Category Archives: Graduate posts

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Student learning outcomes for graduate programs

Student Learning Outcomes in the PhD Program:
1. Mastery of graduate level mathematics in core areas including at least 2 of analysis, algebra, topology, applied mathematics.
2. Familiarity with the breadth of modern mathematics, by successful completion of a range of advanced courses.
3. Deep knowledge of a specific area of specialization.
4. Ability to accomplish significant mathematical research.
5. Ability to write professional quality mathematics.
6. Ability to present advanced research mathematics to a mathematics audience.
7. Ability to learn advanced mathematics independently.

Student Learning Outcomes in the MA Program:
1. Mastery of graduate level mathematics in core areas including at least 3 of analysis, algebra, topology, applied mathematics.
2. Familiarity with the breadth of modern mathematics, by successful completion of a range of advanced courses.
3. Ability to engage in an independent mathematical project.
4. Ability to communicate mathematics effectively in writing.
5. Ability to present advanced mathematical ideas to a mathematics audience.

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Graduate Program in Logic

The Department of Mathematics at University of Hawaii at Manoa has long had an informal graduate program in logic, lattice theory, and universal algebra (People, Courses, Description) going back to Alfred Tarski’s 1963 student William Hanf.

We are offering the following course rotation (courses repeating after two years):

Semester Course number Course title Instructor
Fall 2015 MATH 649B Graduate Seminar Kjos-Hanssen
Spring 2016 MATH 649 Applied Model Theory Ross
Fall 2016 MATH 654 Graduate Introduction to Logic Beros
Spring 2017 MATH 657 Computability and Complexity Khan
Fall 2017
Spring 2018 MATH 649 Applied Model Theory Ross

It is also recommended that students familiarize themselves with undergraduate level logic, which is offered on the following schedule:

Semester Course number Course title Instructor
Fall 2012 MATH 454 Axiomatic Set Theory Kjos-Hanssen
Spring 2013 MATH 455 Mathematical Logic
Fall 2014 MATH 454 Axiomatic Set Theory Ross
Spring 2015 MATH 455 Mathematical Logic Khan
Spring 2016 MATH 454 Axiomatic Set Theory Khan
Spring 2017 MATH 455 Mathematical Logic Ross
Spring 2018 MATH 455 Mathematical Logic Khan
Fall 2018 MATH 454 Axiomatic Set Theory ?

Faculty teaching in the program

David A. Ross, Professor
Bjørn Kjos-Hanssen, Professor
Mushfeq Khan, Temporary Assistant Professor 2014-2018
Achilles Beros, Temporary Assistant Professor 2015-2018

Graduate degree timelines

This page provides some information about when you should accomplish various milestones in your degree and what other events must occur along the way. It is for convenience only. Consult with the Graduate Chair to ensure you have all the information you need.

PhD timeline

The typical time to degree for a PhD here is 5 to 6 years and the maximum length of support is set to 6 years. In your first couple of years, you’ll be taking classes and studying to pass your qualifying exams. It’s also a good idea during that time to try to figure out what type of math you might do research in; attending various seminars, talking to more advanced students about what they do, and asking professors about their research are a few ways you can go about accomplishing this. We encourage you to attempt qualifying as exams as soon as you can. Even if you fail, you’ll have a better idea of what they are about. By the end of the fall of your 3rd year, you need to have attempted at least 2 quals and by the end of the fall of your 4th year, you need to have passed 2 quals.

Once you pass your two qualifying exams, your top priority should be to find an adivsor; getting up to speed on the cutting edge of research, and then doing your own, takes a lot of time! Still, finding an advisor is an important decision and, while your interest in their research is a very important factor, personal chemistry should also be considered. If you’ve spent some of your early years talking to some professors, this important step should go more smoothly.

Your advisor will determine the format of your comprehensive exam. You must pass this exam by the end of your 4th year and you only have two tries. Once this is behind you, you can form a ‘thesis committee’.

Then, you do math.

Once you’ve done math, it’s time to write it up. The way in which you go about this will depend a lot on you and your advisor. As you approach completion, make sure to discuss the timing with your advisor and your committee. You should contact the graduate chair at least a month ahead of defending so that they can ensure all the various forms and announcements go out in time.

MA timeline

The typical time to degree for an MA here is 2 to 3 years and the maximum length of support is set to 3 years.

In your first year, you’ll be spending a lot of your time taking classes. As suggested above for PhD candidates, it’s also suggested that you try to figure out in what general area, and with whom, you’ll want to write your MA paper. Attending various seminars, talking to more advanced students about what they do, and talking to professors about what masters projects they might have in mind are a few ways you can go about accomplishing this.

By the end of the fall of your second year, you will need to have chosen an advisor. You will work with them to produce a masters paper and prepare an oral presentation. As you near completion, you should discuss timing with your advisor, form a masters committee, and talk with the graduate chair to ensure all the various forms and announcements go out in time.

Prospective graduate students

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.

For more information about faculty research, you can check out our research page.

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—at least 10 in total—with a lot of 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 \$17,500 to \$19,000 for the academic year, with waiver of tuition. 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 GRE scores and are strongly encouraged to submit a personal statement describing their reasons for pursuing a graduate degree in math.

Applications for admission in the Fall semester are accepted from August 1 to February 15, and for the Spring semester from May 1 to October 1.

For some of the finer print, see our graduate application page.