Mathematical Sciences, PhD

Program Description

Entering students are expected to have courses in linear algebra, differential equations, a computer language and statistics.

Students in the doctoral program are expected to satisfy the master’s program requirements prior to receiving their doctorate. For the master’s program, both thesis and non-thesis options are available. The curriculum for both options includes foundation courses (often taken prior to entering the master’s program), a breadth requirement, and a concentration area. The doctoral program has a breadth requirement consisting of additional courses beyond the masters’ breadth requirement and a concentration area. Additional information about degree requirements for the PhD program is available in the mathematical sciences graduate student handbook at https://www.clemson.edu/science/departments/math-stat/academics/index.html.

Graduate students in the School of Mathematical and Statistical Sciences have at least three opportunities to participate in international cooperative programs. The first is an exchange program with the Department of Mathematics at Kaiserslautern University in Germany. The second program is a two and one half month summer program in the Center for Industrial Mathematics at the University of Bremen in Germany. The third exchange program is with the Institute of Machine Sciences at the Russian Academy of Sciences (IMASH) in Moscow, Russia. More information about each of these programs is available at  https://www.clemson.edu/science/departments/math-stat/academics/graduate/international-exchange-programs/index.html. Additional information is available at https://www.clemson.edu/science/departments/math-stat/academics/index.html.

Summary of Degree Requirements

This degree requires a minimum of 30 credits beyond the master’s degree, and at least 60 credits beyond the bachelor’s degree. A minimum of 12 credit hours of non-research coursework and a minimum of 18 hours of dissertation research are required.

Coursework must include at least 27 hours of non-research, non-professional development graduate courses at the 8000 level or above. Courses taken in order to fulfill another degree may not be counted. The PhD coursework should also include at least 18 hours of MATH 9910 - Doctoral Dissertation Research . Coursework is planned to give students a comprehensive knowledge of their field of specialization and a mastery of the methods of research. This degree is not awarded solely on the basis of coursework completed, residence, completion of preliminary or comprehensive examinations, or other routine requirements. The final basis for granting this degree is the student’s grasp of the subject matter across a broad field of study, competence in planning and conducting research, and the ability to express themselves adequately and professionally both orally and in writing. Ultimately, only the student’s advisory committee can certify that the student has earned this degree.

Coursework

Coursework must include at least 27 credits of non-research, non-professional development graduate courses at the 8000 level or above. These courses include some breadth courses and some courses in the student’s area of concentration. Courses taken in order to fulfill another degree may not be counted in these credits. The PhD coursework should also include at least 18 credits of Math 9910 (dissertation research).

Breadth Coursework

PhD students are required to complete two breadth courses in each of the following areas:

Algebra

• Recommended courses: MATH 8510 - Abstract Algebra I , MATH 8530 - Matrix Analysis  
• Other options: MATH 8500 - Computational Algebraic Geometry , MATH 8520 - Abstract Algebra II , MATH 8540 - Theory of Graphs , MATH 8550 - Combinatorial Analysis , MATH 8560 - Theory of Error-Correcting Codes , MATH 8570 - Cryptography , MATH 8580 - Number Theory , MATH 9500 - Commutative Algebra , MATH 9510 - Algebraic Number Theory , MATH 9520 - Analytic Number Theory , MATH 9540 - Advanced Combinatorics , MATH 9850 - Selected Topics in Algebra and Combinatorics , MATH 9860 - Selected Topics in Geometry  

Analysis

• Recommended courses: MATH 8210 - Linear Analysis , MATH 8220 - Measure and Integration  
• Other options: MATH 8230 - Complex Analysis , MATH 8250 - Introduction to Dynamical Systems Theory , MATH 8260 - Partial Differential Equations , MATH 8270 - Dynamical System Neural Networks , MATH 8310 - Fourier Series , MATH 8370 - Calculus of Variations and Optimal Control , MATH 8410 - Applied Mathematics I , MATH 9270 - Functional Analysis , MATH 9740 - Selected Topics in Mathematical Sciences , MATH 9820 - Selected Topics in Analysis  

Computational Mathematics

• Recommended courses: MATH 8600 - Introduction to Scientific Computing , MATH 8610 - Advanced Numerical Analysis I  
• Other options: MATH 8630 - Digital Models I , MATH 8650 - Data Structures , MATH 8660 - Finite Element Method , MATH 9830 - Selected Topics in Computational Mathematics  

Operations Research and Stochastics

• Recommended courses: MATH 8030 - Stochastic Processes  and MATH 8170 - Stochastic Models in Operations Research I ; or MATH 8100 - Mathematical Programming  and  MATH 8130 - Advanced Linear Programming   
• Other options: MATH 8000 - Probability , MATH 8030 - Stochastic Processes , MATH 8100 - Mathematical Programming , MATH 8110 - Nonlinear Programming , MATH 8120 - Discrete Optimization , MATH 8130 - Advanced Linear Programming , MATH 8140 - Network Flow Programming , MATH 8160 - Network Algorithms and Data Structures , MATH 8170 - Stochastic Models in Operations Research I , MATH 8180 - Stochastic Models in Operations Research II , MATH 8190 - Multicriteria Optimization ,  MATH (ME) 8740 - Integration Through Optimization , MATH 9880 - Selected Topics in Operations Research  

Statistics

• Recommended courses: MATH 8010 - General Linear Hypothesis I , MATH 8040 - Statistical Inference  
• Other options: MATH 8000 - Probability , MATH 8020 - General Linear Hypothesis II , MATH 8050 - Data Analysis , MATH 8060 - Nonparametric Statistics , MATH 8070 - Applied Multivariate Analysis , MATH 8080 - Reliability and Life Testing , MATH 8090 - Time Series Analysis, Forecasting and Control , MATH 8810 - Mathematical Statistics , MATH 8820 - Introduction to Bayesian Statistics , MATH 8840 - Statistics for Experimenters , MATH 8850 - Advanced Data Analysis , MATH 9010 - Probability Theory I , MATH 9020 - Probability Theory II , MATH 9810 - Selected Topics in Mathematical Statistics and Probability  

Transfer courses and coursed completed as a Masters student en route to the PhD may be counted toward this requirement.

Mathematical sciences courses at the 7000-level are applicable to master’s degree programs in the School of Education only.