Program Overview

Doctor of Philosophy in Mathematics

Program Overview

The Doctor of Philosophy in Mathematics program at the University at Albany is designed to prepare students for a career as a mathematics research scholar. The program focuses on advanced research and teaching, with a strong emphasis on independent study and original research.

Program of Study

• 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. Students 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 the student's 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, students will select a faculty member as their dissertation advisor and the area of specialty for their dissertation. Within two semesters, students will take a qualifying oral exam to test their 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 the student's area of specialization and approved by the department. Students will take a departmental examination before the oral qualifying examination.
• Full-Time Study in Residence: Students 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.
• Continuous Registration of Doctoral Students: Students must maintain continuous registration for each fall and spring session until they have completed all program requirements. Minimum registration consists of 3 credits of approved course work or registration for dissertation load.
• Doctoral Dissertation: Students must be registered for Doctoral Dissertation during the semester in which the degree is conferred. The dissertation is based on the student's independent research and should constitute a significant original contribution to mathematics or statistics.
• Ancillary Duties: In addition to the completion of course requirements, students are required to engage in some ancillary teaching, research, or practicum duties contributing to the academic development.

Career Outcomes

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

Admissions Requirements

• Deadlines:
  • 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 from all schools attended
  • Three letters of recommendation
  • Statement of goals (one to two pages discussing what the applicant has to offer the program and what they wish to get out of the program)

Student Learning Objectives

• 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 chosen area of mathematics.

Supplemental Degree Programs

Graduate students can typically request a supplemental degree in one or more subordinate degrees without needing to go through the full admissions process again. Supplemental programs available with this degree include:

• Africana Studies CGS
• Community College Leadership CGS
• Data Science MS
• Demography CGS
• International Education Management CGS
• Machine Learning CGS
• Mathematics MA
• Topological Data Analysis CGS