Welcome!

Here in the Department of Mathematics at UH Mānoa, we offer both MA and PhD degrees in mathematics. We have about 20 faculty members with a wide range of interests who can mentor you in algebra, analysis, applied mathematics, combinatorics, geometry, logic, number theory, and topology. You would join a group of almost 40 graduate students learning math and pushing the boundaries of mathematical research. We offer introductory and advanced graduate courses, as well as regular ‘topics’ courses changing every year based on professors’ research interests and student demand. We have a vibrant faculty and grad student lounge that offers a lot of opportunity for talking with your fellow mathematicians.

Below are more details about the MA degree, the PhD degree, the application process, funding opportunities, and living in Hawai‘i.

#### Program summaries

##### PhD requirements

The PhD program in the Mathematics Department has four main components: coursework, qualifying exams, a comprehensive exam, and the writing and oral defense of a PhD thesis.

The goal of this program is to develop your abilities to the point where you can contribute original research in mathematics. To this end, we offer a wide range of basic graduate courses as well as advanced topics courses, and the faculty usually run a few seminars every semester. During your time here, you’ll work towards a broad understanding of graduate mathematics, develop your mathematical abilities and creativity, and reach the cutting edge of research in one of the many fields our faculty studies, all culminating in the writing and oral defense of your PhD thesis. Along the way, you’ll have a few milestones to reach: taking at least 10 courses (with some breadth requirements), passing two qualifying exams (out of four: algebra, analysis, applied mathematics, and topology), and completing a comprehensive exam with a faculty advisor.

For more details, see the full requirements page here.

##### MA requirements

The MA program in the Mathematics Department has two main components: coursework and the writing and oral presentation of a masters project.

As a student in this program, you’ll take both introductory and more advanced graduate level courses, with some freedom to choose your own path. By about half way through the two to three year program, you should settle down on an advisor who can mentor you to the completion of a project that you’ll get to write up and present.

For more details, see the full requirements page here.

#### Funding opportunities

Graduate Assistantships are available at stipends which range from approximately \\$19,000 for the academic year, with waiver of tuition. All newly admitted PhD students are assured funding for up to 6 years. Masters students may be funded  on a space available basis. At any given time, about three quarters of our graduate students are supported by teaching assistantships. Some faculty members also have grants that have funds to support students with Research Assistantships. Most graduate assistants teach recitation sections for pre-calculus and calculus courses though other options exist: tutoring, grading, teaching a class, or assisting a professor.

#### Living in Hawai‘i

The university campus is located on the Leeward side of O‘ahu at the mouth of the Mānoa Valley in Honolulu, about two miles from the beaches of Waikiki. The island offers an abundance of opportunity for outdoor activities from hiking to Mānoa Falls or the summit of Diamond Head to snorkeling in Hanauma Bay, and, as you might imagine, surfing. Moreover, Honolulu is a city of a million people with all sorts of cultural and social activities. You can find out about all this and more on the university’s website.

#### Application process

The typical requirement for admission to the graduate program is the completion of a standard undergraduate program in mathematics. The candidate will generally be expected to know linear algebra, the elements of abstract algebra, and elementary real analysis. A student whose degree has been awarded in some other field may be considered if they have had the appropriate background courses. Students should also have current general GRE scores (waived for the 21-22 year) and must submit a personal statement describing their reasons for pursuing a graduate degree in math.

For best consideration for Fall semester, applications should be submitted by February 15, and for the Spring by  October 1. Note that we do not usually have many openings for spring admission.

# Marriott’s doctoral defense

John Marriott, a student of Prof. Monique Chyba, will defend his doctoral dissertation on September 5.

#### Abstract

This work addresses the contrast problem in nuclear magnetic resonance as a Mayer problem in
optimal control. This is a problem motivated by improving the visible contrast in magnetic resonance
imaging, in which the magnetization of the nuclei of the substances imaged are first prepared by
being set to a particular con figuration by an external magnetic field, the control. In particular we
examine the contrast problem by saturation, wherein the magnetization of the first substance is
set to zero. This system is modeled by a pair of Bloch equations representing the evolution of the
magnetization vectors of the nuclei of two di fferent substances, both influenced by the same control
field.
More…

# The zeros of entire functions

Graduate student Rintaro “Yoshi” Yoshida will defend the degree of Ph.D. on Thursday May 2, 2:00pm, in Keller 301.

We invite the reader to consider the entire function
$$\varphi_{_{1/5}}(x) = \sum_{k=0}^\infty \frac{x^k}{(k!)^{(6/5)}}.$$
Do you think this function has any non-real zeros? Does it belong to the Laguerre-Pólya class? See the draft dissertation for answers.