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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
Web: www.math.hawaii.edu

Faculty

*Graduate Faculty

*E. Guentner, PhD (Chair)—geometrical functional analysis
*M. Chyba, PhD—control theory
*K. Dovermann, PhD—algebraic topology
*R. Freese, PhD—lattice theory, general algebra
*P. Guerzhoy, PhD—number theory
*A. Hadari, PhD—geometric group theory
*T. Hangelbroek, PhD—approximation theory
*R. Harron, PhD—algebraic number theory
*M. Jovovic, PhD—operator theory, function theory
*B. Kjos-Hanssen, PhD—computability, logic, probability
*M. Manes, PhD—number theory
*Y. Mileyko, PhD—applied topology, mathematical biology
*D. Myers, PhD—mathematical logic
*S. Post, PhD—mathematical physics, integrate systems
*D. Ross, PhD—logic, probability
*W. Smith, PhD—analysis, function theory
*D. Takagi, PhD—applied math, fluid dynamics
*G. Wilkens, PhD—differential geometry, control theory
*R. Willett, PhD—noncommutative and coarse geometry
*L. Wilson, PhD—singularity theory

Degrees Offered: Undergraduate Certificate in Mathematical Biology, 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 advisors 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 MATH 244, or MATH 253A, and must complete 21 credit hours in mathematics courses numbered between 300 to 4791, which must include:

  • MATH 311 or MATH 307
  • MATH 321
  • MATH 331
  • MATH 480
  • 3 credit hours in a writing-intensive mathematics course
  • 6 credit hours in courses numbered above 400
  • 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 advisor each spring semester prior to fall registration

For information on a Bachelor Degree Program Sheet, go to www.manoa.hawaii.edu/ovcaa/programsheets/.

BS Degree

Requirements

Students must complete PHYS 170/170L, and PHYS 272/272L as well as MATH 244 or MATH 253A. Students must also complete 24 credit hours in mathematics courses numbered above 300 to 479 and 15 credit hours in additional mathematics courses numbered above 300 to 479 or appropriate non-introductory courses in related fields including:

  • MATH 311 or MATH 307
  • MATH 321
  • MATH 331
  • MATH 480
  • 6 credit hours in writing-intensive mathematics courses
  • 6 credit hours in courses numbered above 400
  • 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 advisor each spring semester prior to fall registration

Students must demonstrate an understanding of algorithms and logic, as well as precision of thinking. Contact a math advisor for courses that satisfy this requirement.

For information on a Bachelor Degree Program Sheet, go to www.manoa.hawaii.edu/ovcaa/programsheets/.

Minor

Requirements

Students must complete:

  • MATH 243 or 253A
  • 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

All required courses must be completed with a grade of C or better. Courses used to fulfill core or major requirements cannot be counted for the minor. Exceptions are (a) Engineering students may count their Engineering mathematics electives and technical elective (if taken in mathematics) and MATH 302 or 307 towards a minor in mathematics; (b) Physics students may count their MATH 307 or 311 major requirement towards a minor in mathematics.

If MATH 243 is a requirement for your major, then you must replace it with MATH 244. If MATH 243 and 244 are requirements for your major, then you must replace it with an upper division math course. The requirements include work at the senior level and allow the choice of specific courses which best complement work in the student's major field.

Students who are interested in minoring in mathematics are urged to consult a departmental advisor early in their academic career. Prior to graduation (at least one semester in advance), a Certification of Academic Minor form should be completed in consultation with an departmental advisor.

Undergraduate Certificate in Mathematical Biology

The purpose of the certificate is to induce students to pursue the interdisciplinary study of biology and mathematics together with research. The course work will be similar to, but less than, that required to receive a minor in mathematics or biology. However, the students will also have to do a substantial amount of research in addition to the course work. The emphasis in the certificate is different, however, in that the majority of the work is interdisciplinary.

Students will be considered accepted into the Mathematical Biology Certificate Program upon formal request for acceptance and completion of either MATH 304 or 305 with a grade of C or better. To receive the certificate, students must complete 15 credits of approved course work with no grade below a C and attain a GPA of 2.5 in the collection of courses used to satisfy the certificate requirements. Due to the interdisciplinary nature of the certificate, 6 credits of required electives will differ depending on a student's major. Courses used towards the certificate can only be double-dipped with focus requirements.

Prerequisites to the Certificate

  • BIOL 171 (lab not required)
  • CHEM 161 or 171 (lab not required)
  • year of calculus (MATH 215/216, MATH 241/242, MATH 251A/252A
  • electives may have additional prerequisites

Requirements for the Certificate (15 credits)

  • required courses (9 credits): MATH 304, 305, MATH/BIOL 490 (capstone)
  • math majors (6 credits): BIOL 172, and 265 or 275 (lab not required)
  • life science majors (6 credits): two courses selected from MATH 243/253A, 301, 302, 303, 307, 311, 371, 373, 402, 403, 407, 414, 416, 471, 472
  • other majors: completion of above required courses, and at least 6 credits of electives approved by the Committee

Participation in an interdisciplinary Mathematical Biology research project is required. These projects must be substantial, requiring at least the effort of a 5 credit 400-level course; examples include a senior honors research project, summer Research Experiences for Undergraduate programs, and the Undergraduate Biology and Mathematics Research Program; students are advised to discuss their projects with an advisor from the Mathematical Biology Certificate Coordinating Committee before commencing. A research paper based on this research project must be submitted to and approved by the committee. Students are expected to present their research to an approved symposium or conference.

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 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

Most MA students will select Plan B, which requires the student to complete 30 credit hours of courses in the Department of Mathematics numbered 400-699, subject to the following conditions: at least nine credit hours must come from 601, 611, 621,and 631; and at least six credits must come from 603 or 607, 625, 644, 654 or 655 or 657, and 661. All courses counting towards the 30 credit requirement must be passed with a grade of B- or better, at most six credits can be numbered 400-499, and at most six credits can be numbered 649(Alpha) or 699. With the written approval of the graduate chair, credit towards this requirement may be given for additional courses numbered 649(Alpha) or 699, or for graduate-level courses taken in another department.

Masters candidates must form a two member committee. The student is required to write and defend a paper on a research topic approved by their committee and the graduate chair. The defense will consist of a one hour public presentation on the chosen topic, followed by an oral exam. The department does not have a thesis option (Plan A), and only an exceptional student may be admitted to Plan C at the discretion of the graduate chair.

Doctoral Degree

Requirements

All new students in the PhD program shall complete 30 credit hours of courses in the Department of Mathematics numbered 600-699. These are subject to a distribution requirement which requires the student to demonstrate facility in three of the following five areas: algebra, analysis, applied mathematics, foundations, and topology. All courses counting towards this requirement must be passed with a grade of B- or better, and at most six credits may be in courses numbered 649(Alpha) or 699. With the written approval of the graduate chair, credit towards this requirement may be given for equivalent courses taken in another mathematics department, or for courses taken at UH Mânoa while in the master's program, or for additional courses numbered 649(Alpha) or 699, or for graduate-level courses taken in another department.

To be admitted to PhD candidacy, the student must pass two written qualifying exams and a comprehensive exam. Qualifying exams are offered in the following areas: algebra; analysis; topology; and applied mathematics. The comprehensive exam is a written or oral examination in a field chosen by the student with the approval of the graduate chair.

The most important requirement for a PhD degree is the successful defense of a doctoral dissertation involving original mathematical research.

MATH Courses