Lahore University of Management Sciences

Graduate Programmes

PhD Mathematics

	Overview Structure Admission Fees Financial Aid Calendar Faculty

Programme Structure

All courses taken by a student are subject to approval by the Graduate Committee and student's supervisor (if any). The Graduate Committee will interview each student at least once each year to review progress and approve the course schedule. For PhD Mathematics programme, a student has to complete at least 90 units. At least 27 credits are to be earned out of 500-level (or above) mathematics courses. At least 40 units must be research units and a maximum of 20 units of these can be counted towards the 90 units requirement. At least 9 units must be earned from other departments but no more than 15 such units can count towards the 90 units requirement. At least 55 units must be from math courses. A student may not take an undergraduate-level course which he/she has already taken for his/her previous degree.

A student having M.Phil or MS degree or who has done advanced course work (subject to proof) may ask through an application at the start of his first year to the graduate committee to waive some of the course work requirements. Such students will have to take an oral examination on the course (s) for which waiver is demanded. At most 6 units can be waived out of 27 units of 500-level or above math courses. Research units cannot be waived. Out of 55 math units, at most 24 can be waived. Out of 90 units, at most 30 can be waived. Final decision will be made by the Graduate Committee.

Graduate students are expected to maintain a minimum CGPA of 3.3. A student whose CGPA is below 3.3 will not be hired as a TA or RA (or any other position). If someone's CGPA falls below 3.0, except in the very first quarter, he/she will be separated from the program.

Student has to pass a written qualifying exam from the following subjects:

• Numerical Analysis
• Differential Geometry
• Partial Differential Equations
• Functional Analysis
• Topology
• Complex Analysis
• Measure Theory
• Algebra

The qualifying exam shall be given once a year. A student will have to clear this exam in at most two attempts within first two years of study. Students will be assigned a grade of Fail, Pass, or High Pass. Exit with Master degree: A student who has earned 45 units of regular courses towards the LUMS Ph.D programme, which include at least 21 units of 500 level regular courses, and is separated from the programme, may be awarded MS degree.

A student has to carry at least twelve units every quarter to be a full time student. Before passing Qualifying Examination, at least six of these twelve credits should be from 500-level regular courses. However, undergraduate courses may count towards this requirement if allowed by the graduate committee.

After passing the qualifying exam, the student is required

1. To teach one undergraduate-level course per year
2. To give a colloquium talk every year. Every student has to give three such colloquium talks during his/her study program.

After passing the PhD qualifying examination, before starting substantial work on a dissertation, the student is required to take an oral candidacy examination. This exam will be from the proposed field of specialization in which dissertation is to be written.

After passing candidacy examination, the student has to write and defend a dissertation, which must be submitted within five years from the date of admission to PhD programme. However an extension of up to two years may be granted in special cases. Supervisor's approval is required for the submission of the dissertations.

Dissertation Evaluation

The dissertation will be evaluated by three referees, of whom one will be the supervisor and the other two will be foreign referees. These foreign referees will be chosen by the VC from a list of five people nominated by the Head of Mathematics department. The Board of Advanced Studies and Research, which comprises of the Dean, HOD, supervisor and two other senior faculty members from the mathematics department will examine the reports from referees and decide whether reports are positive or not. If at least two of the three referees give positive reports, the student will go through the final defence of his/her dissertation.

Dissertation Defence Committee

Dissertation Defence Committee will comprise of the Head of mathematics department (convener), Dean, supervisor, one full professor (from LUMS but not from mathematics department) nominated by VC and one external examiner who will be chosen by VC from a list of three people nominated by the Head of mathematics department.