MATHEMATICS
AND COMPUTER SCIENCE
Professors of Mathematics:
Karen Collins, W. Wistar Comfort, Adam Fieldsteel, Chair,
Anthony N. Hager, Michael S. Keane, Fred E. J. Linton, Philip H.
Scowcroft, Carol Wood
Associate Professor of Mathematics:
Mark Hovey, Wai Kiu Chan
Assistant Professors of Mathematics:
Petra Bonfert-Taylor, David J.
Pollack, Edward Taylor
Professor of Computer Science:
Michael Rice
Associate Professors of Computer
Science: Daniel Krizanc, James
Lipton
Assistant Professor of Computer
Science: Norman Danner
GRADUATE PROGRAM
The department's
graduate programs include a PhD program in mathematics and MA programs in
mathematics and in computer science. The research emphasis at Wesleyan at
the doctoral level is in pure mathematics and theoretical computer
science. One of the distinctive features of our department is the close
interaction between the computer science faculty and the mathematics
faculty, particularly those in logic and discrete mathematics.
Among possible fields
of specialization for PhD candidates are algebraic topology, analysis of
algorithms, categorical algebra, combinatorics, complex analysis,
computational logic, data mining, ergodic theory, geometric analysis,
general topology, graph theory, homological algebra, Kleinian groups and
discrete groups, lattice-ordered algebraic structures, logic programming,
mathematical physics, model theory, model-theoretic algebra, number
theory, operator algebras, probability theory, proof theory, topological
dynamics, and topological groups.
Graduate students at
Wesleyan enjoy small, friendly classes and close interactions with faculty
and fellow graduate students. Graduate students normally register for
three classes a semester and are expected to attend departmental colloquia
and at least one regular seminar. The number of graduate students ranges
from 18 to 24, with an entering class of four to eight each year. There
have always been both male and female students, graduates of small
colleges and large universities, and U.S. and international students,
including, in recent years, students from China, Germany, Hungary, India,
Korea, Mexico, Peru, and Poland. All of the department's recent PhD
recipients have obtained faculty positions. Some of these have
subsequently moved to mathematical careers in industry and government.
REQUIREMENTS FOR THE DEGREE OF DOCTOR OF
PHILOSOPHY
The
doctor of philosophy degree demands breadth of knowledge, an intense
specialization in one field, a substantial original contribution to the
field of specialization, and a high degree of expository skill. The formal
PhD requirements consist of the following:
Courses. At
least 16 one-semester courses are required for the PhD degree. Several of
the courses are to be in the student's field of specialization, but at
least three one-semester courses are to be taken in each of the four
areas: algebra, analysis, logic and discrete mathematics, and topology. In
particular, first-year students are expected to take three of the four
two-semester sequences and to take the fourth two-semester sequence in the
second year. The choice of courses will be made in consultation with the
student's advisor and the departmental Graduate Education Committee.
Language
Examinations. It is strongly recommended that the PhD candidate
have or acquire a knowledge of French, German, and Russian sufficient for
reading the mathematical literature in these three languages. Knowledge of
two of these three languages is required.
General Preliminary
Examinations. The general preliminary examinations take place in the
summer after the candidate's first year of graduate work. These written
exams cover the content of the three first-year courses taken by the
candidate.
Special preliminary
examination. The special preliminary examination should occur during
the candidate's third year of graduate work. The candidate is expected to
exhibit sufficient mastery of the chosen specialty to be qualified to
begin research leading to a doctoral dissertation under a faculty thesis
advisor. The candidate demonstrates this mastery by giving a lecture on a
topic, chosen in consultation with an advisor. A faculty committee
evaluates the candidate’s performance.
Dissertation.
The dissertation, to be written by the PhD candidate under the counsel
and encouragement of the thesis advisor, must contain a substantial
original contribution to the field of specialization of the candidate and
must meet standards of quality as exemplified by the current research
journals in mathematics.
Defense of
Dissertation. The final examination is an oral presentation of the
dissertation in which the candidate is to exhibit an expert command of the
thesis and related topics and a high degree of expository skill.
Four to five years are
usually needed to complete all requirements for the PhD degree, and two
years of residence are required. It is not necessary to obtain the MA
degree en route to the PhD degree. Recently, some students have obtained
the MA in computer science and the PhD in mathematics. Any program leading
to the PhD degree must be planned in consultation with the departmental
Graduate Education Committee.
REQUIREMENTS FOR THE MASTER OF ARTS DEGREE
The requirements
for the master of arts degree are designed to ensure a basic knowledge and
the capacity for sustained independent scholarly study. The formal MA
requirements consist of the following:
Courses. Six
one-semester graduate courses in addition to the research units MATH591
and 592, or COMP591 and 592, are required for the MA
degree. The choice of courses will be made in consultation with the
departmental Graduate Education Committee.
Thesis. The
thesis is a written report of a topic requiring an independent search and
study of the mathematical literature. Performance is judged largely on
scholarly organization of existing knowledge and on expository skill, but
some indications of original insight are expected.
Final examination.
The final examination is an oral presentation of the MA thesis, in which
the candidate is to exhibit an expert command of the chosen specialty and
a high degree of expository skill. The oral presentation may include an
oral exam on the material in the first-year courses. A faculty committee
evaluates the candidate’s performance. Three semesters of full-time study
beyond an undergraduate degree are usually needed to complete all
requirements for the MA degree. Any program leading to the MA degree must
be planned in consultation with the departmental Graduate Education
Committee.
Three semesters of work beyond an
undergraduate degree are needed to obtain the M.A. degree at the usual
rate of progress for a full-time student. Any program leading to the M.A.
degree must be planned in consultation with the departmental Graduate
Education Committee.
APPLICATION
No specific courses are required for
admission, but it is expected that the equivalent of an undergraduate
major in mathematics or in computer science with a strong emphasis in
mathematics will have been completed. The complete application consists of
the application form, transcripts of all previous academic work at or
beyond the undergraduate level, letters of recommendation from three
college instructors familiar with the applicant’s ability and performance,
and GRE scores (if available). Students whose native language is not
English should provide TOEFL scores. A request for admission as a
part-time graduate student will be considered.
Applications should be submitted by
February 15 in order to receive adequate consideration, but requests for
admission from outstanding candidates are welcome at any time. Preference
is given to applicants for the Ph.D. program. A visit to campus is
strongly recommended for its value in determining the suitability of the
program for the applicant.
FINANCIAL ASSISTANCE
Stipends. Each applicant for
admission is automatically considered for appointment to an assistantship.
For the 2002–2003 academic year, the stipend is $13,635, plus a dependency
allowance when appropriate, and one-third more is usually available for
the student who wishes to remain on campus to study during the summer.
Costs of tuition and health fees are borne by the University. All students
in good standing are given financial support for the duration of their
studies.
Cost of Study. The only academic
costs to the students are books and other educational materials.
Living and Housing Costs. The
University provides some subsidized housing and assists in finding private
housing. Visit the website for graduate housing:
www.wesleyan.edu/reslife for more information on vacancies and costs.
FACILITIES
The department is housed in the Science
Center, where all graduate students and faculty members have offices. Computer
facilities are available for both learning and research purposes. The
Science Library collection has about 120,000 volumes, with extensive
mathematics and computer science holdings. More than 250 subscriptions to
mathematics and computer science journals, and approximately 100 new
mathematics or computer science books arrive each month. The proximity of
students and faculty and the daily gatherings at teatime are also key
elements of the research environment.
Mathematics and Computer Science Courses
Certain courses listed below may not be
offered each year. Certain courses may not appear below. Please check with
the department for a complete course schedule.
MATH500 Graduate Pedagogy
Identical with: BIOL500
Credit: 0.50
Fall 2005
MATH501/502 Individual Tutorial, Graduate
Topic to be arranged in consultation with
tutor.
Credit: 1.00
MATH503 Selected Topics, Graduate Sciences
Credit: 1.00
MATH504 Selected Topics, Graduate Sciences
Credit: 1.00
MATH507 Topics in Combinatorics
Each year the topic will change.
Credit: 1.00
MATH509 Model Theory
TBA
Credit: 1.00
MATH511/512 Group Tutorial, Graduate
Credit: 1.00
MATH513 Analysis I
Math 513 and Math 514 constitute the
first-year graduate course in real and complex analysis. One semester will be
devoted to real analysis, covering such topics as Lebesgue measure and
integration on the line, abstract measure spaces and integrals, product
measures, decomposition and differentiation of measures, and elementary
functional analysis. One semester will be devoted to complex analysis,
covering such topics as analytic functions, power series, Mobius
transformations, Cauchy's integral theorem and formula in its general form,
classification of singularities, residues, argument principle, maximum modulus
principle, Schwarz' lemma, and the Riemann mapping theorem.
Credit: 1.00
Fall 2005
MATH514 Analysis I
Math 513 and Math 514 constitute the first
year graduate course in real and complex analysis. One semester will be
devoted to real analysis, covering such topics as Lebesgue measure and
integration on the line, abstract measure spaces and integrals, product
measures, decomposition and differentiation of measures, and elementary
functional analysis. One semester will be devoted to complex analysis,
covering such topics as analytic functions, power series, Mobius
transformations, Cauchy's integral theorem and formula in its general form,
classification of singularities, residues, argument principle, maximum modulus
principle, Schwarz' lemma, and the Riemann mapping theorem.
Credit: 1.00
Spring 2006
MATH515 Analysis II
Topics in analysis to be announced.
Credit: 1.00
Fall 2005
MATH516 Analysis II (Topics from Analysis)
Credit: 1.00
Spring 2006
MATH517 Analysis II
Credit: 1.00
MATH523 Topology I
General topology. Introduction to set theory
and cardinal numbers. The axiom of choice and some of its equivalents.
Topological spaces. Separation axioms, continuity, connectedness,
compactness, product spaces, cardinal invariants. Major results, such as:
Urysohn metrization theorem, Baire category theorem, Tychonoff product
theorem, Stone-Cech compactification theorem. Further selected topics.
Credit: 1.00
Fall 2005
MATH524 Topology I
An introduction to algebraic topology. After
reviewing compactness and connectedness from MATH523, the course will
concentrate on homotopy and the fundamental group.
Credit: 1.00
Spring 2006
MATH525 Topology II - Topics in Topology
This course will involve topics in algebraic
topology, possibly including homology, cohomology, homotopy, and generalized
cohomology theories.
Credit: 1.00
Fall 2005
MATH526 Topology II
Credit: 1.00
Spring 2006
MATH543 Algebra I
Group theory including Sylow theorems. Basic
ring and module theory, including structure of finitely generated modules over
principal ideal domains.
Credit: 1.00
Fall 2005
MATH544 Algebra I
Galois theory, classical groups, other topics
as time permits.
Credit: 1.00
Spring 2006
MATH545 Algebra II: Topics in Algebra
This course will be an introduction to
algebraic geometry.
Credit: 1.00
Fall 2005
MATH546 Algebra II
Credit: 1.00
Spring 2006
MATH553 Logic and Discrete Mathematics
This course and its sequel, MATH554, will
present topics in logic and in discrete mathematics, and devote one semester
to each. The topics in logic may include the completeness and compactness
theorems for first-order logic, the incompleteness theorems, and logic
programming; the topics in discrete mathematics may include graph theory,
combinatorics, and the analysis of algorithms.
Credit: 1.00
MATH554 Logic and Discrete Mathematics
The spring-semester continuation of MATH553.
Credit: 1.00
Spring 2006
MATH571 Special Topics in Mathematics
Credit: 1.00
MATH591/592 Advanced Research, Graduate
Credit: 1.00
COMP500 Automata Theory and Formal Languages
Identical with: COMP301
Credit: 1.00
Fall 2005
COMP501/502 Individual Tutorial, Graduate
Credit: 1.00
COMP510 Algorithms and Complexity
Identical with: COMP312
Credit: 1.00
Spring 2006
COMP511/512 Group Tutorial, Graduate
Credit: 1.00
COMP521 Design of Programming Languages
Identical with: COMP321
Credit: 1.00
Spring 2006
COMP522 Compilers
Identical with: COMP322
Credit: 1.00
COMP527 Evolutionary and Ecological
Bioinformatics
Identical with: BIOL327
Credit: 1.00
Fall 2005
COMP531 Computer Structure and Operation
Identical with: COMP231
Credit: 1.00
Spring 2006
COMP550 Bioinformatics and Functional
Genomics
Identical with: BIOL350
Credit: 1.00
COMP551 Foundations Of Computer Science I
An introduction to computational logic.
Topics include equational logic, term rewriting, unification, and typed lambda
calculus.
Credit: 1.00
COMP553 Foundations of Computer Science III
Course content varies from year to year.
Credit: 1.00
COMP554 Principles of Databases
Identical with: COMP354
Credit: 1.00
COMP555 Logic and Discrete Mathematics
Identical with: MATH554
Credit: 1.00
Spring 2006
COMP571 Special Topics in Computer Science
Supervised reading course of varying length.
This course may be repeated for credit.
Credit: 1.00
Fall 2005
COMP572 Special Topics in Computer Science
Supervised reading course of varying length.
This course may be repeated for credit.
Credit: 1.00
Spring 2006
COMP591/592 Advanced Research, Graduate
Credit: 1.00
