Mathematics (Ph.D.)

Mathematics (Ph.D.)

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Why get a Ph.D. in pure mathematics?

The doctoral degree in pure mathematics represents broad study in the fields of analysis, algebra or topology, culminating with a focused dissertation containing publishable results. The degree is the gateway to an academic career in which one can continue to investigate and contribute to modern mathematics at the highest level. A professor of mathematics can look forward to a fruitful and rewarding career of teaching, advising and scholarship. Many of our graduates have gone on to careers at colleges in the region. Others have continued with postdoctoral studies, or have found careers in industry, including software development and actuarial work.  

Why choose UNH’s program in pure mathematics?

Our doctoral program is small enough to offer significant communication between faculty mentors and student peers, yet the department is large enough to offer various specialties, including representation theory, operator theory and algebraic topology. After completion of basic coursework, you’ll broaden your studies through participation in seminars, independent study and reading courses. The program includes a required Ph. D. minor project, allowing you to investigate the fields of statistics, integrated applied mathematics and mathematics education, as well as the Ph. D. major requirement. Enjoy an attractive and convenient location in a small college town, yet with easy access to Boston.

Potential Careers

  • Academia
  • Education
  • Industry


Request Information

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  • Ph.D. Student Aims to Deepen our Understanding of Mathematical Structures
    Sukitha Adappa is a Ph.D. student studying pure mathematics with a focus in operator theory. Adappa was raised in Sri Lanka and graduated from the University of Peradeniya with a Bachelor of Science in mathematics. 1. Why did you choose UNH for your graduate program?   I chose UNH for my graduate...
    Ph.D. Student Aims to Deepen our Understanding of Mathematical Structures
    Sukitha Adappa is a Ph.D. student studying pure mathematics with a focus in operator theory. Adappa was raised in Sri Lanka and graduated from the University of Peradeniya with a Bachelor of Science in mathematics. 1. Why did you choose UNH for your graduate program?   I chose UNH for my graduate...

Curriculum & Requirements

The Mathematics Ph.D. program provides research opportunities in core mathematics, including operator algebras, algebra, algebraic topology, analysis and complex analysis.

Admission Requirement

Applicants for the M.S. and Ph.D. degrees must have completed significant undergraduate coursework in mathematics, preferably in algebra, analysis, and topology.


Please visit the Graduate School website for detailed instructions about applying to the program.

Students are advanced to candidacy after meeting the following requirements:

Required Courses
MATH 951Algebra I3
MATH 952Algebra II3
MATH 953Analysis I3
MATH 954Analysis II3
MATH 955Topology I3
Total Credits15

Mathematics Ph.D. students must pass written comprehensive examinations in algebra, analysis, topology and an elective subject. Elective subjects include functional analysis, algebraic topology, applied mathematics, statistics, advanced algebra, advanced complex analysis, advanced mathematics education, et al.

Advanced coursework in a minor field (usually within mathematics, but possibly in another area of the mathematical sciences), and a major field (that of the student's intended dissertation work) followed by successfully completion of oral examinations in their minor and major areas.

Experience in teaching equivalent to at least half-time for one year.


Students must complete and submit a dissertation that includes original results in mathematics.

  • Students possess doctoral-level competence in the three primary areas of topology, algebra and analysis.
  • Students possess specific and specialized breadth, beyond basic doctoral-level competence and in addition to the area of their dissertation research.
  • With appropriate guidance from faculty member, students produce a research plan and implement it to obtain original results in mathematics suitable for publication.
  • Students possess experience in and instructor-of-record responsibility for university-level mathematics instruction through teaching carried out while in the program.


Applications must be completed by the following deadlines in order to be reviewed for admission:

  • Fall: Feb. 15 (for funding); April 1 (recommended US; final international); July 1 (final)
  • Spring: Dec. 1, Nov. 1 for international students
  • Summer: N/A
  • Special: N/A

Application fee: $65

Campus: Durham

New England Regional: ME

Accelerated Masters Eligible: No

New Hampshire Residents

Students claiming in-state residency must also submit a Proof of Residence Form. This form is not required to complete your application, but you will need to submit it after you are offered admission or you will not be able to register for classes.


If you attended UNH or Granite State College (GSC) after September 1, 1991, and have indicated so on your online application, we will retrieve your transcript internally; this includes UNH-Durham, UNH-Manchester, UNH Non-Degree work and GSC. 

If you did not attend UNH, or attended prior to September 1, 1991, then you must upload a copy (PDF) of your transcript in the application form. International transcripts must be translated into English.

If admitted, you must then request an official transcript be sent directly to our office from the Registrar's Office of each college/university attended. We accept transcripts both electronically and in hard copy:

  • Electronic Transcripts: Please have your institution send the transcript directly to Please note that we can only accept copies sent directly from the institution.
  • Paper Transcripts: Please send hard copies of transcripts to: UNH Graduate School, Thompson Hall- 105 Main Street, Durham, NH 03824. You may request transcripts be sent to us directly from the institution or you may send them yourself as long as they remain sealed in the original university envelope.

Transcripts from all previous post-secondary institutions must be submitted and applicants must disclose any previous academic or disciplinary sanctions that resulted in their temporary or permanent separation from a previous post-secondary institution. If it is found that previous academic or disciplinary separations were not disclosed, applicants may face denial and admitted students may face dismissal from their academic program.

Letters of recommendation: 3 required

Recommendation letters submitted by relatives or friends, as well as letters older than one year, will not be accepted.

Personal Statement/Essay Questions

Prepare a brief but careful statement regarding:

  1. Reasons you wish to do graduate work in this field, including your immediate and long-range objectives.
  2. Your specific research or professional interest and experiences in this field.

Important Notes

All applicants are encouraged to contact programs directly to discuss program-specific application questions.

International Applicants

Prospective international students are required to submit TOEFL, IELTS, or equivalent examination scores. English Language Exams may be waived if English is your first language. If you wish to request a waiver, then please visit our Test Scores webpage for more information.

Inquire with the Department about Research Interests

As part of your application process, we recommend touching base with the academic department or specific faculty about your research interests, fit with the department, and available space. You can Submit an Extended Inquiry and we will inform your desired academic program about your interest. By submitting an inquiry form, you are not guaranteed to hear back from specific faculty. This can be a helpful step before going through the full application process.

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