20212022 Graduate Catalog
Mathematics Major, PhD


Designed to prepare students for industrial employment and for college and university teaching and research.
Concentrations (Optional)
Mathematical Biology
Campus Code
Knoxville Campus
Credit Hours Required
Minimum of 72 graduate credit hours beyond the Bachelor’s or
Minimum of 48 graduate credit hours beyond the Master’s
Required Courses
 These requirements must be completed no later than the start of the student’s seventh year (as a mathematics graduate student at UT).
 Demonstrate competency with a satisfactory performance on two diagnostic examinations in the areas of advanced calculus and linear algebra. (Additional requirements for GTAs can be found in the Mathematics Graduate Student Handbook.) The appropriate courses upon which the exams are based are the MATH 447 MATH 448 sequence and for linear algebra MATH 457 MATH 458 sequence or MATH 453 .
 Pass two written examinations each based on material from a course sequence in the following list:
 Take at least two different onesemester research seminars
 Pass an examination in the field of specialization after requirements in first three bullets 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.
 In addition to the two yearlong sequences chosen for the preliminary examinations, a student must take the following:
1. A 600level sequence outside the student’s area of specialization.
2. Six additional onesemester 500600 level mathematics courses, which must include:
 A one yearlong sequence in a third area (i.e., an area different from those represented in the two preliminary examinations); and
 At least one course in a fourth area (this fourth area must be distinct from the two preliminary exam areas but may coincide with the area of the sequence used to satisfy (1).
 Students must earn a grade of B (B minus) or better in each of these six courses.
 MATH 600 , 24 credit hours
NonCourse Requirements
 Pass an oral defense and complete a written dissertation.
Mathematical Biology Concentration
Designed to prepare students for industrial employment and for college and university teaching and research in which an emphasis on applications of mathematics to ecology and the biological sciences is desired.
Credit Hours Required
Minimum of 72 graduate credit hours beyond the Bachelor’s or
Minimum of 48 graduate credit hours beyond the Master’s
Required Courses
 These requirements must be completed no later than the start of the student’s seventh year (as a mathematics graduate student at UT).
 Demonstrate competency in advanced calculus and linear algebra by either a satisfactory performance on a diagnostic examination or by passing the appropriate 400level 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 MATH 457 MATH 458 sequence or MATH 453 .
 A student must pass written examinations on mathematical ecology (MATH 581MATH 582) and one of the following yearlong sequences –
 Take at least two different onesemester research seminars (MATH 519 , MATH 529 , MATH 539 , MATH 549 , MATH 559 , MATH 569 , MATH 579 , MATH 589 , MATH 619 , MATH 629 , MATH 639 , MATH 649 , MATH 659 , MATH 669 , MATH 679 , and MATH 689 )
 Pass an examination in the field of specialization after requirements in first three bullets 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 oneyear, 600level 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.
 In addition to the two yearlong sequences chosen for the preliminary examinations, a student must take the following:
1) a 600level sequence outside the student’s area of specialization;
2) Six additional onesemester 500600 level courses. Two of those courses may be from the area of biology (courses from the Department of Ecology and Evolutionary Biology, College of Veterinary Medicine or Public Health) approved by their advisor,
 These six courses must include:
a. A one yearlong mathematics sequence in a third area (i.e. an area different from those represented in the two preliminary examinations); and
b. At least one mathematics course in a fourth area (this fourth area must be distinct from the two preliminary exam areas, but may coincide with the area of the sequence used to satisfy (1).
 Students must earn a grade of B (B minus) or better in each of these six courses.
 MATH 600 , 24 credit hours
NonCourse Requirements
 Pass an oral defense and complete a written dissertation.
