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Physical and Mathematical Sciences
Math

Graduate Program Details

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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.‌

    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 540 and Math 541
    3. 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.

  • 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 here https://gradprogress.sim.byu.edu/gradProgressGuide.pdf
  • Thesis: Each student in the program is required to write a thesis (or project) on a mathematical topic at a level well beyond what they encounter in the classroom. The master’s thesis (or project) usually includes an introductory chapter that is a comprehensive survey of the literature on the student’s research topic. Upon completion of the thesis (or project) and before graduation, the student is required to give an oral presentation of his work. The department tracks student publications in professional journals and student presentations in professional meetings.
  • Oral Defense of thesis: Defenses must be scheduled AT LEAST one week before the date of the defense. Students will not be permitted to defend their theses until their faculty advisors have approved their work. To schedule the final oral exam, use the new GRADPROG system (https://gradprogress.sim.byu.edu/).

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.‌‌

  • 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 540 and Math 541
    3. 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.

  • 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://gradprogress.sim.byu.edu/gradProgressGuide.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.

Integrated BS/MS in Mathematics

The department also offers an integrated program in which students earn the BS and MS degree together at the end of 5 years. The program is designed for exceptional students who expect to have taken 4 or more graduate courses that are not needed for their undergraduate degree requirements by the end of their fourth year. This is not a one-year master's program. Applications are due by January 15 of a student's junior year. Interested students should contact the Graduate Coordinator to make an appointment to discuss their suitability for the program and the application process. The program is small; typically only 2--3 students will be accepted into the program per year.

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 (Math 521, 522, 540, 541, 571, 572 may be substituted) with a grade of B or better in each plus 18 dissertation hours (Math 799R). More than nine credit hours of Math 695R being counted towards the coursework hours requires approval of the graduate coordinator. Graduate-level courses in other departments can be counted toward the coursework hours with the approval of the graduate coordinator.
  • Required Courses: Complete six credit hours in one of these three areas: applied mathematics, analysis, and algebra, and complete six credit hours in one of the remaining two areas.
  • Examination Requirement: The examination requirement ensures that PhD students have acquired a sufficient level of mathematical mastery to undertake high-level research. The examination requirement can be met by way of coursework or by way of 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 of a PhD student to meet the examination requirement by the end of year two will result in the discontinuation of funding at the end of year two.

  • Coursework. To meet the examination requirement by way of coursework, a PhD student will need to earn an A- or better in four courses, or their equivalents at another institution, with two of the four courses in one of the three areas and two courses 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 include 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.

    • Written Examinations: To meet the examination requirement by way of written examination. a PhD student will need to pass written examinations in two of the three areas. The written examinations will be based on published syllabi asociated to the basic courses listed below. If a PhD student has earned an A- or better in two courses associated to one of the three areas, but not in another area, the PhD 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 540 and Math 541
      3. Algebra: math 571 and 572

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

  • Prospectus: The Prospectus for a Ph.D. student is a 30-50 minute oral presentation held before the Ph.D. student’s committee (virtual or in-person) as well as an extended abstract or brief description (2-3 pages will suffice). There should be time during and/or after the presentation for the committee to ask the Ph.D. student questions about the oral presentation. The Advisor should work closely with the Ph.D. student before-hand to ensure a well-prepared oral presentation.

    The oral presentation is to be held after the Ph.D. student has fulfilled the Ph.D. Qualifying Exam requirement but no later than the end of the first semester of the third year in the Ph.D. program. The purpose of the oral presentation is to outline the objective(s) of the Dissertation, the background and history associated with the objective(s), and the proposed approaches and/or techniques that may be used in obtaining the main results. This will also ensure that the student has adequate support from their advisor and committee.

    With approval from the graduate coordinator and in accordance with the desires of the dissertation committee, the student may be given a second chance to complete the prospectus requirement within 2 months of the initial attempt. Approval of the Prospectus by the committee is required for the Ph.D. student to continue in good standing in the graduate program.

  • 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://gradprogress.sim.byu.edu/gradProgressGuide.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.