Exam Overview

The comprehensive exam is a mandatory feature of the PhD program in order to pursue the study and gain a PhD degree in Mathematics. This exam measures how well PhD students have understood the range of concepts which they have studied at Master’s and Doctoral level. The exam assesses students’ comprehension of the basic disciplines of mathematics, as well as their chosen major. Students are only eligible to sit the comprehensive exam once they have passed each course on their doctoral program and obtained the degree which qualifies them to pass the course. Students cannot submit their research proposal for the PhD thesis until they have passed such an exam. To achieve this, in consultation with an academic advisor and the department graduate committee, each student has to select three major branches, pass two courses per branch and have their grades verified by their departmental academic advisor. Once a student has passed the comprehensive exam (gained at least 70% per course), he or she is qualified to submit a research proposal for a scientific thesis to the department council, and to agree on the committee who will supervise the thesis.

Exam Objectives

• To measure students’ understanding of both basic and advanced concepts and knowledge across a number of disciplines in the field of mathematics.
• To evaluate the degree to which students are able to harness the knowledge and concepts which they have acquired and apply them correctly when solving mathematical problems.
• To determine to what extent students are able to analyze, make deductions and undertake scientific criticism.
• To assess whether a student is capable of carrying out in-depth scientific processes.
• To establish if a student has familiarized themselves with the rules and practices underpinning standard scientific writing.

Examination Format

The comprehensive exam is a written exam which is held twice each academic year, namely between the first and second semesters and during the summer semester - the department council determines the actual date. The comprehensive exam comprises of nine major branches, including the precise specialization the student wishes to study. The student must select three major branches from the list below:

• Ordinary Differential Equations.
• Partial Differential Equations.
• Algebra and its Applications.
• Applied Mathematics.
• Numerical Analysis.
• Real Analysis.
• Functional Analysis.
• Differential Geometry.
• Topology.

Evaluation

Students who achieve a total score of 70% and above of each major branch are deemed to have passed the exam. The student is allowed a second attempt to sit the exam in the same major branch. Failure on the second attempt means the student is required to withdraw from the PhD Program.

Timing & Location

Exam Time

TBA

Exam Location

Male Section: Science Faculty, Building 91A, 1st Floor, Room 211.
Female Section: Science Faculty, Building 7, Room 1132.

References

The department specifies references for each major branch included in the exam, to enable students to revise and prepare for the exam. A student should consult his academic advisor to aquire the references.