Northeastern
University
Department of
Mathematics
Graduate Office / 571 Lake
Hall
8:30 a.m. - 4:30 p.m.
Mon. - Fri.
617.373.2454
Professor
Richard Porter, Interim Department
Chair
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Gari Horton
Graduate Secretary
567 Lake Hall
(617) 373-2454
g.horton[at]neu.edu
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Prof. Jerzy Weyman
Graduate Coordinator
530 Nightingale Hall
(617) 373-5513
j.weyman[at]neu.edu
|
Dear prospective Student,
Welcome to the Graduate Office for the Department of Mathematics at Northeastern University. Thank you for your interest in our programs. Below, please find information regarding our degree programs, application requirements, application deadlines and financial aid resources. This office is responsible for all aspects of the graduate programs from inquiries, the application process, monitoring student progress, to commencement. This site is intended to give concise and comprehensive information to prospective students to assist them in making an informed and balanced decision when applying for graduate school. If you have questions about the application process, please e-mail g.horton@neu.edu or call 617.373.2454. We hope you find this site useful and informative.
Program Booklet
The Department of Mathematics has an internationally renowned faculty with research interests in a number of fields which include, but not limited to, areas in topology, algebra, analysis, and probability/statistics. Please click on the following links for a complete list of our professors and the research areas they are interested in. In addition to the research, this department hosts a number of seminars and colloquia throughout the academic year as well as a part of a joint mathematical colloquium shared by Brandeis University, Harvard University, and the Massachusetts Institute of Technology.
The Department of Mathematics offers programs on a full-time or part-time basis in Master of Science (MS), Master of Science in Industrial and Applied Mathematics (MSIAM), Master of Science in Operations Research (MSOR), the Doctor of Philosophy (PhD), and as a special student (non-degree, part-time only). In the MS program, we offer degrees with a concentration in Pure Mathematics, Discrete Mathematics, Probability/Statistics, Applied Mathematics, Applied Analysis, and Operations Research. In the Ph.D. program, we offer degrees with a concentration in Algebra, Geometry/Topology, Geometric Analysis/PDE, Probability/Statistics, and Combinatorics. Students with an MA or MS degree in mathematics should apply directly to the Ph.D. program. Students without an MA or MS in mathematics, who would like to enter the Ph.D. program, should instead apply to the MS program. Once students complete their MS degree requirements they may then apply to the Ph.D. program. The majority of students who obtain an MS degree in our program continue on into the Ph.D. program and obtain the Doctorate. It is the hope and expectation that students entering our program will continue toward the Ph.D. For degree and concentration requirements, please click here.
Graduate Executive Committee:
Professors: Jerzy Weyman, Maxim Braverman, Aidong Ding.
On-line Application and Deadlines:
Fall Admission
All Ph.D. Admissions: February 1
MS applicants interested in assistantships: February 1
MS (international applicants): May 1
MS (domestic applicants): August 1
Special Student applicants (domestic only): August 25
Spring Admission
MS (international applicants): October 1
MS (domestic applicants): December 1
Special Student applicants (domestic only): December 15
Please send all application materials to:
Graduate School of Arts and Sciences,
Northeastern University,
124 Meserve Hall,
360 Huntington Ave.,
Boston, MA 02115
GSAS [at] neu.edu
There are different requirements for the programs we offer. Please take a moment to familiarize yourself with the application requirements for the program in which you are interested:
Doctor of Philosophy
Application
Application fee
Personal Statement
Resume (optional)
Official Graduate Record Examination (GRE) test scores***
Offical Subject Graduate Record Examination (SGRE) in mathematics test score***
Official Test of English as a Foreign Language (TOEFL) test score***
Official Undergraduate Transcripts (all institutions attended)
Official Graduate Transcripts (all institutions attended)
Official Transcript Translation*
Three Letters of Recommendation
Master of Science
Application
Application fee
Personal Statement
Resume (optional)
Official Graduate Record Examination (GRE) test scores***
Official Subject Graduate Record Examination (SGRE) in mathematics test score***
Official Test of English as a Foreign Language (TOEFL) test scores*
Official Undergraduate Transcripts (all institutions attended)
Official Transcript Translation*
Three Letters of recommendation
Master of Science in Industrial and Applied Mathematics****
Application
Application fee
Personal Statement
Resume (optional)
Official Graduate Record Examination (GRE) test scores***
Official Test of English as a Foreign Language (TOEFL) test score*
Official Undergraduate Transcripts (all institutions attended)
Official Transcript Translation*
Three Letters of Recommendation
Master of Science in Operations Research****
Application
Application fee
Personal Statement
Resume (optional)
Official Graduate Record Examination (GRE) test scores***
Official Test of English as a Foreign Language (TOEFL) test scores*
Official Undergraduate Transcripts (all institutions attended)
Official Transcript Translation*
Three Letters of Recommendation
Special Student**
Application
Application fee
Personal Statement
Resume (optional)
Official Undergraduate Transcripts (all institutions attended)
Two Letters of Recommendation
*International applicants only (TOEFL Dept. Code is 72. TOEFL Study Tips).
**U.S. citizens and permanent residents only
***GRE codes: Institution Code is 3682. Department Code is 0703 (GRE Study Guide and Study Tips).
****Financial assistance is not available through the Department.
Special notice regarding test scores:
The GRE and Subject GRE test scores are not valid after five years from the test date.
TOEFL test scores are not valid after two years from the test date.
The required TOEFL score for admission is a minimum of 550 for the paper-based test, 213 for the computer-based test, or 79-80 for the internet-based test.
(International applicants: For more information about visas, financial documentation, and foreign student applications, please contact Ms. Sheila Magee-Beare at s.magee@neu.edu, 617.373.3982.
Graduate Degree programs offered (4SH):
1.) Master of Science: total of eight graduate courses (4 semester hours each); course credits earned are valid for a maximum of seven years. Transition to Doctor of Philosophy degree requires passing a series of qualifying exams.
2.) Doctor of Philosophy: total of eight graduate courses (4 semester hours), plus a dissertation
3.) MS in Industrial and Applied Mathematics: total of eight graduate courses (4 semester hours each); course credits earned are valid for a maximum of seven years.
4.) MS in Operations Research: total of eight graduate courses (4 semester hours) two-year program.
Nearly all classes meet Monday-Thursday after 5:00 p.m., 2009/2010 Cost of Study: $1,065.00 per semester hour of credit ($1,065.00 x 4=$4,260.00/course.)
Research:
Algebra, Algebraic Geometry and Algebraic Groups: Commutative Algebra, Flag Varieties, Schubert Varieties, Singularities, K-theory, Moduli Problems, Group Actions, Homogenous Spaces, Invariant Theory, Representation Theory of Algebraic, Kac-Moody and Quantum Groups.
Combinatorics: Studies in Graph Theory, Algorithms, Operations Research, Algebraic Combiantorics and Combinatorial Geometry.
Differential Geometry: Variational Problems, Geometry for Submanifolds. Study of differential forms with applications to lie groups and algebras and their cohomology.
Lie Theory: Structure and Representations of Lie Groups, Noncummutative Harmonic Analysis on Symmetric Spaces.
Ergodic theory: Studies in Measure Theoretic Ergodic Theory, Applications of Number Theory, Spectral Analysis of Ergodic Transformations.
Partial Differential Equations: Studies in Linear and Nonlinear Partial Differential Equations, Elliptic Equations on Noncompact Domains and Manifolds, Spectral Theory of Elliptic Operators, Index Theory, Geometric Applications of Partial Differential Equations.
Topology: Singularities of Maps, Geometry of Spaces with Singularities, Algebraic and Differential Topology.
Statistics: Studies of Statistical Decision Theory, Design of Experiments, Theory of Random Functions, Statistical Inference of Random Functions, Applications of Statistics in Natural Sciences, Public Health, Economy and Finance.
Admissions requirements: Deadline: February 1 for Ph.D. applicants and all applicants seeking financial assistance.
Application, resume or cv, personal statement, $50.00 admission fee.
Official transcript of Bachelor's degree in mathematics or closely related field (math courses should include linear algebra, combinatorics, differential and integral calculus, differential equations, real analysis and computer programming).
Applying for Ph.D. degree program, a transcript of Masters degree.
Three letters of recommendation
Graduate Record Exam (GRE), general and advanced subject (in mathematics).
International applicants: must also include Test of English as a Foreign Language (TOEFL) score.
Financial Aid:
If applying for departmental financial aid, you must apply as a regular full-time student.
Classifications:
Full-time: must maintain 8-semester hours per semester.
Part-Time: must maintaim 4-semester hours per semester.
(There is a seven year time limit for students to complete any degree program).
Degree Requirements:
Required courses for different specializations vary. See the department web page for the latest requirements.
Grade Point Average:
Must maintain a minimum cumulative average of 3.00, equivalent to a grade of B for all graduate courses.
Qualifying Exams:
Exams are given three times a year; September, January, and April. The four exams include Algebra, Analysis, minor concentration and major concentration.
Requirements for Graduate Degrees
MS Degree Program (8 required courses)
Concentration: Pure Mathematics
-
7 Required: Algebra 1, Analysis 1, Algebra 2, Analysis 2, Topology 1, Combinatorial Analysis/Representation Theory, Geometry 1/Algebraic Geometry.
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1 Elective: Algebra 3, Geometry 2, Topology 2, or an advanced course in Analysis.
Concentration: Discrete Mathematics
-
7 Required: Algebra 1, Analysis 1, Algebra 2, Probability 1, Combinatorial Analysis, Discrete & Computational Geometry, Graph Theory.
-
1 Elective: Topology 1 or Probability 2
Concentration: Probability/Statistics
-
7 Required: Algebra 1, Analysis 1, Analysis 2, Probability 1, Probability 2, Mathematical Statistics, Applied Statistics
-
1 Elective: Regression, ANOVA and Design; Topics in Statistics; Nonparametric Methods in Statistics; or Time Series.
Concentration: Applied Analysis
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7 Required: Algebra 1, Analysis 1, Analysis 2, Algebra 2, ODE 1, PDE 1, Numerical Analysis
-
1 Elective: advanced course in Analysis or Geometry 1
PhD degree Program (8 required courses, 2 dissertation courses)
- Conditions required to reach PhD candidacy:
-
8 courses beyond MS degree and 2 PhD dissertation courses (MTHG890) leading to thesis topic. Two of the eight courses must be in a minor speciality, which is different from the thesis area. Here and below the phrase "beyond MS degree" means a course which has course number G300 or higher, or else has a course number G200 and higher and is listed below as required or elective for one of the concentrations.
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Students need to pass four qualifying exams, one in Algebra, one in Analysis, one in their own specialization and one in the minor speciality, see Qualifying Exams for full details. The passing grade is 70%.
-
Obtain a thesis advisor within one year after enrolling in the Ph.D. program
- Conditions required after reaching PhD candidacy:
-
A thesis, consisting of original work, approved by the advisor and a thesis committee of at least 4 members, including at least one member from outside Northeastern University.
Concentration: Algebra
-
4 Required courses: Two courses from each of the following two groups of courses.
Commutative Algebra Group:
Commutative Algebra
Algebraic Geometry 1
Algebraic Geometry 2
Galois Theory
Invariant Theory
Homological Algebra
K-Theory
Any other course which is approved by the Graduate Committee.
Representation Theory Group:
Representations of Finite Groups
Representations of Lie Groups
Representations of Lie Algebras
Quantum Groups
Algebraic Groups
Representations of Quivers
Auslander-Reiten Theory
Topics in Representation Theory
Any other course which is approved by the Graduate Committee.
2 Elective courses 2 courses in a minor speciality (above the MS degree level) 2 PhD thesis dissertation courses
Concentration: Geometry/Topology
4 Required courses: Topology 2, Geometry 2, Topology 3, Geometry 3 -
2 Elective courses, from: Differential Geometry 1, Differential Geometry 2, Topics in Differential Geometry, General Relativity, Topics in Topology, Morse Theory, Characteristic Classes, Topology of Complex Hypersurfaces.
2 courses in a minor speciality (above the MS degree level) 2 PhD thesis dissertation courses
Concentration: Geometric Analysis/PDE
3 Required courses: PDE 1, Functional Analysis, Complex Analysis. -
3 Elective courses, from: ODE 1, Topics in Differential Equations, Partial Differential Equations 2, Mathematical Methods of Classical Mechanics, Mathematical Methods of Quantum Mechanics, Atiyah-Singer Index Theorem, Von Neumann Algebras and Applications, any advanced Analysis course.
2 courses in a minor speciality (above the MS degree level) 2 PhD thesis dissertation courses
Concentration: Probability/Statistics
-
4 Required courses: Topics in Statistics, Optimization and Complexity, Nonparametric Methods in Statistics, Regression, ANOVA and Design.
-
2 Elective courses, from: Time Series; Statistical Decision Theory; Categorical Data Analysis; Stochastic calculus and introduction to no-arbitrage finance; Readings in Probability and Statistics.
2 courses in a minor speciality (above the MS degree level) 2 PhD thesis dissertation courses
Concentration: Combinatorics
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4 Required courses: Algebraic Combinatorics, Geometric Combinatorics, Optimization & Complexity, Topics in Combinatorics
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2 Elective courses: Readings in Combinatorics and Algebra, Readings in Combinatorial Geometry, Readings in Graph Theory (also, Discrete & Computational Geometry or Graph Theory, if not already taken in the MS program).
2 courses in a minor speciality (above the MS degree level) 2 PhD thesis dissertation courses
MS Degree in Industrial and Applied Mathematics Program (8 required courses)
-
3 Required: Introduction to Mathematical Methods and Modeling, Applied Statistics or Mathematical Statistics, Analysis 1 or Algebra 1 or Probability 1.
-
5 Electives: Three must be taken from the graduate courses offered by the Department of Mathematics. Two may be graduate courses taken outside of the Department of Mathematics (with the approval of the program advisor in the Department).
Operations Research Program
Probability 1 or Engineering Probability and Statistics, Probability 2 or Probabilistic Opearations Research, Deterministic Opearations Research, Optimization. Four elective courses from the following list: Mathematical Statistics, Enumeration, Data Structures, Stochastic Calculus and No-arbitrage Finance, Statistical Decisions, Complexity Theory, Economic Decision Making, Multi-criteria Decision Making, Logistics, Warehousing and Scheduling, Reliability and Risk Assessment.
Time limit
Master of Science. Coursework in the MS degree program is valid for seven years. All MS students must complete their degree requirements within seven years of entering the program.
Doctor of Philosophy. Students in the PhD program are required to take 2 thesis dissertation courses in their third year (by their fourth year for part-time students) and required to finish their degree before the end of their eighth year (ninth in the case of part-time students). Students can only get support for up to five years if they progress well. In addition, a maximum of five years after the establishment of doctoral degree candidacy will be allowed for the completion of degree requirements.
Leaves of Absence. Graduate students may request to take a leave of absence for a year. The request must be approved by the graduate coordinator and the Graduate School of Arts and Sciences. Please note that being on an approved leave of absence does not extend the amount of time allowed for degree completion or the make-up of incomplete grades.
Disclaimer: The requirements listed on the Mathematics Department web pages are for informational purposes only. The official requirements are maintained by the Graduate School of Arts and Sciences and the Office of the Registrar, and can be found in the booklet prepared by the Graduate School.
Maps and directions to Northeastern University.
In addition, you may have questions that would be better answered by the following departments. Please feel free to contact them directly.
Graduate School of Arts and Sciences:
www.cas.neu.edu/graduate/welcome.html
gsas@neu.edu
617.373.5990
Off-campus Housing Services:
www.offcampus.neu.edu
617.373.2814
On-campus housing: www.housing.neu.edu/housing
We appreciate your interest in our program(s) and look forward to receiving your application.
Started: July 1, 2005
Last Modified: November 13, 2009
Page created and maintained by: Gari Horton
Comments to:g.horton@neu.edu
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