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Program Requirements for Ph.D. in Mathematical Sciences

Each concentration has 33 hours of concentration-specific coursework. Student is encouraged to choose his/her concentration of study early in the program by consulting with the academic advisor, in order to plan for the coursework to prepare for the qualifying exams.

Students who enter the program with a Master's degree, up to 30 hours of relevant graduate coursework may be transferred depending on individual's background and the chosen concentration in consultation with an academic advisor. The course descriptions and detailed guidelines for qualifying exams, teaching internship, professional non-teaching internship and dissertation can be found in


PART I: Common Core Courses (24 hours)

  • MTH 525 - Modern Algebra II 3(3-0)
  • MTH 623 - The Theory of Groups 3(3-0)
  • MTH 632 - Introduction to Real Analysis and Its Applications 3(3-0)
  • MTH 636 - Introduction to Complex Variables 3(3-0)
  • MTH 761 - Methods for Teaching College Mathematics 3(3-0)
  • MTH 762 - A Survey of Research in Collegiate Mathematics Education 3(3-0)
  • STA 584 - Mathematical Statistics I 3(3-0)
  • STA 684 - Theory of Statistical Inference 3 (3-0)

PART II: Concentration-Specific Coursework

  • II-1: Concentration in Mathematics (33 hours)
  • A. Mathematics Core Courses (9 hours) (Student must select MTH 625, 645 and ONE of MTH 633, 637)
    • MTH 625 - Theory of Associative Rings 3(3-0)
    • MTH 633 - Real Variables 3(3-0)
    • MTH 637 - Complex Variable Theory 3(3-0)
    • MTH 645 - Topology 3(3-0)
  • B-D: Core Electives (15-18 hours) Students must select 15-18 hours from areas B-D. At least three of the courses must be at or above 600-level.
    • B. Core Electives I – Applied Mathematics (3-9 hours) (Students must select MTH 534 as one of the courses from B)
      • MTH 520 - Optimization Theory 3(3-0)​
      • MTH 534 - Applied Mathematics and Differential Equations 3(3-0)
      • MTH 634 - Fourier Analysis 3(3-0)
      • MTH 638 - Theoretical Numerical Analysis 3(3-0)
      • MTH 734 - Partial Differential Equations and Applications 3(3-0)
  • C. Core Electives II – Pure Mathematics (3-9 hours)
    • MTH 527 - Representation Theory of the Symmetric Group 3(3-0)
    • MTH 578 - Combinatorics I 3(3-0)
    • MTH 627 - Representation Theory of Lie Algebras 3(3-0)
    • MTH 644 - Differential Geometry 3(3-0)
    • MTH 678 - Combinatorics II 3(3-0)
    • MTH 732 - Functional Analysis 3(3-0)
  •  D. Core Electives III – Advanced Topics in Mathematics (3-9 hours)
    • MTH 641 - Topics in Geometry 3(3-0)
    • MTH 725 - Topics in Algebra 3(3-0)
    • MTH 730 - Topics in Applied Mathematics 3(3-0)
    • MTH 737 - Topics in Analysis 3(3-0)
    • MTH 778 - Topics in Combinatorics 3(3-0)
  •  E. Area of Specialization Courses (6 hours)
    • MTH 796 - Special Topics in Mathematics 1-6 (Spec)
    • MTH 797 - Independent Study 1-9 (Spec)
  • F. Other Electives (0-3 hours)
    • All other courses with designation of MTH, STA or ACT at 500 level or higher, and approved by the advisor.
  •  II.2: Concentration in Collegiate Mathematics Education (33 hours)
  • A. Mathematics Education Core Courses (18 hours)
    • MTH 763 - Advanced Perspectives In Collegiate Mathematics Education 3(3-0)
    • MTH 764 - Qualitative Research Methods in Mathematics Education 3(3-0)
    • MTH 767 - Seminar I in Collegiate Mathematics Education 3(3-0)
    • MTH 768 - Seminar in Collegiate Mathematics Education II 3(3-0)
    • EDU 614 - Advanced Educational Psychology 3(3-0)
    • PSY 611 - Research Design 3(3-0)
  •  B. Core Electives I (6 hours)
    • MTH 520 - Optimization Theory 3(3-0)
    • MTH 578 - Combinatorics I 3(3-0)
    • MTH 586 - Operations Research I 3(3-0)
    • MTH 625 - Theory of Associative Rings 3(3-0)
    • MTH 638 - Theoretical Numerical Analysis 3(3-0)
    • MTH 644 - Differential Geometry 3(3-0)
    • MTH 645 - Topology 3(3-0)
    • MTH 673 - History of Advanced Mathematics 3(3-0)
    • MTH 678 - Combinatorics II 3(3-0)
    • STA 590 - Applied Statistical Methods II 3(3-0)
    • STA 678 - Categorical Data and Survival Analysis 3(3-0)
    • STA 682 - Linear Models 3(3-0)
    • STA 686 - Multivariate Analysis 3(3-0)
  •  C. Core Electives II (9 hours)
    • These could be courses from either inside or outside of the department, selected in consultation with the student's advisor.
  • II.3: Concentration in Statistics (33 hours)
    • A. Statistics Core Courses (21 hours)
      • STA 575 -​​ Statistical Programming for Data Management and Analysis 3(3-0)
      • STA 582 - Experiment​al Designs 3(3-0)
      • STA 590 - Applied Statistical Meth​ods II 3(3-0)
      • STA 675 - Advanced Statistical Data Managem​ent and Simulation 3(3-0)
      • STA 678 - Categorical Data and Survival Analysis 3(3-0)​
      • STA 682 - Linear Models 3(3-0)​
      • STA 686 - Multivariate Analysis 3(3-0)​
    •  B. Core Electives (12 hours)
      • STA 591 - ​Data Mining Techniques 3(3-0)
      • STA 691 - Advanced D​ata Mining Techniques 3(3-0)
      • STA 694 - Bayesian Statistics 3(3-0​)
      • STA 696 - Special Topics in Statistics 1-6(Spec)​
      • STA 697 - Independent Study 1-9(Spec)​
      • STA 782 - Generalized Linear Models 3(3-0)​
      • STA 784 - Theory of Estimation 3(3-0)​
      • STA 797 - Independent Study 1-9(Spec)​

 

Part III. Qualifying Examination

Qualifying Examinations will be offered in the following subjects, based on the material in the courses listed in the current Graduate Student Handbook of Department of Mathematics.

  1.  Algebra
  2.  Analysis
  3.  Applied Mathematics
  4.  Applied Statistics
  5.  Combinatorics
  6.   Mathematics Education
  7.   Theoretical Statistics
  8.   Topology

 

  • Each doctoral student must pass examinations in three different subjects from those listed above.
    • Students choosing the Concentration in Mathematics must pass examinations in algebra, analysis, and one other subject listed above.
    • Students choosing the Concentration in Collegiate Mathematics Education must pass examinations in mathematics education and two other subjects listed above, at least one of which must be algebra or analysis.
    • Students choosing the Concentration in Statistics must pass examinations in theoretical statistics, applied statistics, and analysis.

 

Part IV: Internship (6 hours)

Students are required to take six (6) hours of internship of which at least three hours must be a teaching internship. The student must earn credits for internship by registering for MTH 766 for teaching internship and MTH 795 for non-teaching professional internship.

  • MTH 766 - Internship: College Teaching 3-6(Spec)
  • MTH 795 - Advanced Practicum/Internship 3-6(Spec)

 

Part V: Dissertation (12 hours)

Students are required to register for 12 hours of MTH 898 (Dissertation) supervised by a graduate faculty. Upon completion of coursework, qualifying examination, internship, and dissertation, the candidate for the Ph.D. degree must pass a final oral examination which is the dissertation defense in a colloquium format. The student's dissertation committee determines whether the student passes the oral examination.

  • MTH 898 - Dissertation 1-30(Spec)

 

Total: 75 semester hours​