# Graduate Program Details

### Masters Degree

##### The master of science is designed to prepare students for positions in business and industry. It also provides preparation for further graduate study leading to a doctoral degree.

#### REQUIREMENTS FOR DEGREE — THESIS PROGRAM

**Credit hours**(30): Minimum 24 coursework hours in approved graduate proposed graduate mathematics*with a grade of C+ or better in each*, and six thesis hours (Math 699R). Three of the course hours must be from one of three areas of Applied Mathematics, Analysis, or Algebra, and another three course hours must be from one of the remaining two areas. With the approval of the graduate coordinator, graduate-level courses in other departments can be used toward the coursework hours.**Examination:**The examination requirement in the thesis program may be met by way of coursework, or by way of the written examination as explained below, in two of three broadly defined areas of Applied Mathematics, Analysis, and Algebra, by the end of year two. Failure by a master’s student to meet the examination requirement by the end of year two will result in the discontinuation of financial support for that master’s student at the end of year two.Continuing master’s students have the option of meeting the examination requirement under the current or new system.

**Coursework,**To meet the examination requirement by way of coursework, a master’s student will need to earn an A- or better in two courses, or their equivalents at another institution, with one course in one of the three areas and another course in one of the remaining two areas. Courses in the area of Applied Mathematics include, but are not limited to, Math 510, Math 511 , Math 521 , Math 522 , Math 611, and Math 636 . Courses in the area of Analysis included but are not limited to Math 532 , Math 540 , Math 541 , Math 565 , Math 641 , and Math 655 . Courses in the area of Algebra include but are not limited to Math 561 , Math 571 , Math 572 , Math 586 , Math 656 , and Math 676 . A graduate course, or its equivalent at another institution, can only be used to count towards one of the three areas. For example, Math 636 (Probability 1) is both Applied Mathematics and Analysis, but it can only be counted for one of these two areas. The Graduate Committee will maintain a list of associations of graduate courses with the three areas. - A master’s student may meet the examination requirement by way of graduate coursework completed as an undergraduate.
**Written Examination.**To meet the examination requirement by way of written examination, a master’s student will need to pass written examinations in two of the three areas. The written examinations will be based on published syllabi associated with the basic courses listed below. If a master’s student has earned an A- or better in one course associated with one of the three areas, but not in another course in another area, the master’s student need only pass one written examination in an area not met by coursework. Written examinations will be offered in August/September, January, and May.1. Applied Mathematics: Math 521

and Math 522

2. Analysis: Math 540and Math 541

3. Algebra: Math 571and Math 572 - The Graduate Committee may change the basic courses associated with any of the three areas, but there will always be two basic courses associated with each of the three areas. No written examinations are available for other courses.

- A master’s student may meet the examination requirement by way of graduate coursework completed as an undergraduate.
**Graduate Program of Study:**Students are required to submit a program of study before the end of the third week of their second semester. The university now uses the GRADPROG system for recording programs of study and other information having to do with a student’s graduate program. Instructions for using GRADPROG may be found at https://math.byu.edu/wp-content/uploads/2020/07/GradProgInstructions.pdf**Thesis****Oral Defense of thesis**

#### REQUIREMENTS FOR DEGREE — NON-THESIS PROGRAM

**Credit hours**(32): Minimum 30 coursework hours in approved graduate proposed graduate mathematics*with a grade of C+ or better in each*, and two hours for the project (Math 698R). Three of the course hours must be from one of three areas of Applied Mathematics, Analysis, or Algebra, and another three course hours must be from one of the remaining two areas. With the approval of the graduate coordinator, graduate-level courses in other departments can be used toward credit hours.**Examination:**The examination requirement in the thesis program may be met by way of coursework, or by way of the written examination as explained below, in two of three broadly defined areas of Applied Mathematics, Analysis, and Algebra, by the end of year two. Failure by a master’s student to meet the examination requirement by the end of year two will result in the discontinuation of financial support for that master’s student at the end of year two.Continuing master’s students have the option of meeting the examination requirement under the current or new system.

**Coursework,**To meet the examination requirement by way of coursework, a master’s student will need to earn an A- or better in two courses, or their equivalents at another institution, with one course in one of the three areas and another course in one of the remaining two areas. Courses in the area of Applied Mathematics include, but are not limited to, Math 510, Math 511 , Math 521 , Math 522 , Math 611, and Math 636 . Courses in the area of Analysis included but are not limited to Math 532 , Math 540 , Math 541 , Math 565 , Math 641 , and Math 655 . Courses in the area of Algebra include but are not limited to Math 561 , Math 571 , Math 572 , Math 586 , Math 656 , and Math 676 . A graduate course, or its equivalent at another institution, can only be used to count towards one of the three areas. For example, Math 636 (Probability 1) is both Applied Mathematics and Analysis, but it can only be counted for one of these two areas. The Graduate Committee will maintain a list of associations of graduate courses with the three areas. A master’s student may meet the examination requirement by way of graduate coursework completed as an undergraduate.

**Written Examination.**To meet the examination requirement by way of written examination, a master’s student will need to pass written examinations in two of the three areas. The written examinations will be based on published syllabi associated with the basic courses listed below. If a Master’s student has earned an A- or better in one course associated with one of the three areas, but not in another course in another area, the master’s student need only pass one written examination in an area not met by coursework. Written examinations will be offered in August/September, January, and May.- Applied Mathematics: Math 521
and Math 522 - Analysis: Math 540
and Math 541 - Algebra: Math 571
and Math 572

The Graduate Committee may change the basic courses associated with any of the three areas, but there will always be two basic courses associated with each of the three areas. No written examinations are available for other courses.

- Applied Mathematics: Math 521
**Graduate Program of Study**

Students are required to submit a program of study before the end of the third week of their second semester. The university now uses the GRADPROG system for recording programs of study and other information having to do with a student’s graduate program. Instructions for using GRADPROG may be found at https://math.byu.edu/wp-content/uploads/2020/07/GradProgInstructions.pdf**Project and presentation:**Write a paper about the project (Math 698R) which should focus on an area of advanced mathematics and present a 45-minute talk based on the paper.

## PhD Degree

### The doctoral program prepares students for a career in research and teaching at the university level or in basic research in a non-academic setting.

#### REQUIREMENTS FOR DEGREE

**Credit Hours**(54): Minimum 36 coursework hours in mathematics courses numbered 600 or above with a grade of B or better in each plus 18 dissertation hours (Math 799R).**Required Courses**: Complete at least 3 hours each in algebra, analysis, applied mathematics, and geometry/topology.-
**Examinations**:**Written Examinations**: At the beginning of the second year after admission to the PhD program, the student is required to pass examinations in three of the four areas of algebra, analysis, applied mathematics, and geometry/topology. Four hours are allotted to each examination. A failed examination may be repeated once at the beginning of the winter semester of the student’s second year, after which permission must be obtained from the department graduate committee to retake the examination. Passed examinations need not be repeated. Syllabi are available for each examination.**Oral Examination**: A student must pass an oral qualifying examination covering the background necessary for research in a specific area. The student, having chosen a research area and having a dissertation advisor approved, will, with the advisor, outline suitable examination topics. These topics must be approved by an examination committee of three (including the advisor) appointed by the department graduate committee, which conducts the examination.

**Graduate Program of Study:**Doctoral students should submit their programs of study during the first year, and in no case later than the third week of the beginning of the second year of study. A doctoral committee must consist of a chair and at least four members The university now uses the GRADPROG system for recording programs of study and other information having to do with a student’s graduate program. Instructions for using GRADPROG may be found at https://math.byu.edu/wp-content/uploads/2020/07/GradProgInstructions.pdf**Defense of Dissertation**: A final oral defense of the dissertation is conducted by a faculty committee consisting of the student’s research advisor, two other readers of the dissertation (one of whom may be an outside examiner), and two other members of the faculty.**Dissertation**