The student must pass four written examinations chosen as described below. The exams are based on material that is covered in the courses listed and on material from undergraduate prerequisites. Credit for passing a similar examination at another university cannot be transferred.
The Qualifying Examinations are written examinations offered twice a year during week long Qualifier Exam Sessions the week before classes start in August and January. Each examination is written and graded by a faculty member or a committee of faculty members chosen by the Graduate Committee.
The following four subject areas are called the Core 4 Areas:.
- Complex Analysis (MA 530)
- Real Analysis (MA 544)
- Abstract Algebra (MA 553)
- Linear Algebra (MA 554)
The qualifier exam subject areas are the Core 4 Areas plus the following Area Exams:
- Numerical Analysis (MA 514)
- Probability (MA 519)
- Partial Differential Equations (MA 523)
- Differential Geometry (MA 562)
- Topology (MA 571)
- Mathematical Logic (MA 585)
The student must pass at least two exams from the Core 4 Areas, including at least one of 544 or 553. They must also pass two more exams from the Area Exams and the unused two exams from the Core 4.
The Qualifier Deadline for students who enter the program with a master’s degree is the January Qualifier Exam Session of their second year. The Qualifier Deadline for students without a master’s degree is the January Qualifier Exam Session of their third year. Students who have not passed the four exams on or before the session of their Qualifier Deadline will have their privileges to continue in the mathematics PhD program terminated.
Each qualifier exam can be attempted a maximum of three times and students may attempt as many qualifier exams as they wish at any Qualifier Session on or before their Qualifier Deadline.
Once an exam is passed, it cannot be retaken to improve the grade from B to A.
Math 544 Real Analysis
Math 553 Abstract Algebra
Math 530 Complex Variables
Math 554 Linear Algebra
Math 562 Differential Geometry
Math 519 Probability
Math 523 Partial Differential Equations
Math 571 Topology
Math 585 Logic
CS 514 Numerical Analysis