
20202021 Graduate Catalog [ARCHIVED CATALOG]
Mathematics Major, PhD


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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.
 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 written examinations (second bullet), a student must take six other onesemester 500600 level courses. At least five of these courses must be chosen from the following list grouped by examination area –
 Algebra (MATH 551 MATH 552 , MATH 555 MATH 556 ),
 Analysis (MATH 545 MATH 546 , MATH 545 MATH 547 ),
 Computational and Applied Mathematics (MATH 571 MATH 572 , MATH 574 , MATH 577 , MATH 578 ),
 Differential Equations (MATH 513 , MATH 515 MATH 516 , MATH 531 MATH 532 , MATH 535 MATH 536 , MATH 537 , MATH 581 MATH 582 , MATH 585 )
 Stochastics (MATH 521 MATH 522 , MATH 523 MATH 524 , MATH 525 MATH 526 ), and
 TopologyGeometry (MATH 561 MATH 562 , MATH 567 MATH 568 )
 The sixth course may be either a 500level course listed above or a 600level mathematics course not used to satisfy the fifth bullet.
 These six courses must contain a yearlong sequence in an area different from the two written examinations and the remaining courses must contain a course representing a fourth area.
 A grade of B or better is required in each of the 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 –
 Analysis (MATH 545 MATH 546 ),
 Computational and Applied Mathematics (MATH 571 MATH 572 ),
 Differential Equations (MATH 535 MATH 536 ),
 Stochastics (MATH 523 MATH 524 ), and
 TopologyGeometry (MATH 561 MATH 562 )
 A student must pass one examination by the middle of their third year and both examinations by the middle of their fourth year. A student cannot take any examinations after four failures.
 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 written examinations (second bullet), a student must take six other onesemester 500600 level courses.
 At least five of these courses must be chosen from the following list grouped by examination area –
 Analysis (MATH 545 MATH 546 , MATH 545 MATH 547 ),
 Computational and Applied Mathematics (MATH 571 MATH 572 , MATH 574 , MATH 577 , MATH 578 ),
 Differential Equations (MATH 513 , MATH 515 MATH 516 , MATH 531 MATH 532 , MATH 535 MATH 536 , MATH 537 , MATH 581 MATH 582 , MATH 585 )
 Stochastics (MATH 521 MATH 522 , MATH 523 MATH 524 , MATH 525 MATH 526 ), and
 Mathematical Ecology/Evolution (MATH 583 , EEB 509 , EEB 511 )
 The sixth course may be either a 500level course listed above or a 600level mathematics course not used to satisfy the fifth bullet.
 These six courses must contain a yearlong sequence in an area different from the two written examinations and at least two areas different from the two written examinations.
 A grade of B or better is required in each of the six courses.
 MATH 600 , 24 credit hours
NonCourse Requirements
 Pass an oral defense and complete a written dissertation


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