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Degree Requirements

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. 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 7301 or higher, or else has a course number 7201 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:

    • Two PhD dissertation courses (MATH9990) leading to thesis topic during the first year of candidacy .  Registration into PhD Continuation (MATH 9996) in subsequent years through graduation.  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 coure 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

  • 4 Required courses: PDE 1, Functional Analysis, Complex Analysis, Geometry 1.

  • 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).

 

MS in Operations Research Program

  • Probability 1 or Engineering Probability and Statisitics, Probability 2 or Probabilistic Operations Research, Deterministic Operations 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 Scheduing, Reliability and Risk Assessment.

 

Time limits

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.