## Mathematics

Part-time (Daytime)

Certificate

Application Deadlines

Fall: May 15
Spring: n/a

Summer: May 1

School/Department

Mathematics
Program Director

Fulton Gonzalez & Xiaozhe Hu
Contact

gradadmissions@tufts.edu
Location

Medford/Somerville
Format

On-campusOnline

Commitment Options

Part-time (Daytime)Average Duration

1 year
Credits

12-16
Tuition per Credit

$998
Our 4-course Post-Baccalaureate Certificate in Mathematics program is intended for students with a bachelor's degree (in any field) who would like to expand or deepen their mathematical skills for use in the workplace or in preparation for graduate programs in mathematics. The program is offered in both an on-campus format and an online summer term intensive.

**Mathematics Post-Baccalaureate Certificate — Online Summer Term Intensive Option**

Earn your mathematics post-bacc certificate this summer online. The certificate program includes 4 mathematics courses: 2 courses taken in Summer 1 and 2 courses in Summer 2. Students also have the option to start their program in either Summer 1 or Summer 2 and complete the certificate in the fall. Most classes in the fall are in-person, though, Math 70 and Math 166 will be available online. *For application purposes, please apply for Fall 2024 and indicate your interest in the Summer intensive on the application by May 1.

Summer 1 (May 22 - June 28) | Summer 2 (July 2 - August 9) |

Choose 2 of the following: | Choose 2 of the following: |

Math 65 | Math 65 |

Math 70 | Math 70 |

Math 87 | Math 123 |

Math 165 | Math 135 |

Upon graduation, you will have achieved a deeper understanding of basic mathematics and how to use quantitative reasoning in a variety of settings, as well as have developed your quantitative and problem-solving skills.

Graduates of the program have the necessary background to pursue a master's degree in Mathematics or Applied Mathematics. Many graduates apply their post-bacc learning and experience directly to their professional work.

- Application fee
- Resume/CV
- Personal Statement
- Official TOEFL, IELTS, or Duolingo English Test, if applicable
- Transcripts
- One letter of recommendation

See Tuition and Financial Aid information for GSAS Programs. We recognize that attending graduate school involves a significant financial investment. Our team is here to answer your questions about tuition rates and scholarship opportunities.

Professor

Mathematics

Professor, Mathematics

**Research/Areas of Interest:**
Noncommutative harmonic analysis, representations of Lie groups, integral geometry, and Radon transforms

Professor

Mathematics

**Research/Areas of Interest:**
Scientific computing and numerical analysis; Parallel multigrid and multilevel methods for large-scale coupled systems; Efficient numerical methods for reservoir simulation, fluid-structure interaction, and other applications.

Program Director, Post-Bac Programs

Eliot-Pearson Department of Child Study & Human Development

Affiliate, Eliot-Pearson Department of Child Study & Human Development

**Research/Areas of Interest:**
Dr. Fiore's current research emphasizes social-emotional learning and development, building and sustaining relationships in educational settings, and promoting strengths-based environments and awareness of the multi-generational effects of adverse childhood experiences (ACEs).

Professor

Mathematics

Professor, Mathematics

**Research/Areas of Interest:**
Scientific computing and numerical analysis: Efficient computational methods for complex fluids, plasma physics, electromagnetism and other physical applications.

Professor

Mathematics

Professor, Mathematics

Professor, Computer Science

Professor, Physics & Astronomy

**Research/Areas of Interest:**
Applied dynamical systems, applied probability theory, kinetic theory, agent-based modeling, mathematical models of the economy, theoretical and computational fluid dynamics, complex systems science, quantum computation
Current research emphasis is on mathematical models of economics in general, and agent-based models of wealth distributions in particular. The group's work has shed new light on the tendency of wealth to concentrate, and has discovered new results for upward mobility, wealth autocorrelation, and the flux of agents and wealth. The group's mathematical description of the phenomenon of oligarchy has also shed new light on functional analysis in general and distribution theory in particular.
Secondary projects include new directions in lattice Boltzmann and lattice-gas models of fluid dynamics, kinetic theory, and quantum computation.

Professor

Mathematics

Professor, Mathematics

**Research/Areas of Interest:**
Anomalous diffusion, mathematical neuroscience

Assistant Professor

Mathematics

Assistant Professor, Mathematics

**Research/Areas of Interest:**
Geometric group theory, low-dimensional topology, CAT(0) spaces

Professor

Mathematics

Professor, Mathematics

(617) 627-3419

177 College Avenue

**Research/Areas of Interest:**
Dynamical systems: Hyperbolicity, invariant foliations, geodesic flows, contact flows, and related topics
—
Hasselblatt's research, undertaken with colleagues from several continents, is in the modern theory of dynamical systems, with an emphasis on hyperbolic phenomena and on geometrically motivated systems. He also writes expository and biographical articles, writes and edits books, and organizes conferences and schools. His publication profile can be viewed at https://mathscinet.ams.org/mathscinet/author?authorId=270790 (with a subscription). Former doctoral students of his can be found in academic positions at Northwestern University, George Mason University, the University of New Hampshire, and Queen's University as well as among the winners of the New Horizons in Mathematics Prize.

William Walker Professor of Mathematics

Mathematics

Professor, Mathematics

William Walker Professor of Mathematics, Mathematics

Professor, Computer Science

**Research/Areas of Interest:**
Numerical Linear and Multilinear Algebra, Scientific Computing, Image Reconstruction and Restoration

Professor

Mathematics

Professor, Mathematics

**Research/Areas of Interest:**
The structure and representations of algebraic groups

Assistant Professor

Mathematics

Assistant Professor, Mathematics

Assistant Professor, Computer Science

177 College Avenue

Professor and Department Chair of Mathematics

Mathematics

Professor, Mathematics

Chair, Mathematics

**Research/Areas of Interest:**
Geometric Group Theory/Topology

Robinson Professor of Mathematics

Mathematics

Professor, Mathematics

Robinson Professorship in Mathematics, Mathematics

(617) 627-3402

177 College Avenue, Room JCC 575

**Research/Areas of Interest:**
Tomography is an inverse problem, and the goal of tomography is to map the interior structure of objects using indirect data such as from X-rays. Integral geometry is the mathematics of averaging over curves and surfaces, and it is the pure math behind many problems in tomography. Integral geometry combines geometric intuition, harmonic analysis, and microlocal analysis (the analysis of singularities and what Fourier integral operators do to them). I have proven support theorems and properties of transforms integrating over hyperplanes, circles and spheres in Euclidean space and manifolds.
Because of the mentorship of Tufts physics professor and tomography pioneer, Allan Cormack (Tufts' only Nobel Laureate) I developed X-ray tomography algorithms for the nondestructive evaluation of large objects such as rocket bodies, and this motivated my research in limited data tomography
In limited data tomography problems, some tomographic data are missing. I developed a paradigm to describe which features of the object will be visible from limited tomographic data and which will be invisible (or difficult to reconstruct). I proved the paradigm using microlocal analysis. Often artifacts are added to tomographic reconstructions from limited data, and colleagues and I recently used microlocal analysis to prove the cause of these added artifacts and to predict where they will occur.
Collaborators and I have developed local algorithms for electron microscopy, emission tomography, Radar, Sonar, and ultrasound. In each case we use microlocal analysis to determine the strengths and weaknesses of the problem and to refine and improve the algorithms.

Professor

Mathematics

Professor, Mathematics

**Research/Areas of Interest:**
To each point on a curve, one can often associate in a natural way a line or plane (or higher dimensional linear variety) that moves with the point in the curve. This set of linear spaces is called a vector bundle. Vector bundles appear in a variety of questions in Physics (like the computation of Gromov-Witten invariants) . Moreover, they provide new insights into old mathematical problems and have been used to give beautiful proofs to long standing conjectures as well as striking counterexamples to some others.

Professor

Mathematics

Professor, Mathematics

**Research/Areas of Interest:**
Algebraic geometry, topology, and differential geometry

Professor

Mathematics

Professor, Mathematics

**Research/Areas of Interest:**
Hyperbolic manifolds and orbifolds, low-dimensional topology, group actions