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The Department of Mathematics at the University of Hawai'i
at Mānoa (UHM) offers MA and PhD programs in the full
spectrum of mathematical sciences — including algebra,
geometry, differential equations, real and complex analysis,
logic, number theory, and probability and statistics, as well
as various topics in applied mathematics.
The department's faculty, whose expertise and interests span
the entire range of modern mathematical research, has the
competence and resources required to provide the basic mathematical
preparation required for any of the professions related to
mathematics. Furthermore, the department attracts excellent
visitors, both short-term and long-term, from institutions
such as Berkeley, Harvard, M.I.T., Princeton, Stanford, Cambridge,
Oxford, Göttingen, L'Ecole Polytechnique, the E.T.H.
and the Steklov Institute.
The department strives for excellence in education and research.
The department's faculty members have published extensively,
including numerous articles in the leading journals and at
least twelve graduate- or research-level books. Two faculty
members have received the University of Hawai'i Excellence
in Teaching Award and several others have been nominated.
Two faculty members have received the University Excellence
in Research Award. In addition, two other members of the department
have received the George Polya Award for expository excellence
from the Mathematical Association of America.
Faculty expertise and research interests include the following:
- Analysis — The department has experts in partial
differential equations, complex analysis, functional analysis,
operator theory and harmonic analysis, which is fundamental
to signal processing and telecommunication theory.
- Algebra — Faculty specialties include field theory,
Frobenius algebra, finite groups, infinite Abelian groups,
quadratic forms and arithmetic groups and their representations.
The department has one of the world's best groups of faculty
in lattice theory and universal algebra. A number of long-outstanding
problems in this field have been solved by this group.
- Transformation Groups — Faculty members study transformation
groups from several points of view: algebraic, smooth or
topological actions by means of surgery, cobordism, index
theory, equivarient cohomology and rational homotopy.
- Differential geometry and topology — Research topics
include singularity theory and applications to control theory.
- Low-dimensional topology — Topics studied include
knot theory and hyperbolic manifolds.
- Other Areas — There is significant faculty strength
in mathematical logic, non-standard analysis, complexity
theory, combinatorics and graph theory. In addition, several
faculty members conduct research on topics at the heart
of contemporary physics: gauge theories, quantization, symplectic
geometry and non-commutative differential geometry.
Depending upon individual interest, MA graduates may pursue
careers in a variety of fields such as teaching, computer
science, operations research, statistics, business, and economics.
PhD graduates may choose to become professors and/or research
mathematicians.
About two-thirds of the department's graduates have found
employment in academia. The majority of those in academia
have stayed in Hawai'i, working either within the University
of Hawai'i system or for other small four-year colleges in
Hawai'i. Many graduates, particularly those without a PhD,
have accepted positions at community colleges. A few alumni
have gone on to conduct research in mathematics at major universities.
Several PhD graduates have accepted postdoctoral positions
at Brown, Dartmouth, Harvard, Purdue, UCLA, and Vanderbilt,
as well as Imperial College (London) and various other foreign
universities. Others in academia have gone into computer science
or mathematics education.
Slightly more than a third of the department's graduates
have found positions in private industry. Those in the industry
hold a varied collection of positions, many of which involve
computers and/or financial mathematics. In particular, the
department has graduates working for Symantec Corporation,
Lucent Technologies, and many smaller software companies.
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MA Degree Requirements
Most students follow Plan B (non-thesis). Plan C (exam)
is also available to selected students. To be admitted to
Plan C, students must demonstrate superior ability in the
diagnostic exam and be recommended for this degree plan by
the graduate chair.
- Plan B requires 30 credits, a directed research project
and a final exam.
- Plan C has no minimum course requirements. Students must
demonstrate competence by passing an exam.
PhD Degree Requirements
The program requires the following:
- five graduate courses in mathematics,
- completion of MA degree requirements,
- demonstrated proficiency in two of the following languages:
French, German, Russian or a computer language,
- college teaching experience,
- comprehensive exam,
- dissertation,
- final oral exam / defense of dissertation.
Courses
To view a listing of courses offered, visit www.catalog.hawaii.edu/courses/departments/math.htm.
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