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Research Training Group: Algebraic Geometry and Representation Theory

Algebraic geometry and representation theory are two extremely active fields of mathematics, with deep connections to other areas of mathematics (for example, number theory, topology, and symplectic geometry) and theoretical physics (for example, string theory, conformal field theory, and statistical mechanics). Algebraic geometry studies curves and surfaces defined by polynomial equations and their higher dimensional analogs, while representation theory studies symmetry. The two subjects interact: geometric objects have symmetries and one can use geometry to study symmetry. This Research Training Group project aims to recruit and train young people by engaging them in research in these exciting areas of mathematics.

Efforts to promote Calculus in the Boston Public Schools

The Boston Calculus Project began in 1994 as an NSF funded project shared by the University and the Mathematics Department with the goal of introducing and/or helping to sustain calculus in more than a dozen inner-city schools of Boston. Currently, the Bridge to Calculus program continues the mission of the Boston Calculus Project and is coordinated by Professors Robert Case and Donald King of the mathematics department.

Bridge to Calculus is a summer math enrichment program that is specifically designed to prepare rising seniors in the inner-city high schools to take calculus in their schools in September; there is an increasing emphasis on preparation for AP calculus. The population in the program mirrors the population of Boston’s inner-city schools, with over 90% of the students of African-American, Hispanic, and Southeast Asian extraction and/or children of new immigrants. The program serves over 100 students each summer. 

The following are important characteristics of the Bridge to Calculus program:

a. Stress is placed on the equal access of city students to a strong mathematics curriculum in their schools; expanding the capacity of the schools themselves is the focus. Instead of having a few students taking a special course on a university campus, the emphasis is assisting the schools in setting up and offering their own calculus course, so that all students would have access in their regular curriculum.

b. Boston high school teachers play an integral role in all facets of the project, with University faculty offering collaboration and support. Ownership lies clearly with the high schools and the teachers. The summer course has been co-taught with university faculty.

c. Preparation for success in college. In particular, the student absorbs not only the curriculum, but also the strategies and personal skills that make for success both in college admission and in persistence in college. This aspect is strengthened by having college students as mentors to the high school students.

d. Preparation for College Acceptance. Bridge to Calculus has formed an alliance with The Bottom Line, a college preparatory counseling group which works with low-income city residents to prepare them for college. The Bottom Line has held several workshops on campus and works with the students during their upcoming senior year.

e. Funding for Bridge to Calculus has come from various sources, including the Nellie Mae Educational Foundation, the Boston Public Schools, donations from alumni and the following units at Northeastern University: School of Education, STEM Education Center and Mathematics Department. New sources of funding are actively being sought.

A recent complementary activity to Bridge to Calculus is Calculus Field Day, sponsored by the Mathematics Department, the STEM Center at NORTHEEASTERN, and NUPRIME. This popular event, held in the spring of the year, brings together teams of students from the high schools of Boston to compete in an array of open-ended problem-solving sessions. The team submissions are graded immediately by a group of teachers, and winners are announced and awards given at the close of the day.

Other Partnerships with Boston Public Schools

Step UP leverages the collective experience and expertise of five Boston-area universities — Boston College, Boston University, Harvard University, Northeastern University, and Tufts University in outreach to public education. The universities work together in a coordinated fashion to provide a comprehensive set of learning support services to ten Boston Public Schools. Specifically, each university is paired with two Step Up schools and charged with developing a set of support mechanisms for students and teachers. Over the course of the five year initiative, the partner universities are investing 5million in direct services to the school sand an additional 5 million in in-kind and other support services. Northeastern is paired with the Curley K-8 School in Jamaica Plain and Orchard Gardens K-8 School in Roxbury. Math faculty serve as advisors to the project.

Aligning Mathematics in the Middle Grades, funded by Title IIB of the No Child Left Behind Act, is a collaborative effort involving the Boston Public Schools, Northeastern University, Education Development Center, Inc., and the University of Washington. It is designed to strengthen mathematics teaching and learning at grades 5 through 8 in Boston over a three-year period. The project provides a cohesive program of professional development that strengthens mathematical knowledge for teaching with a particular focus on number, operations and algebra.  Thus what students are learning in these strands at the elementary grades becomes a more explicitly basis for middle school math teachers, and elementary teachers of math become  more aware of and better able prepare students for middle school math expectations. The project also provides support for professional learning communities in schools, so teachers can continue to deepen their mathematical knowledge for teaching as they plan and debrief lessons, examine student work, and participate in structured visits to each other’s classrooms. Teachers are supported as they enact what they are learning from the project in their own classrooms. Mathematics department faculty participate by co-leading seminars, supporting the leadership conferences which is the main support for the professional learning communities and by advising project leaders. 

Balfour Academy

This is a six-week summer program. Students going into the 7th, 8th and 9th grades study Mathematics, English, Science and Current Events. Students entering the 10th, 11th and 12th grades take English and Mathematics SAT preparation classes. These more advanced students also sit in on a Northeastern University class, usually an introductory liberal arts course; one of the instructional assistants sits in also and the conducts a study skills session using the college course as motivation.

Support is also offered during the school year, in the form of an after-school tutoring program designed to assist students in their homework, studying for tests and understanding concepts with which they may be struggling. The tutors are NORTHEEASTERN students who work on a one-to-one basis with the Balfour students.

The Math Circle

This is a nonprofit organization that runs mathematics courses for pre-collegiate students (ages 5 to 18) at Harvard University and Northeastern University. The courses are not designed to “instruct” the students, so much as to challenge and inspire them with creative problem-solving. The program at Northeastern involves about 40 students in ten 3-hour weekend sessions during each of the Fall and Spring semesters. For more information, go to www.themathcircle.org.