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PhD - Doctor of Philosophy in Mathematics University of California, Santa Barbara



Course info


The Department of Mathematics takes seriously three aspects of mathematics within its graduate training: 1) Applied Mathematics: mathematicians help directly in the solution of problems which arise in other areas of human endeavor, 2) Mathematical Education: training others how to develop solutions on their own, and 3) Pure Mathematics: they expand the reach and clarify the understanding of mathematical thought itself.

Program Learning Outcomes

Students graduating with a PhD in Mathematics should be able to:

Core Knowledge

  • Demonstrate a mastery in three of the four core areas of Mathematics: Algebra, Analysis, Applied, Geometry/Topology, to a level commensurate with current standards in mathematics.
  • Demonstrate mastery of advanced Mathematics within their chosen subfield and demonstrate a breadth of knowledge in contiguous subfields.
  • Demonstrate fluency in comprehension of current methods and problems in the chosen subfield.

Research Methods and Analysis

  • Conduct primary research literature searches in their chosen subfield.
  • Formulate and prove pure mathematical or applied methods to make progress in expanding the frontiers of mathematical knowledge.
  • Students will be able to plan and execute an original research project, analyze relevant findings, and organize results into a coherent argument.


  • Communicate mathematical material to audiences ranging from general to specialized.
  • Present their research effectively through oral presentations and through the development of supporting materials as appropriate.
  • Possess classroom management skills, techniques for effective lecturing, and methods for guiding and assessing undergraduate students.

Scholarly Communication

Communicate effectively the results of their research to professionals within their subfield, and within the broader mathematics community, through both oral presentation and written work.

Independent Research

Complete an original, creative project that demonstrably advances human knowledge within their subfield.

Course options

Here are the different ways in which you can study PhD - Doctor of Philosophy in Mathematics.

Full Time (4 years to advance to candidacy, 6 years to complete the Ph.D)

Tuition fees

$15,102.00 (11,06,968) per year


26 Sep, 01 Oct


College of Letters and Science

2217 Cheadle Hall, MC 2080,

University of California, Santa Barbara,



93106, United States

Entry requirement for international students

To be considered for admission to UCSB, applicants must have received a bachelor’s degree or its equivalent (with a cumulative grade point average of 3.0 or better) from an accredited university prior to the quarter for which admission is sought.

TOEFL scores 550 Paper-Based Test (PBT), 80 Internet-Based Test (IBT) or IELTS (International English Language Testing System) Overall Band score of 7 or higher (if applicable).

* Please check with your chosen school for the exact entry requirements for your programme.

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