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Doctor of Philosophy in

Program of Study


You will begin specializing and focusing your educational path soon after entering the PhD program. Your dissertation advisor will help you set and reach applied research goals throughout your time in the courses. The university has research groups in algebra, combinatorics and number theory, analysis, geometry and topology, and probability and statistics.

Emerge from the PhD program with in-depth knowledge of your specified topic of interest, the communication skills to express that information and the ability to comprehend a second language in writing.

Credit Requirement

A minimum of 60 graduate credits in mathematics as approved by the advisor.

Breadth Requirement

Show proficiency in four of five areas: algebra, topology, complex analysis, real analysis, or probability and statistics. You are required to successfully pass written preliminary examinations in three areas and satisfactorily finish one breadth sequence in an additional fourth area. Breadth Sequence: Two semester sequence in an area complementary to your choice of preliminary exams areas.

  • Foundations of Analysis & Real Analysis
  • Advanced Linear Algebra & Algebra I
  • Topology I & Topology II
  • Complex Analysis I & Complex Analysis II
  • Introduction to Theory of Statistics & Introduction to Theory of Statistics II

Successful Completion of the Oral Qualifying Examination

Within a month of completion of all the breadth requirements, you will select a faculty member as your dissertation advisor and the area of specialty for your dissertation. Within two semesters you will take a qualifying oral exam to test your readiness to begin work on a dissertation.

Completion of a Research Tool

Display a reading knowledge of French, German, Russian, or another foreign language appropriate to your area of specialization and approved by the department. You will take a departmental examination before the oral qualifying examination.

Full Time Study in Residence

You will be engaged in full-time study beyond the master's degree or equivalent at the University in at least two sessions after admission to the advanced program. You must:
a. be registered for 12 credits per semester, or
b. hold a full assistantship and (i) complete one academic year in such a position, (ii) be registered for a minimum of 9 credits per term, and (iii) satisfactory completion of assigned duties.

Continuous Registration of Doctoral Students

You must maintain continuous registration for each fall and spring session until you have completed all program requirements. Minimum registration consists of 3 credits of approved course work or registration for dissertation load.

Doctoral Dissertation

You must be registered for Doctoral Dissertation during the semester in which the degree is conferred. The dissertation is based on your independent research and should constitute a significant original contribution to mathematics or statistics.

Ancillary Duties

In addition to the completion of course requirements, you are required to engage in some ancillary teaching, research, or practicum duties contributing to the academic development.

Additional Information

See the Graduate Bulletin for details.

For more information, contact Marco Varisco at [email protected].

Career Outcomes

The doctoral program in mathematics at UAlbany will prepare you for analysis and problem-solving in business or government, or for research and teaching at the university level.

Whether you choose to share your knowledge with the next generation of advanced mathematics students or commit to further developing your own theorems, career outcomes uniquely suited to math PhD graduates include:

  • College mathematics professor
  • Research mathematician
  • AI and machine learning consultant
  • Investment researcher
  • Insurance actuary
  • Statistician
  • Software engineer



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International Students

This degree is designated as a STEM program. International students maintaining F-1 status are allowed to apply for up to 12 months of post-completion Optional Practical Training (OPT) following completion/graduation from their degree program. Currently, this degree program is also designated by the Department of Homeland Security (DHS) as an eligible degree for the F-1 STEM OPT work authorization extension; students who secure qualifying employment may be eligible to apply for the STEM OPT extension for a cumulative total of up to 36 months of F-1 OPT work authorization.

Admissions Requirements

Departmental Assistantship Consideration

  • Fall: February 1
  • Spring: January 1
  • Summer: Not Available

 No Departmental Assistantship Consideration

  • Fall: August 1
  • Spring: January 1
  • Summer: May 1
Required Application Materials
  • Transcripts all schools attended
  • Three letters of recommendation
  • Official GRE test scores*
  • Statement of goals

*The GRE will be waived as a requirement for admission through Fall 2024.

The statement is generally one to two pages discussing what you have to offer the program and what you wish to get out of the program.  It should include a brief description of the applicant's field of interest, related background, desired area of study and research emphasis or career goals. 

Student Learning Objectives

Learning objectives that UAlbany students are expected to attain through their course of study within their academic program.

  • Gain a deep understanding of fundamental theorems and their proofs in different areas of mathematics.
  • Use the knowledge of fundamental theorems and theories in reconstructing mathematical arguments.
  • Apply the technique and logic arguments in solving questions, with effective and logical writing.
  • Develop working knowledge of the background, feature, and recent advances of one chose area of mathematics.