Graduate Program · Degree Requirements · Class Schedule · Qualifying Exams

Inquiries

Dear Prospective Student,

Hello and thank you for your interest in the graduate program in the Department of Mathematics at Northeastern University. Below please find information regarding our degree programs, application requirements, application deadlines and financial aid resources. For addidtional information and a comprehensive overview of the Department of Mathematics, please go to the Graduate Office web page. If you have questions about the application process, please e-mail g.horton@neu.edu or call 617.373.2454. Once again, many thanks for your interest in the Department of Mathematics.
Sincerely,

Gari Horton
Administrative Secretary
Department of Mathematics
567 Lake Hall
Northeastern University
360 Huntington Avenue
Boston, MA 02115
ph: 617.373.2450
fax: 617.373.5658
e-mail: g.horton@neu.edu
URL: www.math.neu.edu/grad/GradOffice/index

Program Booklet

Program Information:

Northeastern University· Graduate School of Arts and Sciences· Department of Mathematics· Boston, MA 02115· 571 Lake Hall· Telephone: 617.373.2450· Fax:617.373.5658· e-mail: g.horton@neu.edu· Internet: www.math.neu.edu

_____________________________________________________________________________________

Graduate Executive Committee:
Professors: Aidong Ding, Maxim Braverman, Mikhail Shubin, Jerzy Weyman, Marc Levine.

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., 2007/2008 Cost of Study: $980.00 per semester hour of credit (980.00 x 4=$3,980.00/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.

Remember, the above information is a brief summary. Pleasae refer to the Graduate Office webpage (http://www.math.neu.edu/grad/GradOffice/index.html) for full details. Feel free to contact the Graduate Administrative Secretary, Mr. Gari Horton (g.horton[at]ne.uedu or 617.373.2454), for further assistance.

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.
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

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.
- 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

4 Required courses: Algebraic Combinatorics, Geometric Combinatorics, Optimization & Complexity, Topics in Combinatorics
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.

Old Degree Requirements (quarter system)

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 and the course description catalogue produced by the Registrar.

Started: April 15, 2008. Last modified: June 30, 2008
Page created by: Gari Horton
Page Maintained by: Gari Horton
Send comments to:g.horton@neu.edu