The Department of Mathematics and Statistics offers both a Master of Science (MS) and a Doctor of Philosophy (Ph.D.) in Mathematical Sciences, with a concentration in either pure mathematics or applied mathematics. Students interested in graduate-level statistics can pursue a Master of Science in Statistical Sciences or Biostatistical Sciences. The Ph.D. in Complex Systems and Data Science provides strong computational and theoretical training in an interdisciplinary setting. Our Accelerated Master’s Program (AMP) allows students to complete a Master of Science in Mathematics, Statistics, or Biostatistics with only one additional year of study following the completion of a bachelor’s degree.

## Handbook for Graduate Students in Mathematics

This Handbook contains information about the Graduate Program in Mathematics at the University of Vermont. It is useful for potential students, current students, advisors, and professors. Comments or questions may be relayed to Dr. Greg Warrington (Gregory.Warrington@uvm.edu), the Director of the Mathematics Graduate Program.

## Graduate Programs in Mathematics and Statistics

## Graduate Program Learning Outcomes

## Statistics/Biostatistics (M.S.) program

*Graduating Students from the Statistics/Biostatistics (M.S.) program should be able to:*

**Design:**Critically appraise strengths and weaknesses of study designs and identify designs that are appropriate for addressing specific research questions.**Data analysis:**Demonstrate statistical reasoning, formulate problems in statistical terms, use exploratory and graphical data analysis techniques, and use a variety of formal inference procedures.**Theory:**Understand important theoretical results and their role in answering inferential questions.**Computing:**Demonstrate proficiency in use and application of standard statistical software for data management and algorithmic problem-solving.**Communication:**Demonstrate strong communication skills to effectively collaborate as part of interdisciplinary teams, including the ability to communicate the results of a statistical analysis through oral and written reports to non-experts.

## Mathematics (M.S.) program

*Graduating Students from the Mathematics (M.S.) program should:*

- Be prepared for entry into a Mathematics Ph. D. program
- Have a solid understanding of graduate-level real and complex analysis
- Be able to write a clear, precise, and logically rigorous multi-step proof
- Demonstrate mastery of the core mathematical concepts in at least one area of specialty such as:
- Applied Mathematics
- Discrete Mathematics
- Algebra

## Mathematical Sciences (Ph.D.) program

*Graduating students from the Mathematical Sciences (Ph.D.) program should:*

- Have a solid understanding of graduate-level real and complex analysis
- Be able to write a clear, precise, and logically rigorous multi-step proof
- Demonstrate mastery of the core mathematical concepts in at least one area of specialty such as:
- Applied Mathematics
- Discrete Mathematics
- Algebra

- Be an expert in their field of research
- Have created original research
- Have successfully taught a semester-long university level course as the primary instructor
- Be able to formulate new research problems
- Be able to clearly communicate their research both orally and in writing
- Be qualified for a post-doctoral position or for a faculty position at a teaching or research institution

## PH.D. Qualifying Exams and Thesis Templates

## Ph.D. Qualifying Exam Syllabi

## Ph.D. Qualifying Exams - Algebra

- Algebra Qualifying Exam-May 2008 (PDF)
- Algebra Qualifying Exam- September 2008 (PDF)
- Algebra Qualifying Exam-January 2009 (PDF)
- Algebra Qualifying Exam- October 2010 (PDF)
- Algebra Qualifying Exam- January 2014 (PDF)
- Algebra Qualifying Exam- January 2018 (PDF)
- Algebra Qualifying Exam- January 2019 (PDF)
- Algebra Qualifying Exam- August 2019 (PDF)
- Algebra Qualifying Exam- January 2020 (PDF)
- Algebra Qualifying Exam - August 2020 (PDF)
- Algebra Qualifying Exam - January 2021 (PDF)
- Algebra Qualifying Exam - August 2021 (PDF)

## Ph.D. Qualifying Exams - Combinatorics

## Complex Variables Qualifying Exams

## Differential Equations Qualifying Exams

## Numerical Analysis Qualifying Exams

- Numerical Analysis Qualifying Exam- Spring 2010 (PDF)
- Numerical Analysis Qualifying Exam- January 2011 (PDF)
- Numerical Analysis Qualifying Exam- Spring 2014 (PDF)
- Numerical Analysis Qualifying Exam-Spring 2016 (PDF)
- Numerical Analysis Qualifying Exam- Spring 2018 (PDF)
- Numerical Analysis Qualifying Exam- May 2020 (PDF)

## Real Analysis Qualifying Exams

## Real and Complex Analysis Qualifying Exams

- Real and Complex Analysis Qualifying Exam- May 2008 (PDF)
- Real and Complex Analysis Qualifying Exam- September 2009 (PDF)
- Real and Complex Analysis Qualifying Exam- May 2012 (PDF)
- Real and Complex Analysis Qualifying Exam- September 2015 (PDF)
- Real and Complex Analysis Qualifying Exam- May 2018 (PDF)
- Real and Complex Analysis Qualifying Exam- January 2019 (PDF)
- Real and Complex Analysis Qualifying Exam- May 2020 (PDF)
- Real and Complex Analysis Qualifying Exam - August 2020 (PDF)
- Real and Complex Analysis Qualifying Exam - January 2021 (PDF)
- Real and Complex Analysis Qualifying Exam - August 2021 (PDF)

## Graduate Resources

## Department and University Awards for Graduate Students

There are several awards programs in the Department and University for graduate students.

Each year at Honors Day the Department gives the **Kenney Award** to the outstanding graduate student in mathematics. The Department also gives the **Sang Kil Nam Scholarship Award** to an outstanding undergraduate or graduate student in Mathematics.

The Department has one free one-year membership in the Mathematical Association of America (MAA) and several one-year American Mathematical Society (AMS) memberships. Each year the Director of the Mathematics Graduate Program awards these to the most qualified eligible graduate students. Priority for these goes to second-year M.S. students. No student will receive the award more than once.

Each year, the Graduate College holds a university-wide competition for the **Graduate Student Teaching Assistant of the Year**. The Department may nominate up to three students for this award (two in mathematics, one in statistics).

Also administered by the Graduate College is the **Doctoral Student Scholar Award** for outstanding work by a Ph.D. candidate. The recipient receives recognition and a $1,000 prize at the Graduate Hooding Ceremony.

Each summer, the Graduate College offers a number of Graduate Student Summer Research Assistantships. For details, please contact the Graduate College.

Each fall, the University initiates a **Student-Faculty Research Program**. Students (junior/senior undergraduates and first year graduates) may apply for funding of a joint research project with a faculty member. Funding - including a stipend and supplies - is given for either the spring or summer. Application to this program is competitive, and requires submission of a proposal for review by a faculty panel. More information, including deadlines, application forms, etc. is available from UVM's Office of Sponsored Programs (on their web site as well).

Each year the Graduate College hosts a **Graduate Student Research Day** around April 1st. Students engaged in research projects are strongly encouraged to participate.

## Career Opportunities

A graduate degree in the mathematical sciences will give you good preparation for a career in business, industry, government, teaching or research. Graduates of our programs are employed in the computer, communications, information, financial, and pharmaceutical industries; in engineering and consulting firms; in the insurance industry as actuaries; in schools, colleges, and universities; in goverment agencies; and in a wide variety of other occupations requiring strong analytical and problem solving abilities.

### Career Resources

- Career Information (American Mathematical Society)
- Mathematics Careers (Mathematical Association of America)
- Careers in Statistics (American Statistical Association)
- Careers in Applied Mathematics & Computational Sciences (Society for Industrial and Applied Mathematics)
- Society of Actuaries Career Center
- Jobs for Mathematicians (MathJobs.org)
- Occupational Outlook for Mathematicians (Bureau of Labor Statistics)
- Occupational Outlook for Statisticians (Bureau of Labor Statistics)

## Financial Support

All applicants to the Mathematics graduate program are considered for Graduate Teaching Fellowships and Graduate Research Fellowships. The department typically supports a total of 15 GTF's, while individual grants in the department support 5-10 GRF's. These 20-25 positions are distributed among the new and continuing M.S. and Ph.D candidates. Admission to the PhD. program generally carries with it a commitment of the department's financial and human resources sufficient to support the timely completion of the degree.

Below are some links to potential summer funding sources for graduate students.

### On-campus funding sources

*(Note: campus jobs are open to both international and domestic students.)*

### Institutional Funds:

Awarded by the UVM through the Graduate College (may be limited in scope)

### External Funding Sources (Competitive):

• NASA Graduate Student Support*Explore STEM Resources for Colleges, Universities, Technical and Vocational Institutions | NASA*

• National Research Council and Other Funding Opportunities*Fellowships Office (nationalacademies.org)*

• STEM Opportunities for Women and Minorities*Women & Minorities in STEM | OnlineColleges.net*

### Other Searchable Databases:

• InfoEd SPIN Database

• UCLA Graduate Education – Funding Database

• University of Illinois – Graduate College Fellowship Finder

• Zintellect.co

## Housing

While there is some on-campus housing for graduate students, most graduate students live off-campus in shared housing or in apartments.

### Housing Resources

- Office of Student and Community Relations (off-campus housing service)
- Department of Residential Life (on-campus housing)

## Graduate Student Research

From the very beginning of his or her entrance into the PhD program, each student is matched with a faculty advisor possessing expertise in the specific area of interest. The student and advisor then work closely together to select a suitable thesis topic. The advisor makes sure that the student gains the necessary background and the tools to conduct original research on this topic. This process may include independent study courses, seminars and informal discussions involving a community of faculty and student researchers, participation in conferences, and research assistantship positions. Then with the advisor's support, the student completes a professional-quality research project.

Students working towards an MS degree also have the option of writing and defending a thesis in an area of interest. This takes the place of a standard oral examination in that area. Original discoveries are not required in this thesis, but faculty members and students have established that they certainly can happen, and make for a very rewarding experience for all parties involved.

## Graduate Student Funding Sources

### On-campus funding sources

*(Note: campus jobs are open to both international and domestic students.)*

### Institutional Funds

Awarded by the UVM through the Graduate College (may be limited in scope).

### External Funding Source (Competitive)

- NASA Graduate Student Support
*Explore STEM Resources for Colleges, Universities, Technical and Vocational Institutions | NASA* - National Research Council and Other Funding Opportunities
*Fellowships Office (nationalacademies.org)* - STEM Opportunities for Women and Minorities
*Women and Minorities in STEM | OnlineColleges.net*

### Other Searchable Databases

## Director of the Mathematics Graduate Program

Professor, Department of Mathematics and Statistics

gswarrin@uvm.eduAlgebraic Combinatorics, Mathematics of Gerrymandering.