Mathematics

Master of Arts

Students are expected to complete a minimum of 30 credits of graded coursework, including MATH 5330 (Advanced Multivariate Calculus), up to nine credits taken in other departments and up to six credits of thesis research.  Permissible substitutes for MATH 5330 include MATH 7310 (Real Analysis and Linear Spaces I), MATH 7320 (Real Analysis and Linear Spaces II), MATH 7340 (Complex Analysis I), MATH 7751 (Algebra I) and MATH 7752 (Algebra II).

Students are expected to pass a final master’s examination and may elect, in addition, to complete a thesis.

Master of Science

Students are expected to complete a minimum of 30 credits of graded coursework, including:

• MATH 7310 - Real Analysis and Linear Spaces I ,
• MATH 7340 - Complex Analysis I ,
• MATH 7751 - Algebra I ,
• MATH 7752 - Algebra II  ,
• MATH 7800 - Algebraic Topology I ,
• MATH 7820 - Differential Topology , and 
• a passing grade is required on one general examination chosen from algebra, analysis or topology. 

Higher-level substitutes may be approved for the required courses.

Doctor of Philosophy

Of the 72 credits required for the doctoral degree, students are expected to complete a minimum of 24 credits of graded coursework, including:

• MATH 7310 - Real Analysis and Linear Spaces I ,
• MATH 7340 - Complex Analysis I  ,
• MATH 7751 - Algebra I ,
• MATH 7752 - Algebra II ,
• MATH 7800 - Algebraic Topology I , and
• MATH 7820 - Differential Topology .

Students are expected to pass two written general examinations chosen from the areas of analysis, algebra, and topology.  Students are expected to attempt two different general examinations before the beginning of the third semester, to pass at least one general examination before the beginning of the fourth semester, and to pass both exams before the beginning of the sixth semester.

Students are expected to demonstrate their ability to commence dissertation research by passing an oral examination before the conclusion of their fourth semester on material selected by the faculty from among second-year courses. If deficiencies are noted, the examining panel will make recommendations for improvement and meet again with the student before the beginning of the fifth semester.

Students pursing research in the history of mathematics are expected to pass a written translation examination in two foreign languages, typically French and German, by the conclusion of the fifth semester.

Students are expected to complete all requirements stated above by the conclusion of their fifth semester.

Students are expected to write and defend a dissertation.