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.

These requirements must be completed no later than the start of the student’s seventh year (as a mathematics graduate student at UT).

A student must pass written examinations on two of the following year-long sequences – algebra (MATH 551 -MATH 552 ), 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 topology-geometry (MATH 561 -MATH 562 ). A student must pass one examination by the middle of his/her third year and both examinations by the middle of his/her fourth year. A student may not take any examinations after four failures.

In addition to the two year-long sequences chosen for the written examinations, a student must take six other one-semester 500-600 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 576 , MATH 577 , MATH 578 ), differential equations (MATH 513 -MATH 514 , MATH 515 -MATH 516 , MATH 531 -MATH 532 , MATH 535 -MATH 536 , MATH 537 -MATH 538 , MATH 581 -MATH 582 , MATH 585 ), stochastics (MATH 521 -MATH 522 , MATH 523 -MATH 524 , MATH 525 -MATH 526 ), and topology-geometry (MATH 561 -MATH 562 , MATH 567 -MATH 568 ). The sixth course may be either a 500-level course listed above or a 600-level mathematics course not used to satisfy bullet #5. These six courses must contain a year-long 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.

A student must pass written examinations on mathematical ecology (MATH 581 -MATH 582 ) and one of the following year-long sequences – analysis (MATH 545 -MATH 546 ), computational and applied mathematics (MATH 571 -MATH 572 ), differential equations (MATH 535 -MATH 536 ), and stochastics (MATH 523 -MATH 524 ). A student must pass one examination by the middle of his/her third year and both examinations by the middle of his/her fourth year. A student cannot take any examinations after four failures.

In addition to the two year-long sequences chosen for the written examinations, a student must take six other one-semester 500-600-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 576 , MATH 577 , MATH 578 ), differential equations (MATH 513 -MATH 514 , MATH 515 -MATH 516 , MATH 531 -MATH 532 , MATH 535 -MATH 536 , MATH 537 -MATH 538 , MATH 585 ), stochastics (MATH 521 -MATH 522 , MATH 523 -MATH 524 , MATH 525 -MATH 526 , MATH 527 ), and mathematical ecology/evolution (MATH 583 , EEB 509 , EEB 511 ). The sixth course may be either a 500-level course listed above or a 600-level mathematics course not used to satisfy bullet #5.

These six courses must contain a year-long 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.