to a global career in cybersecurity.

Years ago, when Sarah Brown envisioned all the things she might do with a master’s degree in mathematics from the University of Maryland, chasing bad guys was definitely not one of them. 

“I don’t think I knew exactly what I was going to do,” she explained. “I knew there would be job opportunities. I could aim to be a teacher, perhaps a university professor.”

Instead, Brown’s career path has taken her to the rapidly changing world of cybersecurity. For over 15 years, Brown (M.A. ’03, mathematics) has been on the front lines of the global fight against cyber threats. Now based in Delft, Netherlands, she currently works as a senior scientist with the NATO Communications and Information Agency (NCI Agency), ensuring that NATO’s essential communications systems are protected and resilient to compromise.   

“NATO is an alliance of 30 countries from Europe and North America who consult and cooperate in the area of defense and security, as well as conduct multinational crisis-management operations together,” Brown explained. “It’s essential that NATO’s systems can fully support these activities, including from a cybersecurity perspective.”

It all started with math

As an only child who grew up in Columbia, Maryland, Brown discovered a love of mathematics early on.

“I thought math was exciting from an early age, and this definitely came from my parents,” Brown explained. “My dad was a mathematician, and my mom was a manager in a very heavily mathematical research group supporting the government in Ft. Meade, Maryland. A lot of my parents’ colleagues were mathematicians and I would meet them at different functions.”

From problem-solving to the challenges of algebra, topology and complex analysis, Brown particularly loved the field of pure mathematics. 

“I liked my math classes in school, I enjoyed logical thinking and doing fun little puzzles, I enjoyed the other nerds that were on the math team with me,” Brown explained. “It made sense to me and I thought it was a lot of fun.”

At Oberlin College, Brown majored in mathematics and, at the encouragement of her dad, computer science, too. She studied for six months in the Budapest Semesters in Mathematics program for U.S. undergraduates and interned during the summers at the National Security Agency. After getting her undergraduate degree, Brown began her Ph.D. in mathematics at the University of Washington. 

“Coming home”

“The first year of graduate school was tough and I started to think about getting through it with a little more support,” Brown recalled. “Fortunately, I had also been accepted into the mathematics graduate program at the University of Maryland, and after a year in Seattle, it was like coming home.”

During graduate school, Brown worked at Sandia National Laboratories for two summers, where she did research on a type of optimization problem that could be solved using complex simulations called asynchronous parallel pattern search. She also spent a fellowship semester with the National Academy of Sciences, which introduced her to how scientific research and mathematics are used to inform and shape public policy, and she quickly realized that was exactly what she wanted to do.

“I wanted to do a little bit of technical scientific work, but I also want to see the big picture and understand from a business perspective what the priorities in an organization should be and what kinds of mathematical problems or research should be pursued,” Brown said.

After receiving her master’s degree, Brown joined the National Academy of Sciences full time before finding her next career move.

“At some point I came across The MITRE Corporation, and I learned about Federally Funded Research and Development Centers—FFRDCs—which is the model under which MITRE operates,” Brown said. “FFRDCs function as nonprofit, technical experts for the government, with work that involves plenty of technical challenges as well as public policy and strategy.”

MITRE hired Brown in 2004.

“I applied several times to different departments and was ultimately contacted by their information assurance department,” she recalled. “They said, ‘Your math and computer science background is a really good fit, we could definitely use someone like you.’”

Brown had never pictured herself working in this field, but the more she learned about it, the more interested she became.

“I knew about cryptography and the encryption of data from my mathematics studies at Maryland, and computer programming and operating systems, but I didn’t understand the complexities of system security, and cyberthreats until I joined MITRE,” Brown explained. “In my work there, we focused on identity and access management, evaluating product security and how to ensure data confidentiality during communications between systems.”

A big move

While Brown was working at MITRE’s D.C.-area headquarters, her fiancé was offered an opportunity to do research in Amsterdam. Moving to the Netherlands sounded like a great adventure, so Brown started doing some digging.

“I found out MITRE had a scientist working as a liaison to NATO sitting in The Hague,” Brown explained. “I asked my management more about this role and partnership with NATO, and it turned out there was a great opportunity to serve in a similar position.” 

The rest, as they say, is history.

“It was very serendipitous,” she said. “MITRE sent me over for what was supposed to be two years. We got married, packed three suitcases, came overseas and started taking Dutch lessons. We just got up and went.”

That was 2008. By 2013, Brown’s husband had finished his postdoc and settled into a job with a Dutch company, and Brown had gained a great deal of experience in system security from the NATO perspective, with an appreciation for technical collaboration between the U.S. and NATO and the importance of interoperability and coordination between systems and technical teams. Now she was ready for a change, and she found an exciting opportunity with Fox-IT, a well-known Dutch cybersecurity startup.

As principal cybersecurity expert for FoxIT, Brown supported the threat intelligence team, tracking the changing landscape of cybercrime around the world—and threats to banking institutions in particular—providing guidance to help keep customers’ systems safe.

“It was a fascinating experience,” Brown said. “We were doing technical work, collaborating on a daily basis with the banks and trying to understand the latest cybercrime methods, how these complicated attacks were being carried out and what could be done about them.”

Over the next three years, her work involved collaborating with other cybersecurity experts around the world to unravel and disrupt complex cybercriminal schemes that were stealing millions. 

“Many high-profile groups, like GameOver/P2P Zeus, SpyEye and Dridex were coming up with new and never seen before attack techniques that were very effective,” Brown explained. “It takes a big team effort to understand the full picture of what’s going on. We were involved at Fox-IT, but so were a lot of different companies and countries—and in some cases, law enforcement took action. I enjoyed the collaboration in this work, and it was rewarding to be able to make a difference and to be a part of that.” 

“Working for the good guys”

In 2016, Brown returned to NATO, accepting a role as a senior scientist at NCI, the Communications and Information Agency in the NATO Cyber Security Centre. There, she found a welcome change of perspective from her previous work tracking cybercriminals.

“It’s definitely a lot of fun to be kind of a cyber detective, but after some time focused on criminal activities at NATO it felt like, ‘I’m working for the good guys now, focusing on security systems and taking a break from chasing bad guys,’” she said.

Five years later, Brown is a senior scientist with the Communications and Information Agency, which procures, deploys and defends systems for NATO nations and commands, specifically communications, information and cyber systems, intelligence systems and systems. 

“Robust and resilient communications are at the center of our work,” Brown explained. “Security is all about confidentiality, integrity and availability. You want things that need to stay confidential to stay confidential, things that are put into the system should maintain their integrity, they’re not going to get tampered with, and the system’s available and the data is available when you need it.”

This year, Brown focused on updating the agency’s cybersecurity strategy. 

“Our NCI Agency cybersecurity promotes a perspective of resilience,” she said. “That is, we ensure that the work we do is driven, monitored and reported on from a cyber resilience perspective. It’s essential to create a balance between prevention, protection, defense and recovery in a way that manages risks, because realistically, 100% security is not an achievable goal.”

Though Brown never imagined a career in cybersecurity years ago, she loves her work and the mathematics that’s very much a part of it. 

“I don’t have any integrals to solve, which would be nice,” she said, “but in cybersecurity it’s about problem-solving and breaking down complicated problems into logical pieces in the right order. And I think it’s those skills that I still use now more than anything.”

And, after 14 years, the Netherlands feels like home. 

“We arrived with three suitcases, but we now have two girls, ages 10 and 11, and we live in a beautiful little town where we can bike and walk everywhere,” Brown said. “I really enjoy Europe’s healthy work-life balance. People work from 9 to 5 and they’re very focused in those hours, and then at five o’clock they switch the computer off.”

Brown’s work-life balance allows her to spend more quality time with her family, which she hopes will include a lot more math in the future.

“I love the time I have with my girls. As the girls go through school, I look forward to learning with them and encouraging them the way my parents encouraged me,” she said.

Written by Leslie Miller