*College of Natural Sciences*

*Keller 401-A*

*2565 McCarthy Mall*

*Honolulu, HI 96822*

*Tel: (808) 956-4679*

*Fax: (808) 956-9139*

*Web: math.hawaii.edu*

## Faculty

**Graduate Faculty*

*R. Willett, PhD (Chair)—noncommutative and coarse geometry

*M. Chyba, PhD—control theory

*K. Dovermann, PhD—algebraic topology

*D. Erman, PhD—commutative algebra, algebraic geometry, computation and algorithms

*E. Gawlik, PhD—numerical analysis

*E. Gross, PhD—algebraic statistics

*E. Guentner, PhD—geometrical functional analysis

*P. Guerzhoy, PhD—number theory

*A. Hadari, PhD—geometric group theory

*T. Hangelbroek, PhD—approximation theory

*A. Helminck, PhD—symmetric spaces

*M. Jovovic, PhD—operator theory, function theory

*B. Kjos-Hanssen, PhD—computability, logic, probability

*Y. Lodha, PhD—combinatorial, topological, and geometric group theory

*Y. Mileyko, PhD—applied topology, mathematical biology

*F. Nasrin, PhD—algebraic topology, Bayesian statistics, differential geometry

J. Robertson, PhD—noncommutative geometry, pedagogy

*D. Ross, PhD—logic, probability

*D. Takagi, PhD—applied math, fluid dynamics

*S. Widiasih Post, PhD—mathematical physics, integrable systems

*G. Wilkens, PhD—differential geometry, control theory

*C. Xu, PhD—dynamical systems, stochastic processes, mathematical biology

*M. Younsi, PhD—complex analysis

H. Zheng, PhD—geometric and topological combinatorics

**Degrees Offered:** Undergraduate Certificate in Mathematical Biology, BA (including minor) in mathematics, BS in mathematics, BS in mathematics with Data Science Track, BS in mathematics with Computational Science Track, 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 their 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 479, which must include:

- MATH 311 or MATH 307
- MATH 321
- MATH 331
- 3 credit hours in a writing-intensive mathematics course
- 6 credit hours in courses numbered above 400
- Students must also complete MATH 480 (CR/NC only) (final year)
- Only courses in which a student earns a grade of C (not C-) or better will be counted toward fulfillment of major requirements
- All mathematics majors are required to see a mathematics advisor each semester prior to the next semester registration

For information on a Bachelor Degree Program Sheet, go to programsheets/.

### BS Degree

#### Requirements

Students must complete PHYS 170/170L and PHYS 272/272L, as well as MATH 244 or 253A, and must complete 30 credit hours in mathematics courses numbered between 300 to 479 and 9 credit hours in additional mathematics courses numbered above 300 to 479 or appropriate non-introductory courses in related fields including:

- MATH 311 or 307
- MATH 321
- MATH 331
- 6 credit hours in writing-intensive mathematics courses
- 12 credit hours in courses numbered above 400
- Students must also complete MATH 480 (CR/NC only) (final year)
- Only courses in which a student earns a grade of C (not C-) or better will be counted toward fulfillment of major requirements
- All mathematics majors are required to see a mathematics advisor each semester prior to the next semester registration
- Students must demonstrate an understanding of algorithms and logic, as well as precision of thinking.

For information on a Bachelor Degree Program Sheet, go to programsheets/.

### BS Degree, Computational Science Track

Students must complete PHYS 170/170L and PHYS 272/272L, as well as MATH 244 or 253A, and must complete 30 credit hours in mathematics courses numbered between 300 to 479 and 10 credit hours in related ICS courses including the following:

- MATH 304, 305, 307 or 311, 321, 331, 402, 407, 411, and 414
- ICS 211, 212, and 484
- 6 credit hours in writing-intensive mathematics courses
- 12 credit hours in mathematics courses numbered above 400
- Students must also complete MATH 480 (CR/NC only) (final year)
- Only courses in which a student earns a grade of C (not C-) or better will be counted toward fulfillment of major requirements
- All mathematics majors are required to see a mathematics advisor each semester prior to the next semester registration
- Students must demonstrate an understanding of algorithms and logic, as well as precision of thinking

### BS Degree, Data Science Track

#### Requirements

Students must complete PHYS 170/170L and PHYS 272/272L, as well as MATH 244 or 253A, and must complete 30 credit hours in mathematics courses numbered between 300 to 479 and 10 credit hours in related ICS courses including the following:

- MATH 301, 307 or 311, 321, 331, 407, 442 or 475, 471, and 472,
- ICS 211, 235, and 435,
- 6 credit hours in writing-intensive mathematics courses
- 12 credit hours in courses numbered above 400
- Students must also complete MATH 480 (CR/NC only) (final year)
- Students must demonstrate an understanding of algorithms and logic, as well as precision of thinking.

Substitution allowed: ICS 141 and ICS 241 can be substituted for MATH 301 in the Data Science Track only. In that case, students must take another 300-level MATH course and another 300-level course from one of the diversification courses (DA/DH/DL or DS).

For information on a Bachelor Degree Program Sheet, go to 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
- 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) BA Physics, BS Physics, and BS Astrophysics students may count their MATH 307 or 311 major requirement towards a minor in mathematics.

If MATH 243 is a requirement for your major but you did not take MATH 253A, you must complete MATH 244, and complete 12 credits in mathematics courses numbered above 300 that include 3 credit hours in writing-intensive mathematics courses and 6 credit hours in courses 400 and above (excluding MATH 480). If both MATH 243 and 244 are requirements for your major, or if you took MATH 253A for your major requirement, you must complete 15 credits in mathematics courses numbered above 300 that include 3 credit hours in writing-intensive mathematics courses and 6 credit hours in courses 400 and above (excluding MATH 480). 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 a departmental advisor.

## 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 (at most one of 601 or 602), 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 Mānoa 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.