# Program Requirements for each Concentration of the Ph.D. in Mathematical Sciences

Each concentration has 36 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:

- MTH 525 - Modern Algebra II 3(3-0)
- MTH 623 - The Theory of Groups 3(3-0)
- MTH 625 - Theory of Modules and Fields 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)

**Concentration in Mathematics (36 hours)**

**Mathematics Core Courses (6 hours)***(Student must select MTH 645 and ONE of MTH 633 or 637)*- MTH 633 - Real Variables 3(3-0)
- MTH 637 - Complex Variable Theory 3(3-0)
- MTH 645 - Topology 3(3-0)

**Core Electives (15-18 hours)***(Students must select 15-18 hours from Core Electives. At least three of the courses must be at or above 600 level.***Core Electives I – Applied Mathematics (3-12 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)
**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)
**Core Electives III - Advanced Topics in Mathematics (3-9 hours)**- 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 744 - Topics in Geometry 3-9(Spec)
- MTH 778 - Topics in Combinatorics 3(3-0)
**Area of Specialization Courses (6 hours)**- MTH 796 - Special Topics in Mathematics 1-6 (Spec)
- MTH 797 - Independent Study 1-9 (Spec)
**Other Electives (6-9 hours)**- All courses at 500 level or higher, and approved by the advisor.

**Concentration in Collegiate Mathematics Education (36 hours)**

**Mathematics Education Core Courses (18 hours)**- EDU 614 - Advanced Educational Psychology 3(3-0)
- 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)
- PSY 611 - Research Design 3(3-0)
**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 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 580 - Applied Statistical Methods I 3(3-0)
- STA 584 - Mathematical Statistics I 3(3-0)
- STA 585 - Mathematical Statistics II 3(3-0)
- STA 590 - Applied Statistical Methods II 3(3-0)
- STA 684 - Theory of Statistical Inference 3(3-0)
**Core Electives II (12 hours)**- These could be courses from either inside or outside of the department, selected in consultation with the student's advisor.

- Algebra
- Analysis
- Mathematics Education

- Students choosing the Concentration in Mathematics must pass examinations in algebra and analysis.
- Students choosing the Concentration in Collegiate Mathematics Education must pass examinations in mathematics education and at least one of algebra or analysis.

- MTH 766 - Internship: College Teaching 3-6(Spec)

- MTH 898 - Dissertation 1-30(Spec)