Evidence of English proficiency may consist of one of the following:
Students who lack adequate evidence of English proficiency may be admitted
conditionally and evaluated by the English Language Center prior to
registration. Students who do not demonstrate adequate English proficiency will
be required to enroll in the English Language Center Intensive Language Course
for at least one quarter before enrolling in a full academic program. Such
students may be permitted, with approval of the Director of the English
Language Center and of the academic advisor, to enroll in academic course work
at the same time as they participate in Intensive English.
For more information about the GRE, TOEFL, transfer of credits, registration,
grading system and other regulations, please consult the booklet "General
Regulations" from the Graduate School of Arts and Sciences.
If not applying for departmental financial aid:
All of the following documents must be received in order
to process for admission:
The purpose of this program is to offer students who hold a bachelor's degree
in mathematics or related field, an opportunity to broaden their knowledge in
the several fields of mathematics and its applications. The program is
designed to prepare graduates for careers in business, industry, or government,
or for the Ph.D. program in mathematics.
Combinatorics, Computing, Differential Equations, Probability
and Statistics, Pure Mathematics.
Twelve four-quarter-hour graduate courses are required for the degree. To
qualify for the degree, a cumulative average of 3.000, equivalent to a grade of
B, must be obtained. Required courses for different specializations vary.
Some of the courses listed for this concentration are offered in the College of
Computer Science.
Prerequisite: LISP Lab (does not count toward requirements)
In order for students enrolled in the Northeastern M.S. degree program to be
considered for admission to the Ph.D. program, they must pass a series of
qualifying exams (see the description of the Ph.D. program).
Total forty credit hours.
This program will provide training in the basic techniques and theory of
Operations Research and their applications to real world problems. Graduates
should have developed their analytical skills to attack complex, large-scale
optimization problems of both a deterministic and stochastic nature.
Ten four-quarter-hour graduate courses are required for this degree. To
qualify for the degree, a cumulative average of 3.000, equivalent to a grade of
B, must be obtained. Some of the courses listed for this program are offered
in the Department of Industrial Engineering.
Total forty-two credit hours.
The Master of Arts in Teaching Mathematics is a program designed to enhance the
ability of urban Middle and Secondary school teachers to teach Mathematics in a
modern and creative way.
Applicants must have a bachelor's degree in Mathematics or a closely related
field. They must have taken the Advanced Graduate Record Exam (GRE) in
Mathematics. An applicant's undergraduate course work should have included
linear algebra, differential and integral calculus, differential equations and
computer programming. Students deficient in any of these areas may be accepted
provisionally if their overall college work is particularly strong, but they
will be expected to eliminate the deficiency either before enrollment (summer
courses are available) or within their first two quarters at Northeastern
University. They must possess a Massachusetts State Provisional Certification
prior to joining the program. To assist in meeting this requirement,
Northeastern University offers a summer program leading to a provisional
certification.
Northeastern University's MAT programs, focusing on several key disciplines,
cooperate through the Center for Innovation in Urban Education. Through the
Center, the MAT programs are linked, developed, and administered by subject
area specialists and the practicing Middle and Secondary school teachers.
Students are admitted by an individual participating department and earn their
degree from that department. Subject matter requirements are set by these
departments, and the Center administers the core program requirements shared by
all MAT students.
At the end of their first year in the program, students in the master's level
programs may choose the option of a Master's Degree with Thesis. This option
is strongly recommended for students who intend to continue in the Ph.D.
program here or elsewhere. Also, those students wishing to investigate a topic
in depth, while developing their problem solving skills, may wish to undertake
a Master's Thesis, whether or not they will continue in a Ph.D. program. The
thesis will be written under the supervision of a professor; it will give the
student an opportunity to learn some of the know-how of Mathematics as a
profession, and also to test their capacities in real contact with a
professional mathematician (the supervisor).
A student with the Master's Thesis option should register for two Master's
Thesis courses with the supervisor during two consecutive quarters of the final
year of the student's Master's program. These courses will become a part of
the student's course requirements in place of two electives. They cannot
replace any of the required courses. The written thesis may present original
research, or an original approach to a problem, or can be expository in nature.
After the supervisor's approval, the thesis will be reviewed by a referee.
Then there will be an oral presentation of the thesis before a committee of
three faculty members including the supervisor and the referee. A letter grade
(A, B or F) will be given for the thesis after the presentation.
Combinatorics, Differential Equations, Probability and Statistics,
and Pure Mathematics.
A total of eight four-quarter-hour courses beyond the master's degree, and
three Ph.D. dissertation courses leading to a thesis topic must be taken.
Three of the eight courses must be in a minor specialty and should not include
any courses listed below as required for the area of specialization. See the
section on minor specialty for more information. A minimum cumulative average
of 3.000, equivalent to a grade of B, is required for degree qualification. If
not already taken, the following courses must be taken:
Algebra 1 and 2, Real Analysis or Complex Analysis, Enumeration, Coding Theory,
Graph Theory, Complexity Theory, Probability 1 and Optimization.
Algebra 1 and 2, Real Analysis, Complex Analysis, Functional Analysis,
Topology 1 and 2, and Geometry 1 and 2.
Real Analysis, Algebra 1, Probability 1, Statistics 1. Candidates must fulfill
their additional course requirements according to specific guidelines
established by their thesis supervisor in each particular case. Proficiency
in measure theory must be ensured by those guidelines.
Algebra 1 and 2, Topology 1 and 2, Real Analysis, Complex Analysis, Geometry 1
and 2, and Algebra 3 or Functional Analysis.
Qualifying Exams are given twice each year--- in early January and in early
April. They cover Algebra, Analysis, and the student's specialized field.
Students will be given an opportunity to practice on a sample test. Students
must pass these exams by May of their first year in the Ph.D. program in order
to continue in the program.
Each doctoral candidate selects some specific mathematical subject of an
advanced nature, which must be reasonably unrelated to the topic of the
student's dissertation. The student should render work in this area equivalent
to twelve quarter-hours of course work, part of which may constitute taking
four-quarter-hour courses or a project equivalent to a master's level thesis.
Such a project will be evaluated same way as a Master's Thesis. Approval of
the area and the plan of work should be obtained in advance from the advisor or
the thesis supervisor.
Ability to read and translate mathematical texts and journals in one foreign
language must be established by the candidate. The language may be chosen from
French, German and Russian; any other choice requires special approval.
Students should notify the chair of the Graduate Committee when they are
prepared to be examined on a language. The examination is conducted by a
member of the faculty of the Mathematics Department.
Some teaching experience is required while in the program. This requirement
may be satisfied by teaching an undergraduate course, or by presenting at least
two talks in conferences or departmental seminars.
Each doctoral student must complete a dissertation that embodies the results of
extended research and makes an original contribution to the field. This work
should give evidence of the candidate's ability to carry out independent
investigation and interpret in a logical manner the results of the research.
There are two stages to this process.
The purpose of this course is to provide a prerequisite for the
courses Analysis of Algorithms (MTH3534)
and Automata Theory (MTH3521).
The topics covered are growth of functions, summations, recurrences, sets
(relations vs functions; graphs, trees), counting and probability.
Elementary proof techniques include mathematical induction,
pigeon hole principle, contradiction, diagonalization, and
propositional logic.
An introduction to linear algebra and group theory, covering: vector
spaces, linear maps, matrices and matrix algebra, row and column
operations and their application to normal forms, determinants,
characteristic subspaces, the characteristic and minimal polynomials,
and symmetric groups. This course is given as a preparation for
MTH3102, and should be taken in addition to the required course work
in mathematics.
An introduction to real analysis and advanced calculus, covering:
topology of metric spaces and Euclidean spaces, numerical sequences and
series, limits and continuity, uniform convergence, differentiation and
integration of functions of a single variable. This course is given as
a preparation for MTH3010, and should be taken
in addition to the required course work in mathematics.
Differential Calculus: topology of R^n, compact and
connected sets, continuous maps, uniform convergence,
differentiable maps, the inverse and implicit function
theorems, Riemann integration, change of variables.
Prereq: An undergraduate analysis course. This course is taken
in addition to the required course work in mathematics.
Integration, differentiation, Lebesgue theory, L^p-spaces,
linear functionals, Riesz representation theorem, Hilbert space,
Radon-Nikodym theorem, product measures and Fubini theorem.
Prereq: MTH3010 or equivalent
Symmetric, Hermitian and unitary matrices, Jordan canonical form.
Quadratic forms, multi-linear algebra, the symmetric, exterior and
tensor algebras. Introduction to group theory.
Examines complex function theory: holomorphic and meromorphic
functions, calculus of residues, conformal mappings.
Prereq: MTH3010 or equivalent
Continuation of group theory: Sylow theory, examples
and classification of groups of small order. Rings:
homomorphisms, ideals, quotient rings, integral domain,
extension of rings, unique factorization domain, Chinese
remainder theorem, Gauss' lemma. Modules: homomorphisms,
submodules, quotient modules, exact sequence, structure of
matrices and finitely generated modules over a PID, structure
theory of finitely generated abelian groups.
Prereq: MTH3102 or equivalent
Explores elements of point set topology, including general
topological spaces, compactness and connectedness, products and quotients,
Also considers elements of algebraic topology, including homotopy,
fundamental group and covering spaces. Provides applications to simplicial
complexes.
Analyzes topological linear spaces, normed spaces and Banach spaces, linear
functionals, weak topology, linear operators and Hilbert spaces.
Prereq: MTH3101
Singular homology groups, induced homomorphisms, exact homology
sequence of a pair, excision, Mayer-Vietoris sequence, homology of
CW complexes and applications (eg: Jordan Curve Theorem, Ham Sandwich
Theorem, Lefschetz Fixed Point Theorem). Prereq: MTH3105
This is the first of a three quarter sequence (2 hours per quarter) in linear
algebra, discrete math, and calculus. There are no prerequisites for these
courses; review of high school math is integrated as needed. This course
treats linear equations and inequalities, slope, graphs, matrices, solution
of systems of equations using matrices, the inverse of a matrix, linear
programming, simplex algorithm, applications, probability. These courses
and MTH3214 may not be taken for credit by mathematics graduate students.
Sets, graphs, trees, binary search trees, truth tables, combinatorial
circuits, Karnaugh maps, finite state machines.
The derivative, slope, rate of change, graphing functions, techniques of
differentiation, exponential and logarithmic functions, antiderivatives,
integration, improper integrals as applied to probability.
Probability, discrete and continuous probability distributions, sampling
distributions, hypothesis testing and simple regression. Prerequisite or
corequisite: MTH3213. Not for math graduate credit.
Considers level to measurement, central tendency, dispersion, relatedness
and significance to differences, analysis of data through correlation,
regression, F-test, Chi square tests, T-test, analysis of variance,
and analysis of covariance. Uses computer-based statistical subroutine
packages. Not for math graduate credit.
Includes propositional calculus and quantificational logic;
first order theories and their models; formal arithmetic;
the Gödel First and Second Incompleteness Theorems.
Studies finite extensions of fields, automorphisms, structure of finite
fields, normal and separable extensions, Galois group, Fundamental Theorem
of Galois Theory, cyclotomic fields, solvability of equations by radicals,
and applications (for example, coding theory). Prereq:
MTH3104 or equivalent.
Topics in representation theory, varying according to the interests
of the instructor and students. Some possible topics include:
representations of the symmetric groups, representations
of the classical groups, root systems, highest weight modules, Verma modules,
Weyl character formula, Schur commutator lemma, Schur functors and symmetric
functions, Littlewood-Richardson rule. Prereq:
MTH3104.
Focusing on various advanced topics in algebra, the specific subject
matter depending on the interest of the instructor and students. Possible
topics include: homological algebra, commutative algebra, representation
theory, or combinatorial aspects of commutative algebra. Prereq:
MTH3104 and MTH3332.
Covers prime ideals, localization, integral extensions; primary
decomposition; Krull dimension; chain conditions, Noetherian and Artinian
modules: and additional topics from ring and module theory as time
permits. Prereq: MTH3321 or equivalent.
Existence and uniqueness theorem, methods of explicit solution for
equations and linear systems, regular singular points, Sturm-Liouville
systems, expansions in eigenfunctions.
Linear systems, Existence and uniqueness of solution. Introduction to
dynamical systems: flows, stability, electric circuits, Poincaré-Bendixson
theorem, closed orbits.
Advanced topics in dynamical systems determined by instructor. For
example, Chaos or Hamiltonian Systems.
First-order quasilinear and general non-linear equations:
characteristics; second-order hyperbolic, elliptic and
parabolic equations: separation of variables, potential theory and
Fourier transform. Applications to geometric optics: light, sound and
water waves; electric field theory; heat diffusion.
Prereq: Undergraduate differential equations.
Topics in nonlinear second order partial differential equations: method of
successive approximations, hyperbolic systems, local and global existence
for nonlinear diffusion equations, variational and fixed-point
methods for nonlinear elliptic equations. Applications may include gas
dynamics, simple models of turbulence, and differential geometry.
Prereq: MTH3353.
Floating point arithmetic, root finding, divided differences,
interpolation and approximation, numerical integration, solution
of differential equations, numerical linear algebra, with some
instructor discretion in the choice of these or additional topics.
Students are expected to be reasonably proficient in Pascal, FORTRAN or C
and will be expected to write some programs.
Considers linear and nonlinear control problems defined by ordinary
differential equations, relaxed controls, existence theorems, and
Pontryagin's maximum principle.
Convex sets, including polyhedral sets, extreme points, facets and
representations; linear programming, including the simplex method, duality,
Kuhn-Tucker conditions, and Karmakar's algorithm; non-linear programming,
including Kuhn-Tucker conditions and Lagrange multipliers.
Examines Lie groups and Lie algebras, the exponential map, examples,
basic structure theorems, representation theory, and applications.
Additional topics vary with the instructor and may include infinite
dimensional Lie algebras, algebraic groups, finite groups of Lie type,
geometry, and analysis of homogeneous spaces.
Manifolds, differentiable structures, tangent bundle, tensors, Vector
fields and differential equations, Frobenius integrability theorem,
differential forms. Prereq: MTH3010 and
MTH3102.
Concentrates on the techniques of algebraic geometry arising from
commutative and homological algebra, beginning with a discussion of the
basic results for general algebraic varieties and developing the
necessary commutative algebra as needed. Considers affine and projective
varieties, morphisms of algebraic varieties, regular and singular points,
and normality. Discusses algebraic curves, with a closer look at the
relations between the geometry, algebra and function theory.
Examines the Riemann-Roch theorem, together with its many applications to
the study of the geometry of curves. Studies the singularities of
curves. Prereq: MTH3102 and
MTH3104.
Integration on manifolds, Stokes' theorem, singular homology and cohomology,
v Cech cohomology, deRham cohomology and the deRham theorem.
Prereq: MTH3400.
Characters, orthogonality relations, the regular representation.
Semisimplicity, Maschke's theorem, Wedderburn's theorem, decomposition into
matrix algebras. Prereq: MTH3104.
Rings of integers, Dedekind domains, factorization of ideals,
ramification, the decomposition and inertia subgroups. Units in rings of
integers, Minkowski's geometry of numbers, Dirichlete's unit theorem. Class
groups, zeta functions, and density of sets of primes. Prereq:
MTH3321.
Analyzes geometry of surfaces in the Euclidean space, with emphasis on the
global aspects, using the technique of tensor calculus. Explores elements
of Riemannian geometry, connections and holonomy.
Basic geometry for Riemannian manifolds, including connections, curvature
tensors, geodesics, the Riemannian geometry of submanifolds, minimal
submanifolds. Emphasis on computational techniques and examples.
An introduction to complex manifolds. The elementary local theory in
several variables will be discussed, including Cauchy's integral formula,
Hartog's extension theorem, the Weierstrass preparation theorem, and Riemann's
extension theorem. The global theory includes the definition of complex
manifolds, sheaf cohomology, line bundles and divisors, Kodaira's vanishing
theorem, Kodaira's embedding theorem, and Chow's theorem on complex
subvarieties of projective space. Special examples of dimension one and two
will illustrate the general theory. Prereq: MTH3400 and
MTH3103.
Measure theory is not a prerequisite for this course. Some concepts from
measure theory will be introduced as needed. This course will cover the
following topics: sample space, probability measure, random variables,
standard distributions (such as the normal, exponential and Poisson) and modes
of convergence, independence and dependence of variables, properties of
expectation and conditional expectation, and characteristic functions.
This course covers topics in stochastic processes. Selected topics may
include renewal theory, Markov chains and processes, martingales and
Brownian motion. Prereq: MTH3431.
Introduces mathematical statistics, emphasizing asymptotics (large samples).
Estimation, mean squared error, asymptotics of sample mean and sample
median (via Taylor series), maximum likelihood estimation, consistency of MLE.
Asymptotic distribution of MLE, Cramer-Rao bound, sufficiency and
completeness. Rao-Blackwell theorem.
This course covers: statistics as a game, loss and utility, subjective
probability, priors, Bayesian statistics, minimaxity, admissibility and
complete classes, James-Stein estimators, empirical Bayes.
Discussion of one-sample and two-sample test; one-way break ANOVA;
factorial and nested designs; Cochran's theorem; regression; analysis of
convariance; and simultaneous confidence intervals.
Includes multivariate statistics and clustering; biostatistics; Stein's
paradox and admissibility, foundation; and probabilistic and inferential
aspects of reliability theory.
Presents methods for analyzing data that is not necessarily normal.
Emphasizes comparing two treatments (the Wilcoxon test,
Kolmogorov-Smirnov test), comparison of several treatments (the
Kruskal-Wallis test), randomized complete blocks, tests of randomness and
independence and asymptotic methods (the 8 method, Pitman efficiency).
Focuses on the analysis of data in tables, that is, with cross-classified
data. Includes loglinear models (a generalization of analysis of variance
methods) and logistic regression. Includes homework problems involving
real data and sometimes focusing on theoretical issues.
Introduces the methods of pattern recognition: multivariate normal
distribution, linear discriminant analysis, logistic regression, tree
structured classification, cluster analysis, jackknifing and
bootstrapping and cross-validation. This course is intended for students
interested in computer science or applied statistics.
Homology with coefficients, cohomology groups, cup and cap products, the
cohomology ring, Künneth theorem, spectral sequence of a fibration,
duality in manifolds and applications. Prereq: MTH3107
Advanced topics in topology; the specific topics vary depending on the
interests of the instructor and students.
Basic structures for representing and manipulating data in computer
programming: arrays, lists, stacks, queues, dequeues, trees, binary trees.
Applications to non-numeric computations. Searching and sorting. Students
are required to write programs to implement these structures on a computer.
Offers topics in algebraic algorithms in a different subspeciality each
time. Topics will be chosen from: computational group theory,
computational number theory, algorithms for computing with finite fields,
the discrete Fourier Transform and its applications, the Knuth-Bendix
algorithm for finitely presented algebras, polynomial factorization and
related topics in computer algebra. Same as COM3741 offered by the
College of Computer Science.
Considers algorithms and theories for parallel computation on
fixed-connection networks and on concurrent systems having a fixed number
of processors, Includes algorithms for sorting, priority queues, graph
algorithms, matrix multiplication and FFT. Allows students use of a
network of micros to implement some of these algorithms, May include
applications to VLSI design. Same as COM 3640 offered by the College of
Computer Science.
Explores formal models of computation and regular expressions; properties
of regular sets; context-free languages and pushdown automata; Chomsky
hierarchy; and computability and undecidability. Same as COM3710.
Examines searching, goals, plans, heuristics and representation of
knowledge: nets, frames and inheritance. Covers logic and its role in
artificial intelligence and selected applications of these ideas in other
areas of artificial intelligence. Prereq: MTH3501 and
another computer related course. Same as COM3410.
This course will look at various types of mathematical models of a discrete
nature and develop the mathematical tools needed to understand them.
In this course we learn various counting techniques such as generating
functions, recurrence relations, principle of inclusion-exclusion, Polya's
theorem. We obtain various identities involving binomial and multinomial
coefficients, Stirling numbers, Euler's numbers, Fibonacci numbers, etc.
We learn to count the number of sets, multisets, permutations, functions,
partial orders, etc. satisfying special properties. Some applications of these
counting techniques will also be discussed.
Explores block designs, including-designs, orthogonal Latin Squares,
difference sets and finite geometries. Includes algebraic coding,
including cyclic codes, Reed-Solomon Codes, BCH Codes and Reed-Muller
codes. Prereq: MTH3102.
Examines graphs and subgraphs; trees; connectivity; Euler tours and
Hamilton cycles; matchings, edge colorings; independent sets and cliques;
vertex colorings; planar graphs; directed graphs; networks, the cycle
space; and bond space.
Focuses on topics in combinatorics in a different subspecialty each time.
Includes topics such as game theory, combinatorial geometry, measurement,
and algebraic combinatorics.
This course deals with advanced topics in algebraic geometry. These
include cohomology theory of algebraic schemes, study of singularities,
geometric invariant theory, flag varieties and Schubert varieties.
Discusses design and analysis of fast algorithms. Topics include advanced
data structures: representing partitions, union-find algorithms and
priority queues; graph algorithms: biconnectivity, maximum flow, shortest
path and matching minimum spanning tree; algebraic problems:
Multiplication, polynomial multiplication, string matching and linear
programming; and Probabilistic algorithms: tests for primality and
factoring polynomials and integers. Same as COM3390.
Analyzes theory of relationships among complexity classes of algorithms.
Covers sequential, deterministic, parallel, non-deterministic and
probabilistic models of computation and Turing and decision tree models.
Considers the class NP and questions of completeness, especially
NP-completeness, reducibility and hierarchy of complexity classes.
Individual study and research for PhD candidates.
The Department offers an assortment of 4QH courses under the general headings
''Seminar'' and ''Readings'' in all major fields --- MTH 3804 through MTH 3841.
At the outset of each quarter, times for organizational meetings for these courses
will be posted. Schedule and content are negotiated at these meetings.
Students and faculty with interest in the specialty of the seminar (or
readings) are encouraged to attend the organizational meeting.
Introduction
The graduate programs offered by the Department of Mathematics are designed to
provide students with both a broad overview of current Mathematics and also a
strong command of some area of specialization. The department provides
opportunities for graduate students to work with an internationally recognized
faculty in a diverse range of research programs of both a pure and applied
nature. Because of its location in Boston, one of the foremost mathematical
centers in the world, the mathematical life at Northeastern is enlivened by
frequent visits from eminent mathematicians. Numerous departmental and regional
seminars also give the student an ample opportunity to learn of recent and
important advances in mathematics.
Faculty
CHAIR
Fields: Algebraic and differential topology, Massey products, deRham theory
with applications to the fundamental group and group cohomologyPROFESSORS
Field: Differential topology
Fields: Differential geometry and algebraic topology
Fields: Singularities of mappings and its applications to algebraic and
differential geometry
Fields: Algebraic topology, three manifolds, mathematics education
Field: Geometry of spaces with singularities
Fields: Ergodic theory and analysis
Fields: Algebraic geometry, commutative rings and their deformations,
singularities of maps, families of points on a variety, Gorenstein algebras
Fields: Algebraic geometry, algebraic groups, representation theory
Fields: Algebraic geometry and algebraic K-theory
Fields: Statistics and optimal design, random processes and probability
Fields: Discrete geometry, combinatorics, group theory
Field: Artificial intelligence
Fields: Partial differential equations, micro local analysis, spectral theory,
index of elliptic operators, geometric analysis
Field: Differential geometry
Fields: Commutative algebra, algebraic geometry, representation theory
Fields: Representation theory, algebraic geometry, algebraic combinatorics,
discrete geometry, special functions
ASSOCIATE PROFESSORS
Fields: Mathematics education, computer assisted instruction, numerical and
constructive algebra, commutative algebra
Fields: Mathematical logic and Socratic teaching of mathematics
Fields: Measure theoretic ergodic theory, applications to number theory,
spectral analysis of ergodic maps
Fields: Artificial intelligence and natural language
Fields: Commutative algebra and homology of local rings
Fields: Statistical decision theory, mathematical statistics, probability and
quantum mechanics
Fields: Classifying spaces, homeomorphism groups, homology of groups,
foliations
Fields: Lie groups, Lie algebras, Weyl groups, Lie algebra cohomology,
noncommutative ring theory
Fields: Mathematical physics, quantum mechanics, knot theory
Fields: Low-dimensional dynamical systems and numerical analysis
Fields: Graph theory, complexity theory, optimization
Fields: Homological algebra, representation-theoretic methods in local
algebra
Fields: Algebraic geometry and singularities
Fields: Partial differential equations, equations on manifolds, functional
analysis
Fields: Commutative algebra and graph theory
Field: Partial differential equations
Fields: Non-commutative harmonic analysis, symmetric spaces, Lie groups,
numerical analysis
Fields: Algebraic and geometric topology
Fields: Representation theory of Artin algebras, non-commutative algebra
ASSISTANT PROFESSOR
Fields: Mathematical statistics, prediction and confidence intervals,
artificial neural networks
VISITING ASSISTANT PROFESSOR
Fields: Representation theory, combinatorics, algebraic geometry
PROFESSORS EMERITI
Fields: Complex analysis and computer-assisted instruction
Field: Probability theory
Fields: Optimal control theory, optimization, non-smooth analysis
Research
The department has strong and active research mathematicians in
a variety of areas. Below is a partial list of current
research areas and some of the studies being undertaken, a list
that constitutes a rich cross section of the whole of
mathematics.
The Graduate Programs
The Mathematics Department offers M.S. and Ph.D. degree programs in Mathematics
and, in addition, an M.S. degree in Operations Research in conjunction with
the Department of Industrial Engineering, and a Master of Arts in Teaching
(M.A.T.) degree with concentration in Mathematics. At present, the Department
offers both full-time and part-time programs leading to an M.S. degree, but
only a full-time program leading to a Ph.D. degree and only a part-time program
leading to an M.A.T. degree. In addition to the course requirements, a thesis
is required for the Ph.D. program. A thesis is optional in place of two
electives in all the three master's level programs. See the sections on
Master's Thesis and Ph.D. dissertation for more details.
Admissions Requirements
Applicants must have a bachelor's degree in mathematics or a closely related
field. They must have taken the Advanced Graduate Record Exam (GRE) in
Mathematics, and international students must demonstrate proficiency in
English. (For more details, see the International Student Applications
section.) An applicant's undergraduate course work should have included linear
algebra, combinatorics, differential and integral calculus, differential
equations, real analysis and computer programming. Students deficient in any of
these areas may be accepted provisionally if their overall college work is
particularly strong, but they will be required to eliminate the deficiency
either before enrollment (summer courses are available) or within their first
two quarters at the Northeastern University. Placement exams in algebra and
analysis will be given to all entering students. Applicants to the Ph.D.
program must, in addition, have a master's degree in Mathematics or a closely
related field. The admissions requirements for the M.A.T. program differ
slightly. See the corresponding section for additional information.
Applications
Application material can be obtained by sending a request either by e-mail to
mathdept@neu.edu or by writing to:
Completed applications, two letters of recommendation by former professors,
and complete official transcripts should be sent directly to the
Mathematics Department. Applicants should arrange to have official
reports of the Advanced GRE sent to the Graduate School of Arts and Sciences.
Financial Awards
Each year, the Mathematics Department offers a limited number of Research
Assistantships (RAs), Teaching Assistantships (TAs), and Northeastern
University Tuition Assistantships (NUTAs) to some promising full-time students.
A RA includes tuition and stipend, and a recipient could be required to
complete a project for a professor each quarter. A TA includes tuition and a
stipend, and a recipient will be required to teach a basic undergraduate course
each quarter. For this reason, international students receiving a Teaching
Assistantship should be able to speak English fluently. An NUTA covers tuition
only, and a recipient will be required to assist with grading and tutoring each
quarter. Candidates for financial aid should indicate that fact to those who
will supply references. Candidates who want to be considered for an NUTA only,
should mention that fact in the application. MAT students are not eligible for
this support. However, some funds for tuition scholarships are awarded by the
MAT program on a competitive basis. Additionally, the University awards
need-based aid to graduate students in the MAT program through the Federal
Perkins Loan, Federal Work Study, and Federal Stafford Loan programs. A
limited number of a minority fellowships and Martin Luther King Jr.
Scholarships are also available.
International Student Applications
In addition to the previously mentioned application procedures, international
students are required to have a Declaration and Certification of Finances form
and evidence of English proficiency on file with the Graduate School office at
least twelve weeks before the beginning of the quarter in which they expect to
begin a program.
International Teaching Assistant Orientation
All international students receiving a Teaching Assistantship for the first
time must participate in a week-long intensive orientation prior to the
beginning of the Fall quarter. This orientation is intended to provide the
teaching assistants with the opportunity to sharpen their speaking and
presentation skills, as well as to introduce them to the culture of the
American classroom. This orientation and the weekly seminars that are offered
throughout the Fall quarter are mandatory for first-time international teaching
assistants.
Part-Time Program
Nearly all graduate courses in the Mathematics Department meet after 5:00 p.m.,
Monday through Thursday, so that students who work during the day may take one
or two courses each quarter at night. Students in the part-time program may
progress according to their abilities and available time, subject to the
seven-year limitation established by the University.
Special Student Status
Students with a bachelor's degree who are not matriculating in a degree
program, but like to take a few graduate level courses should also complete the
application and must satisfy all admission's requirements with the exception
of taking the GRE. Also, if the student's transcripts are more than three
years old, recommendation letters will not be needed. Instead, all such
applicants must submit their most recent curriculum vitae.
Deadlines for Receiving Applications
If applying for departmental financial aid, a candidate must apply for the Fall
quarter and as a regular full-time student. Deadline: March 15.
Semester Deadline* Fall August 1 Winter November 1 Spring February 1
For International applicants:
Graduate Advisor
All graduate students must have a graduate advisor. A list of possible
advisors can be obtained from the graduate secretary. An advisor will monitor
the student's progress and advise the student on the courses to take. Any
courses taken outside the Department and some courses from within the
Department will require approval from the advisor. An advisor should assist
the Ph.D. students in finding a thesis supervisor. The thesis supervisor will
act as the advisor for the student and will also guide the student through the
dissertation.
Placement Exam
All entering students into the M.S. and Ph.D. programs will be offered two
placement exams, one on the material covered in Modern Algebra, and one on the
material covered in Fundamentals of Analysis. A student who fails the algebra
test will have to take Modern Algebra, and likewise, a student who fails the
analysis test will have to take Fundamentals of Analysis. These courses will
not be counted toward the degree.
The Master of Science Degree
Total forty-eight credit hours.
Areas of specialization
Course Requirements
Transition to Ph.D. Program
Master of Science Degree in Operations Research
Course Requirements
Master of Arts in Teaching (M.A.T.) Degree
Admissions Requirements
The MAT Programs At Northeastern University
Core Program Requirements
Mathematics Requirements
Part-Time Program
Students in this program may progress according to their
abilities and available time, subject to the seven years
limitation established by the Graduate School of Arts and
Sciences. Students who are deficient in any of the mathematics
courses required for admission to the degree program are
required to satisfy their deficiencies by taking courses given
for this purpose. Such courses carry graduate credit, but that
credit is regarded as additional to regular degree
requirements.
The Doctor of Philosophy Degree
The Doctor of Philosophy degree is awarded to candidates who show evidence of
high scholastic attainment and research ability in their major field.
Areas of Specialization
Course Requirements
Qualifying Exams
Minor Specialty
Language Requirements
Teaching Requirement
Dissertation Requirement
Course Descriptions
The following is a listing of all departmental course offerings.
Most of the courses are offered on a regular basis; a few are offered
on demand.
Math Department Home Page
Directory
Last modified: September 11, 1996
Comments to:
alexsuciu@neu.edu