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Mathematics

College of Natural Sciences
Keller 401-A
2565 McCarthy Mall
Honolulu, HI 96822
Tel: (808) 956-4680
Fax: (808) 956-9139
E-mail: patg@math.hawaii.edu
Web: www.math.hawaii.edu

Faculty

*Graduate Faculty

*T. Craven, PhD (Chair)—commutative algebra
*C. Allday, PhD—algebraic topology, transform group
*E. Bertram, PhD—group theory and combinatorics
*D. Bleecker, PhD—differential geometry
*R. Brown, PhD—algebra and number theory
*M. Chyba, PhD—control theory
*G. Csordas, PhD—complex function theory
*K. Dovermann, PhD—algebraic topology
*R. Freese, PhD—lattice theory, general algebra
*M. Gotay, PhD—mathematical physics, symplectic geometry
*E. Guentner, PhD—geometrical functional analysis
*H. Hilden, PhD—geometric topology
*G. Hile, PhD—partial differential equations
*T. Hoover, PhD—operator theory
*W. Lampe, PhD—universal algebra
*R. Little, PhD—algebraic topology
*A. Mader, PhD—group theory
*D. Myers, PhD—mathematical logic
*J. Nation, PhD—lattice theory
*M. Ortel, PhD—complex function theory
*L. Ramsey, PhD—harmonic analysis
*D. Ross, PhD—logic, probability
J. Siu, MA—mathematics education
*W. Smith, PhD—analysis, function theory
*D. Stegenga, PhD—analysis
*J. Weiner, PhD—differential geometry
*G. Wilkens, PhD—differential geometry, control theory
*L. Wilson, PhD—singularity theory

Degrees Offered: BA (including minor) in mathematics, BS in mathematics, MA in mathematics, PhD in mathematics

The Academic Program

The mathematics (MATH) program offers preparation in the full spectrum of mathematical sciences, including algebra, geometry, differential equations, real and complex analysis, topology, logic, number theory, and probability and statistics, as well as various topics in applied mathematics. Mathematics majors begin with the study of calculus and linear algebra. After completion of these fundamental courses, students may choose to specialize. The department advises each prospective major on requirements and course options to meet his or her needs and interests. Departmental advisers are also available every day to all students.

Depending upon individual interest, students of mathematics may pursue careers in a variety of fields such as teaching, computer science, operations research, statistics, business, and economics. In addition, students who continue on to the graduate program may choose to become professors and/or research mathematicians. The faculty has the competence and resources required to provide the basic mathematical preparation required for any of these professions.

A goal of all non-survey mathematics courses is the development of precision of thought and expression. This receives special emphasis in the many writing-intensive courses the department offers.

Undergraduate Study

BA Degree

Requirements

Students must complete 21 credit hours in mathematics courses numbered above 300, including:

  • MATH 321
  • MATH 480
  • 3 credit hours in a writing-intensive mathematics course
  • 6 credit hours in courses numbered above 400
  • 6 credit hours in a sustained two-course sequence approved by the department
  • Only courses in which a student earns a grade of C (not C-) or better will be counted toward fulfillment of major requirements
  • A cumulative 2.0 GPA in all completed upper division mathematics courses is required
  • All mathematics majors are required to see a mathematics adviser each spring semester prior to fall registration

BS Degree

Requirements

Students must complete 24 credit hours in mathematics courses numbered above 300 and 15 credit hours in additional upper division mathematics courses or appropriate non-introductory courses in the natural or information sciences, including:

  • MATH 321
  • MATH 480
  • 6 credit hours in writing-intensive mathematics courses
  • 6 credit hours in a sustained two-course sequence approved by the department
  • Only courses in which a student earns a grade of C (not C-) or better will be counted toward fulfillment of major requirements
  • A cumulative 2.0 GPA in all completed upper division mathematics courses is required
  • All mathematics majors are required to see a mathematics adviser each spring semester prior to fall registration

Students must also demonstrate the ability to program scientific problems on a computer.

Minor

Requirements

Students must complete MATH 243 plus 12 credit hours in mathematics courses numbered above 300, including:

  • 3 credit hours in a writing-intensive mathematics course
  • 6 credit hours in courses numbered above 400

Graduate Study

Prospective graduate students are expected to have adequate undergraduate preparation in linear algebra, advanced calculus, and abstract algebra. Applicants must submit to the department their scores for the GRE General Test; applicants for the graduate assistant positions are strongly encouraged to submit scores for the subject test in mathematics as well. The department requires a score of at least 650 on the quantitative section of the GRE General Test for admittance as a regular student. The department requires a general examination of all incoming graduate students for course placement purposes. This diagnostic examination consists of two parts, algebra and analysis, and is designed to evaluate the student’s command of undergraduate mathematics in the areas of linear algebra, advanced calculus, and abstract algebra.

Master’s Degree

Requirements

The department does not have a thesis option (Plan A) for the MA, and most students will select Plan B. Plan B requires 30 credit hours of course work. Each Master’s candidate must form a two member committee and pass an oral examination on a topic chosen by the student and committee. An exceptional student may be admitted to Plan C at the discretion of the graduate chair.

Doctoral Degree

Requirements

For the PhD degree, the department requires that the student show proficiency in two of the following languages: French, German, Russian, or a computer language. Teaching experience is required of all PhD students. To be admitted to PhD candidacy, the student must satisfy the language requirements and pass three written examinations: (a) linear algebra and abstract algebra; (b) real analysis and the basic facts of complex analysis and general topology; and (c) a third field chosen by the student with the approval of the graduate chair. All new students in the PhD program shall complete a minimum of five mathematics department courses numbered between 600 and 690, other than 611, 612, 621, 631, 632, 644, 645, 649. These five courses may be taken under the CR/NC option. Exceptions: Up to two 3-credit 649 (alpha) seminars (meeting three hours/week) may be substituted for (up to) two of these required five courses, with the written approval of the graduate chair. Also, with the written approval of the graduate chair, credit may be given for equivalent courses taken in another mathematics department or for graduate-level courses taken in another department that are recommended by the student’s thesis adviser and directly related to the dissertation topic; such credit for graduate courses taken in another department is limited to a total of no more than two courses.

MATH Courses