northeastern university seal
EXPLORE NORTHEASTERN

Mathematics

He Knows the Secrets to Unlocking the Universe
From Geometry to Topology, Here’s Our List of Weekly Seminars
The Bridge to Calculus Program

Two planes are heading for the same destination 8000 miles away.

Plane A leaves at 1:00 pm, averaging 450 mph. Plane B leaves at 6:00 pm, averaging 400 mph. Which plane gets there first? 

You’ve heard a problem like this before, but never outside a classroom. Because in the real world, it’s much less black and white. 

That’s because life has invisible variables. For instance, it will depend on the accuracy of weather pattern predictions to account for delays. It will depend on assessments about the plane’s material parts and fuel efficiency. It will depend on the air traffic controllers issuing course corrections in real time. All these factors will contribute to when the planes will arrive.

So what’s the answer? The truth is that the answer is too small for the real question. The world depends on more than just calculations — it requires people who have the foresight and perspective necessary to keep the planes arriving on time. 

The College of Science mathematics degree prepares students not only to solve for (x), but to see the whole equation.

Degree Options

Applied Mathematics Masters

New applications of mathematics are constantly being discovered, and established techniques are being applied in new ways and in emerging fields. Northeastern’s Master of Science in Applied Mathematics is catered to students who are looking to enter or who are currently working in a variety of applied math careers, such as financial service and investment firms; data science and high-tech firms; computer information and software firms; and academic institutions and research institutes.

Coursework and Requirements
Depending upon your career objectives, mathematics electives are generally selected from one of three tracks:
Interactive Mathematics
MATH 1213

Develops problem-solving skills while simultaneously teaching mathematics concepts. Each unit centers on a particular applied problem, which serves to introduce the relevant mathematical topics.

Mathematics of Art
MATH 1220

Presents mathematical connections and foundations for art. Topics vary and may include aspects of linear perspective and vanishing points, symmetry and patterns, tilings and polygons, Platonic solids and polyhedra, golden ratio, non-Euclidean geometry, hyperbolic geometry, fractals, and other topics.

History of Mathematics
MATH 2201

Traces the development of mathematics from its earliest beginning to the present. Emphasis is on the contributions of various cultures including the Babylonians, Egyptians, Mayans, Greeks, Indians, and Arabs.

Co-Op Stories

Many math students choose to participate in the university’s signature co-operative education program because it offers excellent preparation and exposure to exciting careers. Here’s what our students are saying:

Ruo Yang, Consumer Analytics and Insights Co-op Program, Fidelity Investments

“I am currently doing a co-op with Fidelity Investments. It is an extraordinary experience to learn and apply mathematical skills into the real world rather than with academics only. The fantastic program (co-op in applied mathematics) is the way to transform the abstract mathematical knowledge to the different actual projects which increase the interests with math.”

Xiaofan Liu, Pension Analyst, Towers Watson

“The co-op experience made my MSOR program more colorful as well as is the stepping stone to my future career life.”

Hua Zhao, Sales Analyst, Gryphon Networks

“Co-op is the best way to gain real world experiences off campus! Also a great way to discover the industry and find your real interest before going to the real world.”

Liu Li, Data Modeling, Custom Portfolios

“I encountered new problems every day, learned new theories and practiced new models in every project. Working in industry is not the same thing as doing course projects at school. You have to learn things fast and keep pace with the development of new techniques.”

Shaokang Du, Data Scientist, Omni Claim

“In order to be a strong candidate for co-op I recommend preparing a challenging and skillful project experience if you don’t have much professional experience and keep an attitude and willingness to learn.”

Faculty Research

Mathematics
Topology and Singularities Group
The study of those properties that are preserved through continuous deformations of objects. It can be used to abstract the inherent connectivity of objects while ignoring their detailed form.
Mathematics
Emergent Epidemics Lab
Research in the Emergent Epidemics Lab spans a broad range of topics in complex systems and network science, with an emphasis on infectious disease dynamics and forecasting/predictive models.
Mathematics
Partial Differential Equations and Dynamical Systems Group
The Partial Differential Equations and Dynamical Systems Group falls under the field of mathematical analysis, which is a broad branch of mathematics that encompasses many fields, generally sharing a basis in calculus. Historically, analysis has played a crucial role in solving problems in physics ..
Mathematics
Singularities in Analytic Geometry Group
Analytic geometry generalizes algebraic geometry by considering spaces and maps defined locally by analytic functions.
Mathematics
Algebraic Geometry Group
Algebraic geometry generally uses tools from algebra to study objects called algebraic varieties that are solution sets to algebraic equations
Mathematics
Algebra Group
Modern algebra has its roots in the mathematics of the ancient world, arising out of the basic problem of solving equations. Following an explosive development in the twentieth century, it is now a vibrant, multi-faceted and wide-ranging branch of mathematics, having ties with almost every field of..
Mathematics
Symplectic Geometry
Symplectic geometry studies objects with structure generalizing that of the phase space of certain dynamical systems.
Mathematics
Probability and Statistics Group
Encompasses a broad array of topics in pure and applied mathematics, and has applications in almost every field of scientific research. By its nature, the field is driven by real-world applications.
Mathematics
Mathematical Physics Group
The Mathematical Physics Group falls under the field of mathematical analysis, which is a broad branch of mathematics that encompasses many fields, generally sharing a basis in calculus. Historically, analysis has played a crucial role in solving problems in physics and engineering; recent years ha..
Mathematics
Differential Geometry Group
Differential geometry uses tools from analysis to study objects called manifolds that generalize Euclidean space.
Mathematics
Combinatorics and Discrete Math Group
Perhaps the fastest growing area of modern mathematics. It has a wealth of real-world applications, especially in computer science, which have greatly contributed to its rapid growth.
Mathematics
Geometric Analysis Group
The Geometric Analysis Group falls under the field of mathematical analysis, which is a broad branch of mathematics that encompasses many fields, generally sharing a basis in calculus. Historically, analysis has played a crucial role in solving problems in physics and engineering; recent years have..
Mathematics
Ergodic Theory Group
The Ergodic Theory Group falls under the field of mathematical analysis, which is a broad branch of mathematics that encompasses many fields, generally sharing a basis in calculus. Historically, analysis has played a crucial role in solving problems in physics and engineering; recent years have see..
Mathematics
Discrete/Combinatorial Geometry
Discrete geometry studies combinatorial properties of finite or discrete objects.
The Minds Behind COS Mathematics
Faculty Spotlight
Ana-Maria Castravet
Mathematics
“Math is not just a game and it’s not as shallow as it looks. There is a scientific theory that can connect different things in profound ways and it’s very beautiful actually, and I just like that,” said Northeastern Math Professor Ana-Maria Castravet. Funded by a National Science Foundation grant, she is working on the moduli spaces of rational curves.
Jonathan Mboyo Esole
Mathematics
Assistant professor in the College of Science, grew up in the Democratic Republic of the Congo, studied at top institutions around the world, and has been awarded the Albert Einstein Fellowship. Since arriving in fall 2016, Esole has taught calculus and mathematical methods of quantum mechanics.
Paul Hand
Mathematics
is an assistant professor of mathematics and computer science, has received a CAREER award from the National Science Foundation to figure out how neural networks can be used to construct images, while searching for the mathematical theories behind those networks.
,

Recipients of the 2020 College of Science Excellence in Teaching Awards

The College of Science Excellence in Teaching Awards recognize and reward outstanding NU College of Science faculty for their significant contributions to student learning. We are pleased to announce this year’s winners.

Oyindasola (Oyinda) Oyelaran

Dr. Oyelaran Is a Teaching Professor in the Department of Chemistry and Chemical Biology.  She joined Northeastern in 2011 and since then has taught more 35 sections of organic chemistry to hundreds of students from several majors.

Despite the difficulty of the material, Oyinda is overwhelmingly evaluated by students has highly effective, and is even described as inspirational and life-changing.  She is praised for her classroom engagement and out of class support and mentoring.

She is a leader in the practice of evidence-based teaching, which includes conducting and presenting her own research.  Oyinda demonstrates leadership as the Co-PI for a Research Experiences for Undergraduates grant from the National Science Foundation and for her service on University committees to facilitate the “One Faculty” initiative.


Prasanth George

Dr. George is an Associate Teaching Professor in the Department of Mathematics.  He joined Northeastern in 2014 and in just the last three years has taught seven different classes, most of them multiple times.  His effectiveness in teaching difficult material to large numbers of students from several majors is truly remarkable.

The words students often use to describe Prasanth include, “best”, “favorite”, and “incredible.” In 2017 he received the College of Engineering Outstanding Teacher of First Year Students Award.

Prasanth has also been a leader in the overall management and delivery of the mathematics undergraduate curriculum serving as the Undergraduate Director, Assistant Undergraduate Advisor, Mathematics Tutoring Center Director, Trainer of Teaching Assistants, and member of the College of Science Undergraduate Curriculum Committee.

 

July 09, 2020

He Knows the Key to Unlocking the Secrets of the Universe

Ever feel overwhelmed by the chaos and variability of the day to day? Maybe you’re in the wrong field. Try studying representation theory—it lets you predict things that you might otherwise never see, like how individual microscopic particles spin.

If you’re “absolutely awed” by this hack, you’re in good company. As an undergraduate, Valerio Toledano Laredo didn’t even know the field of study existed, but he was a quick convert. Now a mathematics professor at Northeastern in his third decade of research, he’s helping others, through education and outreach, begin their own journeys.
His started with the electron.

“There’s a very complicated microscopic particle and these very complicated lab experiments to do to understand its behavior,” says Toledano Laredo, whose professor at the time put representation theory on his radar. “But you can just sit back in your chair with a paper and pen and, in half a page, actually predict some of these properties—just by pure thought.”

So what’s the secret sauce for learning about something you can’t see?

Symmetry.

The symmetries of an object, or the transformations you can make without fundamentally changing it (think rotating a square 90 degrees), manifest in different ways. Mathematicians call these manifestations “representations,” hence “representation theory.”

Here’s how to think about this theory in everyday terms: If I closed my eyes while you rearranged playing cards facedown, I’d have no way of knowing whether you even rearranged them. Similarly, a monochrome ball would look the same no matter how many times you spun it around.

This quality is considered a symmetry, and it shows up—in the form of representations—in very different objects. On the subatomic level, representations of this symmetry manifest in electrons and photons, two distinct kinds of particles.

Electrons and photons are fundamentally different particles because of how they behave. You don’t have to be a physicist to recognize this: We’ve all seen lasers (“social” photons piling on top of one another) and electricity (“asocial” electrons keeping their distance from one another and stretching a signal along).
Toledano Laredo says that knowing, through representation theory, that these particles are also somehow similar helps mathematicians and scientists understand how these tiny components of the universe behave—and prepares researchers to conduct new experiments without going in blind.
But it’s not always obvious when distinct objects share symmetries, which, Toledano Laredo says, is what makes representation theory so important to study.

Now he wants to give the next generation of researchers the tools to learn more about this complex theory, along with the related fields of algebraic geometry and mathematical physics.

As part of a team funded by an ongoing research and training grant from the National Science Foundation, he’s working to prepare students to excel in the science, technology, engineering, and math fields through programs such as Bridge to Calculus, which prepares high schoolers in Boston to succeed in their math classes.

Training the coming generations of mathematicians, he says, will enable our understanding of the universe to expand.

“There’s so much more to know,” says Toledano Laredo. “For me, for math, for physics—for the whole scientific community.”

This story was originally published on News@Northeastern on September 13, 2019.

July 09, 2020

Northeastern Mathematics Hosts Quantum Structures Conference

The Northeastern Mathematics Department will be hosting a conference on Quantum Structures in Algebra and Geometry from August 26-30. The conference will focus on the interaction between Representation Theory (the mathematical study of symmetry), Algebraic Geometry (the study of curves and surfaces defined by polynomial equations, and their higher dimensional analogs) and Mathematical Physics.
It is sponsored by the National Science Foundation, through a $2.3M RTG grant for 2017-2022, MIT, the Clay Mathematics Foundation, the College of Science and the Mathematics Department.
A detailed program can be found at here.

July 09, 2020

Looking Back on Bridge to Calculus 2019

For the past 25 years, Northeastern University has been partnering with Boston Public High Schools to give rising junior and senior students the skills they need to succeed in their fall calculus classes through the Bridge to Calculus program. As the 2019 session, which started June 24th, draws to a close this Thursday, August 1st, we’d like to give a shoutout to this year’s talented group of Northeastern University PhD Graduate students (Cancan Zhang, Changchang Liu, Chen Li, Hiu Ying Man, Jiewei Feng, Jieying Jin, Lei Yang, Mohamed Elbehiry, Tomas Skacel, and Xuezhu Lu) and Boston Public High School Math teachers (Anthony Bernazzani of Boston Latin Academy, Phuong Cao of Boston Latin Academy, Noemi Famador of East Boston High School, Mike Sheehan of Boston Community Leadership Academy, and Juan Tapia of John D. O’Bryant School). Thank you for lending your time and expertise! We’re already looking forward to another great session next summer.

 

So why should you participate in the Bridge to Calculus program? We talked to two educators working with Bridge to Calculus, Noemi M. Famador, a Precalculus and AP Calculus teacher at East Boston High School and Michael Sheehan, who works at the Boston Community Leadership Academy, to find out.

1. Why are your participating in the Bridge to Calculus?

Noemi Famador: Teaching math in the regular school year, I have to deal with a lot of unmotivated students. I still do my very best since it’s precisely this group of students that I want to convince that math is not that bad and that with the right attitude and extra effort one can actually learn it and love it. This challenging work can be stressful and discouraging. This is also why I always look forward to teaching in the BTC summer program. Students in the summer program are really motivated to learn because they do it to be ready for their AP Calculus class in the fall. They do have their struggles- financial, work, family issues, health, etc – but they are all still willing to come to learn at 7:30 am everyday for six weeks.

Michael Sheehan: I have always loved teaching BPS students, as I feel we each have something to offer each other as a result of our different backgrounds.  I especially love teaching BPS students when they truly want to learn.  Bridge To Calculus students show up voluntarily, early in the morning.  They listen and are not always trying to sneak in some text conversation on their phones like so many of my students during the school year.  By putting in the kind of effort they do, these students get the maximum benefit from what I have to offer them.  I also enjoy being able to treat them as adults; they can wear hats if they like;  they can get up and use the bathroom when they see fit instead of having to raise their hands and ask for a pass.  It’s just an all-around healthy and productive relationship.

Noemi Famador, Precalculus and AP Calculus teacher at East Boston High School, speaks during the Bridge to Calculus award ceremony

Noemi Famador, Precalculus and AP Calculus teacher at East Boston High School, speaks during the Bridge to Calculus award ceremony

2. How did you come to know about the Bridge to Calculus?

NF: Summer of 2008, my math department head (Mr. Francisco Garnica) asked me to take his place in the bridge program. He used to teach it but because of his workload he couldn’t do it anymore. He also wanted me to get to know my AP Calculus kids earlier by teaching them in the summer program. It was a perfect arrangement and I got hooked since then.

MS: I came to know about Bridge To Calculus through its founder, Professor Bob Case.*

3. How long have you been involved with the Bridge to Calculus?

NF: Since summer 2008.

MS: I have been involved with the program since its inception (roughly 1994 or 1995 if my memory is accurate).  I was originally an assistant in the classroom for a few years, then taught a class, then a week, and then became a full time instructor.

4. Why do you love Math?

NF: My love for math started when my Grade 3 teacher would bring me around our city (Cebu City, Philippines) to join math competitions. The training, although gruelling, was also very rewarding especially when I would get some medals and this made my parents really happy and proud. This love for math became deeper such that in college I chose a scholarship to take up BS in Math for Teachers instead of one for Engineering. At that time, there was already that desire in my heart to make other people see the beauty of math. I was thinking I could do that if I teach math. After teaching math in the Philippines for 20 years and then teaching math here in the US for another 20 years – I’m still on that mission. Everyday in class, I always try my best to make the students know more of the beauty of math so they become less afraid of it. Hopefully when they are less afraid, they can learn it better and thus love it a little bit more. I know this is challenging but if I can make a difference everyday in class, then it’s a worthy endeavor.

MS: I enjoy the challenge of math, and believe that developing discipline in math has benefits in other areas of life.  Also, ever since I was a high school student myself, I have felt like math is one of the few areas in life where people from all countries and all walks of life agree on the same solutions to problems (assuming they all understand the problem!)

 

*the program was originally called “Boston Summer Advanced Math”

July 09, 2020

Your Career Starts Here. Apply Now.