**Abstract and Bio:**

Among the most basic objects that one can study in geometry are arrangements of lines in the plane —configurations of straight lines and points with specified incidence conditions, like “this subset of four lines intersect at that point”. The set of all configurations of lines satisfying chosen incidence conditions is a simple example of an object known as a moduli space, a concept that appears naturally in geometry, representation theory, physics, and even genetics. I’ll try to explain a remarkable phenomenon displayed by these spaces of arrangements of lines, known as “Mnev Universality”, which states that these simple configuration spaces of lines encode in them the same complexity as arbitrary Diophantine polynomial systems. This is a fancy way of saying that these spaces of configurations can become “as complicated as any object defined by polynomials”. Time permitting, I’ll also explain some consequences of this for moduli spaces in algebraic geometry.

Dhruv Ranganathan is presently a CLE Moore Instructor at the Massachusetts Institute of Technology and a member of the Institute for Advanced Study. He earned his PhD in mathematics from Yale University in 2016 and a BS in mathematics from Harvey Mudd College. Dhruv’s research centers around combinatorial algebraic geometry, an age old tradition that turns difficult problems in algebraic geometry into impossible problems in combinatorics. He has a passion for working with students, and has mentored numerous undergraduate and high-school research projects since early in graduate school. To become a mathematician, he cast aside what would have been certain successful careers in countless sports, as well as likely starring roles in Hollywood movies. As a firm proponent of quantum mechanics and the many-worlds interpretation of it, he likes to believe that there is a parallel universe version of himself in which these sacrifices weren’t made.

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**Abstract:**

What is applied mathematics? In these talks, I offer an historical examination of the changing conceptions regarding applied mathematics over the past three centuries.

*Talk 1:* Focuses on the history of mathematics from the beginning of the seventeenth until the end of the nineteenth century. It was then that applied mathematics established itself as a distinct professional identity separate from pure mathematics. As I demonstrate, it is impossible to answer the question, ‘what is applied mathematics?’ without attending to the more vexing question, what *is* mathematics.

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Talk 2:* Independent of the first, focuses on the growth of applied mathematics in the United States during the twentieth century. I examine the emergence of the discipline in the aftermath of World War II. Such an historical perspective, I hope, will illuminate contemporary concerns about the breadth and range of applied mathematics.

**Bio:**

Dr. Steingart received a BS in Mathematics from Columbia University before she joined MIT’s Program in History, Anthropology, and Science, Technology, and Society as a doctoral candidate. She spent one year at the Max Planck Institute in Berlin as a pre-doctoral research fellow and, after receiving her Ph.D., she was nominated fro the highly prestigious Harvard Society of Fellows Junior Fellowship. Her recently finished first book: *Pure Abstraction, Mathematical Thought and High Modernism* investigates how what counts as mathematics to mathematicians has changed, sometimes quite significantly, during the 20th century. In addition, she’s written brilliant papers on the rise of animations in understanding mathematics, examining new techniques by which mathematicians represent abstract ideas in multiple media. In her papers Steingart calls for a broader conception of what counts as mathematical activity, beyond the lone mathematician working with paper and pencil.

President **Siddhi Desai** and Vice President **Amanda Soliman**, both from the Class of 2017, founded the Council to bring together math secondary education majors at TCNJ and form a network of future match teachers. Former math faculty member **Dr. Farshid Safi** and current advisor **Dr. Cathy Liebars** had encouraged Desai and Soliman to start the student organization and establish it as a chapter of the National Council of Teachers of Mathematics (NCTM). Dr. Liebars remembers, “When Siddhi and Amanda came to me and Dr. Safi with the idea of starting a student organization that would be an affiliate of NCTM on campus, I was thrilled! As a student affiliate, the organization gets a free membership in NCTM, which is the leading organization for mathematics teachers. It has numerous resources for pre-service and in-service math teachers to learn more about the profession and stay current on mathematics education resources,” says Dr. Liebars.

Shortly after its founding, the Council was indeed recognized as a student affiliate of the NCTM – the first in the state – at the 25th annual conference of the Association of Mathematics Teachers of New Jersey (AMTNJ). The organization later received its official charter at the national conference in Boston in April 2015. “One of the best college experiences I have had was attending the NCTM Conference in Boston. In addition to receiving our official affiliate charter, it was pretty awesome meeting and attending sessions led by math educators whose journal articles I’ve read,” says Desai.

The club gives math education majors the opportunity to explore their interests as well as being part of an intellectual and vibrant organization. “As a senior math secondary education major, I was very interested in joining CSTM when it first came on campus because I knew it would be very helpful to me in pursuing a career in teaching middle or high school math,” says **Stavroula Kontogiannis ‘16**.

“CSTM being content-specific to math was what drew me towards the club,” says **Jessica Martin ‘16**. “I felt that the meetings and events would be not only beneficial to my career, but I also felt a sense of community among math education majors. I was extremely excited to be a part of the founding executive board because I felt that it gave me and my peers the opportunity to create something amazing for students. It is a support system that is beneficial to have when choosing classes to take, studying for the Praxis exam, or preparing for practicum experiences.”

The members take pride in community outreach and volunteering on and off campus. “We just began Praxis Tutoring which I am very excited about. I lead one of the Math Content Knowledge groups,” says Martin. Kontogiannis adds, “CSTM volunteers at math education conferences, such as the NCTM and AMTNJ events. I had the opportunity to volunteer at both and we were able to listen in on lectures and talk to many math education representatives there.” CSTM Community Liaison **Jennifer Stranz ’17** adds, “It was amazing to be surrounded by a group of people so passionate about math education. There were so many sessions available for future teachers of mathematics at any grade level. I have learned so much more about the profession since joining and have been exposed to great speakers and events.”

CSTM also hosts panels and discussions on campus, which allow for interactions between faculty and students outside the classroom, creating a vibrant and intellectual environment for future math teachers as well as a warm community between professors and students. “CSTM is a great environment to collaborate with peers and meet other future teachers. We also host a variety of speakers and are always open to new ideas for topics or presenters that the members would be interested in,” says Stranz. Kontogiannis adds, “The goal of CSTM is to create a sense of community among all math education majors, which I believe they have done very successfully.”

Some of these events have provided very useful information about the Common Core, Math Anxiety, and the Use of Technology in Math Education. There have also been other panels such as the TCNJ Math Education Faculty Panel, the Administrative Panel, and the Junior Field Experience (JFE) Panel. Martin adds, “I love it when CSTM holds panels. As math majors we are required to attend colloquium talks prior to graduation. While they are always interesting, I feel that they are so much more geared towards applied and pure math majors. Our panels give math education majors so much information and so many ideas,” states Martin. While the CSTM panels are geared towards math secondary education majors, all math majors are welcome to attend. “My favorite event was a professor panel as it gave students the opportunity to get to know our professors on a more personal level. It’s great to see them outside of an academic setting and learn about things they enjoy doing and how they got to where they are today,” adds Martin.

The JFE panel was especially beneficial as it gave members of the club the opportunity to ask questions about experiences, expectations, and more. Martin, who had gone through JFE, recalls, “We walked the students through everything that goes into the experience – from school placement to lesson planning. The most exciting part of being on the panel was being able to share my experience at Trenton Central West with students who will soon be there too. It is a great feeling to be able to give them advice and answer their questions honestly that they might be afraid to ask a professor.”

The group meets and organizes events once a month and currently has around 30 members with an active executive board of six members. CSTM works with two other math department clubs on campus – the Mathematics and Statistics Club and the math honor society Pi Mu Epsilon – to host one event each semester to create community for all math and statistics majors as well as faculty and staff. The executive boards of all three of the math clubs collaborate to plan a holiday party in the fall and a department picnic in the spring. “These faculty-student interactions help us form a close-knit community within the department,” adds Desai.

TCNJ is known for its small class sizes and approachable faculty, which are especially beneficial to future math secondary education majors. Soliman adds, “I chose TCNJ because of its welcoming, dedicated professors, small class sizes, and above all, for its experience-based pre-service teacher undergraduate program.” These unique experiences for math education majors start at the underclass level. Sophomores begin participating in tutoring or research practicums and, in the spring, they begin observing inside a classroom looking at a teacher’s approach and classroom culture. By junior year, students start learning methods of teaching through field experience. This exciting opportunity is not offered at other colleges until graduate school. “CSTM is all about creating a network for the math education community. Whether it’s getting to know professors, networking at conferences, or working with fellow teachers, students learn the value of collaboration and are better prepared to confront the daily challenges of teaching,” says Soliman.

Clearly CSTM at TCNJ is leading the way for making math education inspiring for students. Kontogiannis says, “Other students should get involved in CSTM because of the great events, activities, and opportunities it provides. CSTM is a great club to be part of mostly because I have become friends with other members that share the same interest as me. We are able to come together at meetings and events and learn more about math education outside of the courses we take together. I would, without a doubt, recommend this club to anyone interested in math education.” Martin sums it up perfectly. “I strongly encourage all future teachers of mathematics in all levels – whether it is early education, elementary, or secondary – to come to our meetings and events so that we can better prepare ourselves to be the best teachers we can be.”

– Gabrielle Okun

**For More Information:**

“There are days when I am really overwhelmed with homework, or my class introduced something really new and I am stumped on it,” says Tucker. “So I sometimes go into the week a little bit frustrated, but then I go to Math and Stats club. Being around the other members helps me relax a little bit, and I feel like I’m ready for the rest of the week.”

However, being a math expert is not a requirement for students interested in joining. With a relatively young executive board (the co-presidents are sophomores), the Math and Stats club has evolved throughout the years to become not only a source of connection for students in the Department of Mathematics and Statistics but a place where students know they can find a smiling face and a helping hand. **Dr. Carlos Alves**, associate professor of mathematics and one of the faculty advisors for the club, says “It’s an outstanding e-board, even though they are all young. It’s a lot of fun to work with them because they are willing to ask for advice, they’re receptive to our feedback, and they are self-sufficient.”

**Kate O’Connor**, a freshman math education major who is also the club’s publicist, believes the organization has helped her realize her own leadership potential. She says, “I was always very shy in high school, and just by putting myself out there and becoming a part of the executive board, I have improved my communication skills, learned to relax a little bit, and realized that there is a fun side to school.”

Every Wednesday from 12:00pm to 1:00pm, members of the club come together to talk about their days, play math-oriented games, and help each other with their course work. Vice-President and junior **Emily Thompson**, a math and elementary education major, explains how meetings can consist of Mathlete Matchup to Cramium (with an m) to discussing their next field trip. In fall 2015, the organization put on its first Mathlete Matchup, a family feud-style game in which a team of five students face off against a squad of five professors.

“I know most of the professors by now just because of the events that we have had when we were able to talk to them outside of the classroom setting,” says Co-President and sophomore math elementary education major, **Marisa Pope**. She fondly remembers playing Cramium, a jeopardy-style game played frequently with students and faculty. Dr. Alves believes that events like these “help the students see us as people, that we can goof around and have a good time outside of the classroom.” On a recent field trip, the club visited the National Museum of Mathematics, Manhattan’s only hands-on mathematical science center and the largest public outdoor demonstration of the Pythagorean Theorem.

The organization also provides opportunities for members to learn about which classes are being offered the following semester and also allots time for professors to talk about what the courses will entail. Pope says she highly benefited from the discussions about registration when she was new to the TCNJ: “You really get introduced to the classes you’re going to be taking not only next semester, but in the future as well.”

Contrary to common misconception, the Math and Stats Club does not only consist of students who are majoring in these fields. Students studying biology, psychology, and engineering frequent the meetings and events. Thompson believes this is because the club provides a support network and shows the fun side of a subject that is known to present challenges. “Someone over the semester called it ‘The Math Family,’” says Thompson. “And it really is – it’s a way to find your place.”

In spring 2015, the club hosted its first ever Candy Casino Night, where participants tried their hand at card games like blackjack, roulette, and Texas hold ‘em – with the prize being candy, of course. The event also included a mocktail bar that featured “square rootbeer floats” and “minimum and maximumosas.”

“Don’t be afraid to come to one our Math and Stats Club events. You’ll see what a laid back and fun environment it is,” says Thompson.

– Kaitlyn Njoroge

**For More Information:**

Recipient of the 2014 “Distinguished College of University Teaching of Mathematics” award from the New Jersey Section of Mathematical Association of America (MAA), **Dr. Karen Clark** has been inspiring and influencing many students who have entered her classroom at TCNJ for 20 years. Professor Clark knew when she enrolled in New York University for mathematics that she would go into teaching.

Her high school math teachers had helped her to enjoy the subject and motivated her to enter academia. She continued her studies at New York University (NYU), completing her Ph.D. on mathematical modeling of composite materials. This involves applied math and theories to study materials with different properties mixing together to obtain a different set of properties. Some examples of everyday composite materials include concrete and fiber-reinforced polymers, which are utilized in buildings, vehicles, and other structures.

Looking into other ventures, Clark has starting to learn about climate modeling, which focuses on the interactions of the atmosphere, sun, ice caps, and oceans. She also continues to teach mathematical courses at TCNJ such as calculus and linear algebra. However, the MAA award-recipient’s current focus is writing a linear algebra textbook.

“I’ve taught the course enough to get the sense of what topics go well together and what order is nice to do it in.” Clark explained. Her topics course on linear algebra has no textbook available and she feels that it would benefit the students if there were one.

A basic definition of linear algebra is *the study of equations and their transformations that can be represented by a matrix*. Clark described applications of linear algebra with real world examples, including how Google ranks the hits when you search for something and how pictures you take are processed. “It all connects to the subject of linear algebra.” She said.

“What is difficult is that you want a lot of examples for students to do, and the examples have to work out nicely, so students don’t get frustrated.” Clark admitted that she did not anticipate this problem when writing a textbook. She has been working on this project for the past year during a sabbatical, and is continuing to do so while teaching.

Prior to TCNJ, Clark conducted post-doctoral studies at the University of Michigan for a year, followed by a year teaching at Stevens Institute of Technology. She has enjoyed working at TCNJ, in part due to the students and teaching environment at the College.

“Here at TCNJ, with the smaller classes, you really get to know the students,” Clark remarked, “especially having them semester after semester. You really can build relationships with students.”

“She is not afraid to challenge students,” **Vince Longo (’15)**, mathematics major, said about Clark. Longo had taken Clark’s linear algebra class. Although he found it difficult, he received a greater appreciation and solid foundation on the subject. “I felt like she pushed me outside my comfort zone in her class,” Longo continued, “but not so far out that the material and assignments were out of my reach.”

Professor Clark feels that the TCNJ classroom cultivates participation and discussion among her students. This experience not only is beneficial for her as a teacher, but for students as well in their undergraduate education. The kind of relationship that Clark builds with her students made it no surprise when she received the MAA award.

“Karen is very concerned about her students’ progress and understanding, and she will spend many office hours with them outside of class.” **Dr. Cathy Liebars**, Co-Chair of the mathematics and statistics department, revealed.

Liebars and Clark started their careers at TCNJ the same year and have become great colleagues and friends. Liebars added that her friend was a great academic advisor to students as well. “I know this because she advises Math Secondary Education majors and I get her advisees in their junior year. They always are prepared and know what they are doing.”

In addition to making sure that her students understand her linear algebra course, Clark had brought up the importance of students exploring what the different topics their major has to offer to find their interests. College is a time for exploration and figuring out what you really enjoy doing.

“It’s going to go by really fast.” Clark commented on the years that students have at TCNJ. “They [students] are such different people four years later from when they come in.”

When she is not cultivating future math educators, Clark loves to travel with her family. “My students might not be aware that I have a bunch of children.” Clark added. She has four children at home, and every summer, she tries to spend a few weeks with her family traveling; her favorite destinations are national parks. “Travel as much as you can,” she urged. “This is a huge world.”

– Danielle Leng

**For More Information:**

While there is no cure for the disease, Michael Ochs, TCNJ associate professor of mathematics and statistics, and a colleague of his at Johns Hopkins, are a step closer to identifying patients who stand the best chance of benefitting from treatment.

“The treatment is very unfriendly—typically Interferon—and if you have the mild form of the disease, you don’t want to treat it so aggressively,” says Ochs.

Ochs, who worked at Hopkins before coming to TCNJ in 2013, helped to analyze a database of tissue samples that Jerry Spivak, the director of Hopkins’ Center for Chronic Myeloproliferative Disorders, had collected from over 600 patients with polycythemia vera.

It sounds a bit complicated, but for Ochs the task—and his research—boils down to estimating the probability of certain molecular changes occurring in cancer.

After controlling for differences in the disease connected to gender, Ochs and Spivak split the group into two: those they knew had the more aggressive form of polycythemia vera and those with the milder—or “indolent”—form.

The men ultimately identified six pairs of genes as a biomarker for the more aggressive form of the disease. The team’s findings were published in *The New England Journal of Medicine* on August 28.

Ochs has had a long and varied career, earning his bachelor’s at Haverford College in chemistry, a master’s in Celtic languages and literature at Harvard, and his Ph.D. from Brandeis in physics. He worked for a large defense contractor for a year, delved into solar energy, and spent two years in a lab studying simian AIDS.

Admittedly, he says, “It’s been a meander.”

“I’d like to think that what I do is what a scholar has always done,” says Ochs. “What I want to work on is what’s interesting, or what’s an interesting problem. It’s something we’re losing a bit in academia. I think it’s becoming harder and harder not to be a narrow specialist.”

Looking ahead, Spivak and Ochs have submitted a grant request to the Leukemia and Lymphoma Society to continue their research on the biomarker. “Can we start to understand the biology that drives the biomarker?” asks Ochs. “If you want a new treatment option for the aggressive form, we need to understand that.”

—*Renée Olson, with reporting by Mary Jo Patterson*

Since childhood, Dr. Andrew Clifford seemed to know he would enter the world of Mathematics.

“According to my mom, in kindergarten, the teacher said, ‘what do you want to be when you grow up’ and we had to draw a picture of it.” Clifford reminisced, “I had my paper and drew a line down the middle. On one side I drew a picture of a carpenter and on the other I drew a picture of a mathematician.”

He admitted that at the time he only knew that a mathematician was, as his teacher explained it, “Someone who studies numbers that no one had thought up yet.” This appealed to the young professor. Clifford said, “I was going to either be that or a carpenter because I like saws.”

For undergraduate study, Clifford went to State University of New York (SUNY)–Binghamton for Mathematics. Then in his senior year with the guidance of his advisor, he decided to go to SUNY–Albany for graduate school.

“My interest was in topology, which is kind of like geometry.” Clifford explained, “I liked the low dimensional stuff, but it turned out to understand the low-dimensional topology, you needed algebra. My [current] area is where algebra meets topology.”

Clifford’s area is called combinatorial group theory. “Geometry is shapes. Algebra is the study of operations—addition, subtraction, and multiplication. We are used to doing that on whole numbers; you can make an abstract set on which you can do one operation. That would be a group.” Clifford explained, “It turns out that groups can also describe the symmetry of things, the way you can move things around so it still looks the same. That’s the connection between studying topology and studying groups.”

To explain his interest, Clifford provided a piece of paper as an example of his research in group theory. Imagine a blank piece of paper, which you folded up into different origami shapes. Clifford clarified, “The manipulation is called automorphism.” No matter what origami folds you did, when you unfold it, you would always have that same blank piece of paper. The structure—symmetry—of the paper did not change.

After receiving his Ph.D. in Mathematics from SUNY–Albany in 1994, Clifford embarked into the job market. “I sent out more than 190 applications, and only had two phone interviews,” he said. His first position was as a visiting professor at Western Illinois University for a year. He then taught for another year at the University of Wisconsin–Parkside before getting hired by Trenton State College.

Clifford joked he never has gotten a paycheck from Trenton State College. He explained, “Between the time I was hired and when I started working, they changed the name.” An unforeseen perk of the new job was that he met Dr. Marcia O’Connell, a faculty member in the Biology Department. Within three years, they were married. Their daughter Norah arrived two years later.

“I have to say, it is the students.” Clifford replied when asked about what he liked best about teaching at TCNJ. “They are anxious to do well and want to learn how to get good at this [mathematics].”

Clifford enjoys meeting with his students outside of class. “When they have questions, they are willing to spend the time to come in and wrestle with them.” he said. “Then they go off on their own and wrestle some more.”

Even as I waited outside of his office for an interview, he was having one of those discussions with a student. The math professor’s enthusiasm and availability to discuss various math topics both outside and inside the scope of the course are qualities that his students admire and spark their interest for the subject.

“He entertains my questions and provides just enough insight to spark my curiosity, forcing me (willingly of course) into more research about the topic,” said **Chris Woidill** (‘14), math major and one of Clifford’s senior capstone students.

Clifford’s enthusiasm for the subject is as infectious as his smile, and he is able to help students unravel the mysterious and seemingly complicated topics. This makes him an essential factor of the academic equation that produces inquisitive scholars.

“He knows his subject matter well and has a way of passing his enthusiasm onto the student.” **Michael Muller** (’14), math major, added, “I can certainly say that he’s a very accessible and helpful professor equipped with great skill in elucidating the more difficult parts of the topic.”

Some of the courses Clifford has taught include senior capstone, geometry, and calculus. “I love teaching calculus, where students are just finding out what college math is like and getting beaten up by it a little bit.” Clifford said, “You can imagine not everyone is excited to be in calculus, but our students are. They might hate test day and that kind of stuff, but all in all they want to be engaged in figuring it out. And as you know, I have taught other places, and it is truer here than it was there. So, we [TCNJ] give great students to our faculty.”

“If you ever have a chance,” said Woidill, “observe one of his classes or stop in his office because you have to be there to appreciate his abilities as a professor and a mentor.”

– Danielle Leng

**For More Information:**

Associate Professor and Co-Chair of the Mathematics and Statistics Department, Coordinator of the Mathematics Education program, advisor for Mathematics Secondary Education students, and member of the Teacher Education Program Council, **Dr. Cathy Liebars** is always working hard.

“Teaching was the natural thing to do with math at that time,” said the mathematics education coordinator about her reason for pursing math education. Since high school, she stated that she was always interested in math, a subject that came easy to her and enjoyed. She also added that having excellent teachers helped make her decision.

Liebars attended Kutztown University for Mathematics and Secondary Education. Toward the end of her four years of undergraduate study, Liebars was encouraged by a professor to apply for a fellowship program at Lehigh University for women and minorities to pursue graduate studies and research in mathematics.

“They are basically paying you to study,” Liebars explained. “So it sounded like a good deal. I decided to apply. At that point, I never intended to get a PhD in math. I still thought I was going to teach high school math afterwards. I would just get to study more math.”

Accepted into the fellowship program, Liebars participated in the three-year fellowship program at Lehigh after graduation. When she enjoyed the atmosphere of graduate school, Liebars decided to stay at Lehigh University for an additional two years to receive a PhD in Mathematics. Right after graduating, Liebars came to TCNJ to join the faculty here.

“My doctorate is in mathematics, but I’ve always had an interest in education from my undergraduate degree. [TCNJ] wanted someone with a background in math, but someone interested in teaching education courses in math,” said Liebars on joining the TCNJ faculty.

As current Mathematics Education Coordinator, Liebars oversees the mathematics education program at TCNJ. Her job includes coordinating field experiences for students to apply for student teaching, and finding supervisors for student teachers. Additionally, her involvement with the Education Department makes sure she can give the students and faculty up-to-date information of the State of New Jersey’s teaching requirements. Liebars also coordinates, schedules, and hires professors for all math education courses in the department.

“I focus more on math secondary education because their first major is in mathematics,” explained Liebars. “I advise all the juniors and seniors. Junior year is when the students are officially in the program, meaning that is when they start applying for student teaching. I have to make sure they are meeting all their requirements for their junior year before they start student teaching. So I might as well become their advisor!”

As one of her advisees, **Evan Levy (’14)** enjoys talking to the co-chair. “She provides honest advice and makes sure you are on the right track.”

Not only is Liebars an advisor for students, but also she works with the student advisory board. “She is very open to thinking of new ways to improve a department that is already excellent.” Levy said of Liebars involvement with the advisory board.”

Currently, Liebars is working on revising TCNJ’s Masters of Arts in Teaching program in STEM fields through the Woodrow Wilson Teaching Fellowship Grant. Through the fellowship, selected students would receive a stipend and reduced tuition to pursue the master’s degree program. Liebars explained that the selected students must commit to three years of teaching in a high-needs district after graduating.

“We have a strong undergraduate program at TCNJ, so I wanted to strengthen the master’s program and bring it up to that level,” said Liebars. She stated that the first cohort of students in the program would start next summer (2014).

Somehow on top of everything else, Liebars continues to do what she always wanted to do, teach. She currently teaches Methods of Teaching Mathematics course. “She is very engaged in the classroom,” said **Jessica Gonzalez ****(’15),** an advisee and student of Liebars. “Dr. Liebars is obviously dedicated to her work, and her positive attitude and excitement towards education inevitably rubs off onto her students.”

Liebars commitment to her students is shown through the extra steps she takes to provide them help when needed. Gonzalez has been working personally with Liebars on a research paper. “We have met several times to simply discuss ideas I have for the thesis.” She explained, “many of these discussions could have been done over e-mail, but Dr. Liebars took time out of her busy schedule to work with me in person.”

Helping future math teachers and enhancing the math programs, Liebars is also involved in theater, which is an activity she has always enjoyed. “I sing, act, and dance,” said Liebars. “I do community theater, and I advise the musical theater organization at TCNJ as well.”

“Once I had Dr. Liebars as a professor and advisor, I felt like I belonged in the math department. She turns the math department into a community” said Levy when asked for additional comments about the Mathematics Education Coordinator. “She made me view mathematics as a future, not just a job.”

– Danielle Leng

**For More Information:**

Dr. Aigli Papantonopoulou, known to her students as “Dr. P.,” is a professor of mathematics at the College. She attended Barnard College for her undergraduate studies, and then attained her Ph.D. at University of California, Berkeley in algebraic geometry. Algebraic geometry is Dr. P’s passion. She enjoys being able to write down relationships and solving those equations. She sees equations as tangible representations of abstract mathematics.

After finishing her Ph.D., Dr. P. completed two post-doctoral studies, one at the University of Pennsylvania, and the second at Bryn Mawr College. She then traveled back to home country of Greece for one year, and then she returned to the United States.

Ironically, Dr. P. was a physics major as an undergraduate. She realized that she only liked physics because of the intense mathematics that was involved. Dr. P. specifically studies abstract mathematics, not applied mathematics. She enjoys proofs, which allow her to determine why arguments follow from certain premises.

Dr. P joined the faculty at TCNJ about 26 years ago; she chose TCNJ for her career because she really wanted to teach at an undergraduate college.

When she is not working, Dr. P. loves to travel. Additionally, she reads a lot of miscellaneous history. If Dr. P. comes across an event in history about which she is interested, she finds a book on that event and reads it. Dr. P. also walks four miles per day every morning.

Dr. P. has a husband, who teaches at Princeton, and two sons, one who teaches at Stanford, and the other who is a graduate student of anthropology at New York University.

– Andrew Miller

]]>From her earliest days in school, Professor **Jana Gevertz** was beguiled by the elegance and precision of mathematics. But as her experience widened, she also felt the pull of biology, a powerful, hands-on force in such critical arenas as health care.

“I love how beautifully logical math is. You can’t fight me on a proof—there is no bias. What I love about biology is its ability to impact people and how we live our lives. I’m drawn to the human side of it. So for me, the ideal career was one that used math to benefit people in society,” she says.

Her eureka moment came during her junior year in college when she took the course Differential Equations in Biology and realized “it was possible to work at the interface of math and biology.” That discovery led her to cancer research, where mathematicians, scientists, and clinicians are teaming up to exploit reams of new data—much of it at the molecular level—to advance their understanding of cancer growth and treatments.

As a specialist in mathematical biology, Gevertz, an assistant professor in the Department of Mathematics and Statistics, devises equations that model the progression of tumors. To date, she has focused on glioblastoma, a complex and deadly form of brain cancer that poses a persistent challenge to researchers and clinicians.

“When I first started researching in this field, mean survival times for these patients hadn’t budged since the 1970s, while we were seeing progress in treating other types of cancer. While tons of data was being gathered about glioblastoma, it was not translating into improved clinical outcomes for patients. So much remained unknown about the disease,” she recalled.

Gevertz was particularly drawn to an aspect of cancer progression that was not well understood: the interactions between different elements of a tumor and the surrounding healthy tissue that lead to its growth. These elements include the genes expressed by cancer cells, the blood vessels that give the tumor oxygen, the stiffness of the surrounding healthy tissue, and immune system responses. While the tumor is initially constrained by its host, it works to reshape its environment so it can thrive.

“Imagine a scenario in which a 17th-century scientist finds a modern-day computer,” she says, by way of analogy. “The scientist would try to understand how each component functions, for instance, the hard drive, the keyboard, and the mouse. But even if the function of each computer part were understood, the scientist would still need to figure out how these pieces interact to produce a functioning computer.

Increasingly, researchers are focusing on pinpointing the interactions that allow the tumor to overcome normal physiological defenses against cancer and coming up with ways to inhibit them. A primary goal of the field, she adds, is to develop a “virtual patient,” a computer program that would use specific information about a patient’s disease to predict how their particular tumor will grow and what treatments would be most effective.

“Patients with the same cancer respond differently. Some people are cured by chemotherapy and some are not. Some people have awful side effects, others none,” she says. “The holy grail of the field is to obtain clinical data on a singular patient, plug that into a computer, and be able to figure out how best to treat them. This is what we call individualized medicine, and it’s something many are striving for in all branches of medicine.”

The relationship between math and biology is not new, Gevertz notes. She points to Gregor Mendel, often called the father of modern genetics, who used comparatively simple math in the 1800s to derive his laws of inheritance, based on breeding experiments with pea plants. The partnership between the two fields has become increasingly productive, however, in recent years.

“There was a boom in the 1990s when biologists began gathering large amounts of data, necessitating a more quantitative approach to their field,” she says. Advances in molecular biology had given them the ability to identify the genes that are mutated in cancer, as well as the proteins expressed by these genes that abet tumor growth. A leap in computing power gave mathematicians powerful new analytical tools.

On occasion, math-based insights can seem counterintuitive, she notes, citing an example in which her equations suggested that using an on/off schedule for a drug that prevents a tumor from growing its own blood supply was more effective than deploying the drug continuously, at full-blast.

“Sometimes you learn things you weren’t expecting to be true,” she says.Supported in graduate school by National Science Foundation and Burroughs Wellcome Fund fellowships, Gevertz comes to her career with a research-intensive background. But she discovered earlier in her academic life that teaching was also important to her.

“What sold me on a career in math ultimately was tutoring. I love working with people and communicating complicated ideas in a way that others can understand,” said Gevertz, who teaches courses ranging from introductory calculus to upper-level classes in applied mathematics. She is thrilled to see her students embracing interdisciplinary subjects as well.

“Students’ interest in fields like mathematical biology is growing rapidly,” she says, noting that her course on the topic next semester is already over-enrolled.

This summer, she will be working on research projects with two of her TCNJ students: a physics major who will study the way cancer cells invade normal tissue and a math major looking at the interactions between a tumor and the body’s immune system. Both students will be using mathematical and computational techniques to tackle challenging biological problems.

“I’m excited that these students are engaging in real scientific research, and also pleased that they will come away from it appreciating that there are multiple ways to approach these important problems,” she says.

– Tracey Regan, *Originally Published in TCNJ Magazine*