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Mathematics, Ph.D.

  • Application Deadline
  • 72 months
University rank #201 (ARWU) Knoxville, TN, United States
A student must pass written examinations on two of the following year-long sequences – algebra , analysis, computational and applied mathematics, differential equations, stochastics , and topology-geometry.
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For the PhD program in mathematics, the student must meet the following five requirements in addition to those of the Graduate Council.

  • Demonstrate competency in advanced calculus and linear algebra by either a satisfactory performance on a diagnostic examination or by passing the appropriate 400-level course with a grade of B or better by the end of the student’s first year of graduate school. The appropriate course for advanced calculus is the MATH 447-MATH 448 sequence and for linear algebra is the MATH 457-MATH 458 sequence or MATH 453. 
  • Satisfy either the standard program or the interdisciplinary mathematical ecology/evolution concentration. A student intending to work in mathematical ecology/evolution may complete either but is encouraged to complete the interdisciplinary mathematical ecology/evolution concentration. 
  • Take at least two different one-semester research seminars and MATH 599. 
  • Pass an examination in the field of specialization after requirements in bullets 1-3 have been met. This examination will be given by a committee appointed by the department head. A student may take this specialty examination no more than two times. 
  • Pass a one-year, 600-level sequence in mathematics outside the student’s area of specialization. The sequence selected to fulfill this requirement must be approved by the department head and the student’s doctoral committee.

Detailed Programme Facts

  • Programme intensity Full-time
    • Full-time duration 72 months
  • Credits
    72 alternative credits
  • Languages
    • English
  • Delivery mode
    On Campus

Programme Structure

Courses include:

  • Honors: Analysis
  • Honors: Abstract Algebra
  • Matrix Algebra
  • Seminar in Mathematical Presentations
  • Modern Algebra
  • Real Analysis
  • Numerical Mathematics 
  • Partial Differential Equations
  • Probability
  • Topology

English Language Requirements

  • Minimum required score:


    The IELTS – or the International English Language Test System – tests your English-language abilities (writing, listening, speaking, and reading) on a scale of 1.00–9.00. The minimum IELTS score requirement refers to which Overall Band Score you received, which is your combined average score. Read more about IELTS.

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  • Minimum required score:


    The TOEFL iBT ® measures your English-language abilities in an academic setting. The test has four sections (reading, listening, speaking, and writing), each with a score range of 0-30, for a total score range of 0-120. Read more about TOEFL iBT ®.

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General Requirements

Admission requirements:

  • The completed online Graduate Application for Admission 
  • A non-refundable application fee 
  • One unofficial transcript from all colleges and universities attended submitted on-line at the time of application to the Graduate School
  • The submission of official transcripts and degree certificates
  • Departmental application
  • Reference letters or rating forms

Tuition Fee

  • International

    31538 USD/year
    Tuition Fee
    Based on the original amount of 31538 USD per year and a duration of 72 months.
  • National

    13120 USD/year
    Tuition Fee
    Based on the original amount of 13120 USD per year and a duration of 72 months.
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Living costs for Knoxville

  • 885 - 1460 USD/month
    Living Costs

The living costs include the total expenses per month, covering accommodation, public transportation, utilities (electricity, internet), books and groceries.


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