Jul 29, 2021  
2013-2014 Graduate Catalog 
    
2013-2014 Graduate Catalog ARCHIVED CATALOG: CONTENT MAY NOT BE CURRENT. USE THE DROP DOWN ABOVE TO ACCESS THE CURRENT CATALOG.

Doctor of Philosophy - Mathematical Sciences


Return to {$returnto_text} Return to: Graduate Plans

Plan Description


UNLV’s Mathematical Sciences Ph.D. program is Nevada’s only Ph.D. program in the Mathematical Sciences. It is relatively new (established in 2005) and includes concentrations in Applied Math, Pure Math, Computational Math, and Statistics to serve students in many different areas of Mathematical Sciences.

The main part of the Ph.D. is the dissertation. The degree requirements also include: credit requirement, qualifying examination requirement, subject area breadth requirement.

The qualifying examination requirement and the subject area breadth requirement are tailored according to the area of concentration.
 

Learning Outcomes  

www.unlv.edu/degree/phd-mathematical-sciences

Plan Admission Requirements


In addition to the requirements of the Graduate College, applicants must satisfy the admission requirements of the Department of Mathematical Sciences summarized as follows. Applicants seeking direct admission to the doctoral program without a previously earned master’s degree must have a minimum GPA of 3.00 for all undergraduate work or a minimum GPA of 3.25 for the last two years of undergraduate mathematics work. Applicants with a master’s degree must have a minimum GPA 3.00 for all graduate work and at least 15 credits of graduate course work in Mathematical Sciences with a grade of B or better. Applicants must submit the official score of the GRE General Test with a minimum score in the top 35% on the GRE quantitative.

To apply for admission to the Ph.D. Program, applicants must submit application materials to both the Graduate College and the Department of Mathematical Sciences.

Firstly, applicants must submit to the Graduate College the following materials:

  1. A completed application form.
  2. The official transcripts from all colleges and universities the student has attended.

Secondly, applicants must submit to the Department the following materials:

  1. Copies of all official transcripts sent to the Graduate College.
  2. At least three letters of recommendation from persons familiar with the applicant’s academic record and potential for advanced study in mathematical sciences.
  3. The official GRE General Test score
  4. A completed application for Graduate Assistantship, if interested.
  5. A statement of purpose describing the aim in applying for graduate study, the particular area of specialization within the mathematical sciences (if known), and any additional information that may aid the selection committee in evaluating preparation and aptitude for graduate study.

Details of the admission procedure for the Ph.D. Program can be found on the Department’s web site.

All domestic and international applicants must review and follow the Graduate College Admission and Registration Requirements.

Subplan 1 Requirements: Post-Bachelor’s - Applied Mathematics Track


Total Credits Required: 78

Course Requirements 

Required Courses Part 1– Credits: 6

Complete two analysis or two theory courses:

MAT 707 - Real Analysis I 

MAT 708 - Real Analysis II 

OR

MAT 709 - Complex Function Theory I 

MAT 710 - Complex Function Theory II 

Required Courses Part 2 – Credits: 6

MAT 771 - Applied Analysis I 

MAT 772 - Applied Analysis II 

Subject Area Courses – Credits: 12

Complete two of the following one-year course sequences:

MAT 703 - Abstract Algebra III 

MAT 704 - Abstract Algebra IV 

 

MAT 723 - Advanced Ordinary Differential Equations I 

MAT 724 - Advanced Ordinary Differential Equations II 

 

MAT 729 - Partial Differential Equations I 

MAT 730 - Partial Differential Equations II 

 

MAT 733 - Topology 

MAT 734 - Topology 

 

MAT 765 - Advanced Numerical Analysis 

MAT 766 - Advanced Numerical Analysis 

 

STA 767 - Mathematical Statistics I 

STA 768 - Mathematical Statistics II 

Additional Courses – Credits: 12

Complete 12 credits of 700-level MAT or STA courses (excluding MAT 711 & 712), or other advisor-approved courses.

Elective Courses – Credits: 24

Complete 24 credits of 600- or 700-level MAT or STA courses (excluding MAT 711 & 712), or other advisor-approved courses.

Dissertation – Credits: 18

MAT 799 - Dissertation 

Degree Requirements 

See Plan Degree Requirements below.

Graduation Requirements 

See Plan Graduation Requirements below.

Subplan 2 Requirements: Post-Bachelor’s - Computational Mathematics Track


Total Credits Required: 78

Course Requirements 

Required Courses Part 1 – Credits: 6

Complete two analysis or two theory courses:

MAT 707 - Real Analysis I 

MAT 708 - Real Analysis II 

OR

MAT 709 - Complex Function Theory I 

MAT 710 - Complex Function Theory II 

Required Courses Part 2 – Credits: 6

MAT 765 - Advanced Numerical Analysis 

MAT 766 - Advanced Numerical Analysis 

Subject Area Courses – Credits: 12

Complete two of the following one-year course sequences:

MAT 703 - Abstract Algebra III 

MAT 704 - Abstract Algebra IV 

 

MAT 723 - Advanced Ordinary Differential Equations I 

MAT 724 - Advanced Ordinary Differential Equations II 

 

MAT 729 - Partial Differential Equations I 

MAT 730 - Partial Differential Equations II 

 

MAT 733 - Topology 

MAT 734 - Topology 

 

MAT 771 - Applied Analysis I 

MAT 772 - Applied Analysis II 

 

STA 767 - Mathematical Statistics I 

STA 768 - Mathematical Statistics II 

Additional Courses – Credits: 12

Complete 12 credits of 700-level MAT or STA courses (excluding MAT 711 & 712), or other advisor-approved courses.

Elective Courses – Credits: 24

Complete 24 credits of 600- or 700-level MAT or STA courses (excluding MAT 711 & 712), or other advisor-approved courses.

Dissertation – Credits: 18

MAT 799 - Dissertation 

Degree Requirements 

See Plan Degree Requirements below.

Graduation Requirements 

See Plan Graduation Requirements below.

Subplan 3 Requirements: Post-Bachelor’s - Pure Mathematics Track


Total Credits Required: 78

Course Requirements 

Required Courses Part 1 – Credits: 6

Complete two analysis or two theory courses:

MAT 707 - Real Analysis I 

MAT 708 - Real Analysis II 

OR

MAT 709 - Complex Function Theory I 

MAT 710 - Complex Function Theory II 

Required Courses Part 2 – Credits: 6

MAT 703 - Abstract Algebra III 

MAT 704 - Abstract Algebra IV 

Subject Area Courses – Credits: 12

Complete two of the following one-year course sequences:

MAT 701 - Foundations of Mathematics III 

MAT 702 - Foundations of Mathematics IV 

 

MAT 717 - Analytical Solution Methods for Partial Differential Equations, I 

MAT 718 - Analytical Solution Methods for Partial Differential Equations, II 

 

MAT 723 - Advanced Ordinary Differential Equations I 

MAT 724 - Advanced Ordinary Differential Equations II 

 

MAT 733 - Topology 

MAT 734 - Topology 

 

MAT 771 - Applied Analysis I 

MAT 772 - Applied Analysis II 

 

STA 767 - Mathematical Statistics I 

STA 768 - Mathematical Statistics II 

Additional Courses – Credits: 12

Complete 12 credits of 700-level MAT or STA courses (excluding MAT 711 & 712), or other advisor-approved courses.

Elective Courses – Credits: 24

Complete 24 credits of 600- or 700-level MAT or STA courses (excluding MAT 711 & 712), or other advisor-approved courses.

Dissertation – Credits: 18

MAT 799 - Dissertation 

Degree Requirements 

See Plan Degree Requirements below.

Graduation Requirements 

See Plan Graduation Requirements below.

Subplan 4 Requirements: Post-Bachelor’s - Statistics Track


Total Credits Required: 78

Course Requirements 

Required Courses Part 1 – Credits: 6

STA 767 - Mathematical Statistics I 

STA 768 - Mathematical Statistics II 

Required Courses Part 2 – Credits: 6

STA 761 - Regression Analysis I 

STA 762 - Regression Analysis II 

Subject Area Courses – Credits: 12

Complete two of the following one-year course sequences:

STA 713 - Experimental Design 

STA 715 - Multivariate Statistical Methods 

 

STA 750 - Time Series Analysis 

STA 751 - Spatial Statistics 

 

STA 755 - Stochastic Modeling I 

STA 756 - Stochastic Modeling II 

 

STA 753 - Bayesian Data Analysis 

STA 765 - Statistical Decision Theory 

 

STA 763 - Analysis of Variance I 

STA 764 - Analysis of Variance II 

 

MAT 707 - Real Analysis I 

STA 731 - Probability Theory and Its Applications 

Additional Courses – Credits: 12

Complete 12 credits of 700-level MAT or STA courses (excluding MAT 711 & 712), or other advisor-approved courses.

Elective Courses – Credits: 24

Complete 24 credits of 600- or 700-level MAT or STA courses (excluding MAT 711 & 712), or other advisor-approved courses.

Dissertation – Credits: 18

STA 799 - Dissertation 

Degree Requirements 

See Plan Degree Requirements below.

Graduation Requirements 

See Plan Graduation Requirements below.

Subplan 5 Requirements: Post-Master’s - Applied Mathematics Track


Credits Required: 48

Course Requirements 

Required Courses Part 1– Credits: 6

Complete two analysis or two theory courses:

MAT 707 - Real Analysis I 

MAT 708 - Real Analysis II 

OR

MAT 709 - Complex Function Theory I 

MAT 710 - Complex Function Theory II 

Required Courses Part 2 – Credits: 6

MAT 771 - Applied Analysis I 

MAT 772 - Applied Analysis II 

Subject Area Courses – Credits: 12

Complete two of the following one-year course sequences:

MAT 703 - Abstract Algebra III 

MAT 704 - Abstract Algebra IV 

 

MAT 723 - Advanced Ordinary Differential Equations I 

MAT 724 - Advanced Ordinary Differential Equations II 

 

MAT 729 - Partial Differential Equations I 

MAT 730 - Partial Differential Equations II 

 

MAT 733 - Topology 

MAT 734 - Topology 

 

MAT 765 - Advanced Numerical Analysis 

MAT 766 - Advanced Numerical Analysis 

 

STA 767 - Mathematical Statistics I 

STA 768 - Mathematical Statistics II 

Elective Courses – Credits: 6

Complete 6 credits of 600- or 700-level MAT or STA courses (excluding MAT 711 & 712), or other advisor-approved courses.

Dissertation – Credits: 18

MAT 799 - Dissertation 

Degree Requirements 

See Plan Degree Requirements below.

Graduation Requirements 

See Plan Graduation Requirements below.

Subplan 6 Requirements: Post-Master’s - Computational Mathematics Track


Total Credits Required: 48

Course Requirements 

Required Courses Part 1 – Credits: 6

Complete two analysis or two theory courses:

MAT 707 - Real Analysis I 

MAT 708 - Real Analysis II 

OR

MAT 709 - Complex Function Theory I 

MAT 710 - Complex Function Theory II 

Required Courses Part 2 – Credits: 6

MAT 765 - Advanced Numerical Analysis 

MAT 766 - Advanced Numerical Analysis 

Subject Area Courses – Credits: 12

Complete two of the following one-year course sequences:

MAT 703 - Abstract Algebra III 

MAT 704 - Abstract Algebra IV 

 

MAT 723 - Advanced Ordinary Differential Equations I 

MAT 724 - Advanced Ordinary Differential Equations II 

 

MAT 729 - Partial Differential Equations I 

MAT 730 - Partial Differential Equations II 

 

MAT 733 - Topology 

MAT 734 - Topology 

 

MAT 771 - Applied Analysis I 

MAT 772 - Applied Analysis II 

 

STA 767 - Mathematical Statistics I 

STA 768 - Mathematical Statistics II 

Elective Courses – Credits: 6

Complete 6 credits of 600- or 700-level MAT or STA courses (excluding MAT 711 & 712), or other advisor-approved courses.

Dissertation – Credits: 18

MAT 799 - Dissertation 

Degree Requirements 

See Plan Degree Requirements below.

Graduation Requirements 

See Plan Graduation Requirements below.

Subplan 7 Requirements: Post-Master’s - Pure Mathematics Track


Total Credits Required: 48

 Course Requirements 

Required Courses Part 1 – Credits: 6

Complete two analysis or two theory courses:

MAT 707 - Real Analysis I 

MAT 708 - Real Analysis II 

OR

MAT 709 - Complex Function Theory I 

MAT 710 - Complex Function Theory II 

Required Courses Part 2 – Credits: 6

MAT 703 - Abstract Algebra III 

MAT 704 - Abstract Algebra IV 

Subject Area Courses – Credits: 12

Complete two of the following one-year course sequences:

MAT 701 - Foundations of Mathematics III 

MAT 702 - Foundations of Mathematics IV 

 

MAT 717 - Analytical Solution Methods for Partial Differential Equations, I 

MAT 718 - Analytical Solution Methods for Partial Differential Equations, II 

 

MAT 723 - Advanced Ordinary Differential Equations I 

MAT 724 - Advanced Ordinary Differential Equations II 

 

MAT 733 - Topology 

MAT 734 - Topology 

 

MAT 771 - Applied Analysis I 

MAT 772 - Applied Analysis II 

 

STA 767 - Mathematical Statistics I 

STA 768 - Mathematical Statistics II 

Elective Courses – Credits: 6

Complete 6 credits of 600- or 700-level MAT or STA courses (excluding MAT 711 & 712), or other advisor-approved courses.

Dissertation – Credits: 18

MAT 799 - Dissertation 

Degree Requirements 

See Plan Degree Requirements below.

Graduation Requirements 

See Plan Graduation Requirements below.

Subplan 8 Requirements: Post-Master’s - Statistics Track


Total Credits Required: 48

Course Requirements 

Required Courses Part 1 – Credits: 6

STA 767 - Mathematical Statistics I 

STA 768 - Mathematical Statistics II 

Required Courses Part 2 – Credits: 6

STA 761 - Regression Analysis I 

STA 762 - Regression Analysis II 

Subject Area Courses – Credits: 12

Complete two of the following one-year course sequences:

STA 713 - Experimental Design 

STA 715 - Multivariate Statistical Methods 

 

STA 750 - Time Series Analysis 

STA 751 - Spatial Statistics 

 

STA 755 - Stochastic Modeling I 

STA 756 - Stochastic Modeling II 

 

STA 753 - Bayesian Data Analysis 

STA 765 - Statistical Decision Theory 

 

STA 763 - Analysis of Variance I 

STA 764 - Analysis of Variance II 

 

MAT 707 - Real Analysis I 

STA 731 - Probability Theory and Its Applications 

Elective Courses – Credits: 6

Complete 6 credits of 600- or 700-level MAT or STA courses (excluding MAT 711 & 712), or other advisor-approved courses.

Dissertation – Credits: 18

STA 799 - Dissertation 

Degree Requirements 

See Plan Degree Requirements below.

Graduation Requirements 

See Plan Graduation Requirements below.

Plan Degree Requirements


  1. Students in a post-bachelor’s track must complete a minimum of 60 credits of course work (excluding dissertation), at least 18 of which must be at the 700-level.
  2. Students in a post-master’s track must complete a minimum of 30 credits of course work (excluding dissertation), at least 18 of which must be at the 700-level.
  3. A student must enroll in a minimum of 18 credits of Dissertation.
  4. In consultation with his/her advisor, a student will organize a dissertation committee of at least three departmental members. In addition, a fourth member from outside the department, known as the Graduate College Representative, must be appointed. An additional committee member may be added at the student and department’s discretion. Please see Graduate College policy for committee appointment guidelines.
  5. Qualifying Examination. The purpose of the Qualifying Examination is to measure the student’s knowledge of basic graduate course work in selected areas and to make sure that the student is prepared to proceed to more advanced studies.
    1. A doctoral student normally takes the Qualifying Examination within the second year after entering the program, based on the core courses in the student’s concentration.
    2. Doctoral students must pass the Qualifying Examination within three years.
    3. The Qualifying Examination consists of two parts, corresponding to Required Courses Part 1 & Part2.
    4. A student who fails the Qualifying Examination on the first attempt will be placed on probation and must complete a second examination within the next twelve months.
      1. A post-bachelor’s track student who fails the second examination may be allowed to complete a M.S. degree with the consent of the Graduate Studies Committee. Such a student will not be permitted to seek readmission to the Doctoral Program in Mathematical Sciences at UNLV.
      2. A post-master’s track student who fails the Qualifying Examination a second time will be separated from the program.
  6. Subject Area Breadth Requirements. With the goal of encouraging students to be exposed to a broad spectrum of mathematics during their graduate studies, doctoral students are required to take at least two one-year sequence courses with a grade of B or better, in addition to the core courses tested by the Ph.D. Qualifying Examination.
  7. The purpose of the Comprehensive Examination is to measure a doctoral student’s knowledge of the advanced level graduate work that will be required as the student begins to do original research in his or her area of concentration.
    1. After passing the Qualifying Examination, a student will engage in the approved course work specified by the Doctoral Advisory Committee and submit to the latter a dissertation proposal.
    2. Usually one year after passing the Qualifying Examination, a student will complete the Comprehensive Examination, designed and administered by the Doctoral Advisory Committee, based on the student’s course work with focus on his/her ability to perform research on the dissertation proposal.
    3. A student who fails the Comprehensive Examination on the first attempt must complete a second examination within the next semester. A student who fails the examination a second time will be separated from the Doctoral Program.
    4. A student who has successfully passed the Comprehensive Examination will be admitted to Candidacy for the Ph.D. degree and thereby be allowed to proceed with the approved dissertation proposal.
  8. A doctoral candidate is expected to complete a dissertation embodying the results of significant original research, which is performed independently by the student, and is acceptable to the student’s advisory committee.
  9. Skills in foreign languages, computer programming and/or interdisciplinary areas, dependent on the concentration of a student’s program, will be determined by the Doctoral Advisory Committee and the Graduate Studies Committee in consultation with the Department Chair.
  10. Dissertation Defense. After submitting to the Doctoral Advisory Committee a dissertation draft that was approved by his/her Dissertation Advisor, a candidate will defend orally the dissertation before the Doctoral Advisory Committee and any other graduate faculty members who wish to attend. The Doctoral Advisory Committee will recommend to the Graduate Coordinator/Department Chair whether the dissertation and defense are both satisfactory.
  11. Specific degree requirements, including those listed above, are described in detail in the Graduate Student Handbook for the Ph.D. Program, available on the department’s web site. The listing of graduate courses is constantly under review. Graduate students will automatically receive new listings. Since some courses are taught on an “on demand” basis, course prerequisites for each of the four concentrations are considered guidelines with courses roughly equivalent accepted as prerequisites, subject to approval of the Graduate Studies Committee and the student’s Doctoral Advisory Committee.
  12. A student will be placed on academic probation if a minimum of 3.00 GPA is not maintained in all work taken in the degree program. A grade of C or less in one graduate-level course will cause a student to be placed on academic probation and will elicit a critical review of the student’s program by the Graduate Studies Committee.
  13. The Graduate College requires a minimum of 50 percent of the total credits required to complete the doctoral degree, exclusive of transferred credits and/or the dissertation, must be earned at UNLV after admission to a graduate degree program.

Plan Graduation Requirements


  1. The student must submit all required forms to the Graduate College and then apply for graduation up to two semesters prior to completing his/her degree requirements.
  2. The student must submit and successfully defend his/her dissertation by the posted deadline. The defense must be advertised and is open to the public.
  3. The student must submit his/her approved, properly formatted hard-copy dissertation to the Graduate College, and submit the approved electronic version to ProQuest by the posted deadline.

Return to {$returnto_text} Return to: Graduate Plans