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Degree, Minors and Certificates Offered

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Requirements for Undergraduate Degrees from the Colleges of Arts and Sciences

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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

*L. Thomas Ramsey, PhD (Chair)—harmonic analysis
*C. Allday, PhD—algebraic topology, transformation groups
*M. Chekroun, PhD—dynamical systems, climate dynamics
*M. Chyba, PhD—control theory
*T. Craven, PhD—commutative algebra
*G. Csordas, PhD—complex function theory
*K. Dovermann, PhD—algebraic topology
*A Faber, PhD—number theory, algebraic geometry
*R. Freese, PhD—lattice theory, general algebra
*E. Guentner, PhD—geometrical functional analysis
*P. Guerzhoy, PhD—number theory
*T. Hangelbroek, PhD—approximation theory
*H. Hilden, PhD—geometric topology
*B. Kjos-Hanssen, PhD—computability, logic, probability
*R. Little, PhD—algebraic topology
*M. Manes, PhD—number theory
*D. Myers, PhD—mathematical logic
*J. Nation, PhD—lattice theory
*M. Ortel, PhD—complex function theory
*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
*J. van Erp, PhD—index theory, noncommutative geometry
*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 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 and completed within one year
  • 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/. For more information on the major, go to www.advising.hawaii.edu/artsci/pages/resources/lib_art_degrees/majorskills/majorskills_math.asp#MATH_SCHED.

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 related fields 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 and completed within one year
  • 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 also demonstrate the ability to program scientific problems on a computer.

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 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

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)

  • 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 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

Most MA students will select Plan B, which requires 30 credit hours of course work, including 611, 612, 631, and 644. Masters candidates must form a two member committee. The student is required to write and defend a paper on a research topic approved by the student's master's 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

For the PhD degree, the department requires that the student show proficiency in one of the following languages: French, German, or Russian. 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, 631, 632, 644, 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 advisor 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. The most important requirement for a PhD degree is the successful defense of a doctoral dissertation involving original mathematical research.

MATH Courses