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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 mostly repeating after two years):

Semester Course number Course title Instructor
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 course break - -
Spring 2018 MATH 649 Applied Model Theory Ross
Fall 2018 MATH 654 Graduate Introduction to Logic Kjos-Hanssen
Spring 2019 MATH 655 Set theory Williams
Fall 2019 course break - -
Spring 2020 MATH 657 Computability and Complexity Kjos-Hanssen

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 Kjos-Hanssen
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 Ross
Spring 2019 MATH 455 Mathematical Logic Ross
Fall 2019 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 2015-2019
Kameryn Williams, Temporary Assistant Professor 2018–2019

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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.

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.