PhD (Mathematics) Degree Programme (Three Years-Six Semesters)

The Department of Mathematics, National University of Modern Languages (NUML), Islamabad offers Graduate Programs leading to the degree of PhD in Mathematics. The diversity of graduate courses offered in the department give the student an opportunity to specialize in one of the several fields of

1. Pure Mathematics,
2. Applied Mathematics,
3. Computational Mathematics

OBJECTIVES OF THE PROGRAM

This program is designed to develop most recent knowledge and up to dated research in Mathematics. We have experts in many major areas of Mathematics covering applied, computational and pure Mathematics. The main focus of the program is to prepare a workforce of mathematicians who are well familiar with current and new trends in the subject.

ADMISSION

Admission  to  Ph.D.  (Mathematics)  Programmeme  will  be  made           as  per  rules  and regulations of National University of Modern Languages Islamabad, and on HEC criteria for Ph.D. Programme.

Admission Requirement

For admission to PhD (Mathematics) programme, minimum CGPA 3.0 (out of 4.0 in the Semester System) or First Division (in the Annual System) in M.Phil/M.S/Equivalent (with research) is required. 

Subject Test  

A subject test conducted by the National Testing Service (NTS) or ETS, USA in the subject of Mathematics must be cleared prior to admission in the PhD (Mathematics) Programme. 

In  the  case  of the GAT  Subject  test  (http://www.nts.org.pk/GAT/GATSubject.asp),  a minimum of 60% marks is required to pass the test. or In the case of the GRE subject test, a minimum of 60% Percentile Score will be acceptable. A Committee comprising at least 3 PhD faculty members from Department of Mathematics NUML approved by the Rector NUML will conduct the Test at par with GRE Subject Test and qualifying score for this will be 70% .

COURSE WORK

 Ph.D. (Mathematics) is a 42 Cr Hrs programme, that includes:

a.    Course Work:                                   – 18 Cr Hrs

b. Comprehensive Exam + Viva Voce: – 06 Cr Hrs

c.    Thesis + Oral Defence:                    – 18 Cr Hrs

Passing criteria of course work and comprehensive exam will be as follows:

• Comprehensive Exam of 150 marks will be taken from Six subjects, four from BS/MSc and two from MS/PhD with the consent of the supervisor. Viva Voce exam will be of 50 marks.
• ·Number of chances to pass the comprehensive exam will be two.
•  Course work/Comprehensive Exam must be cleared within the first two years from the date of admission.
•  The Ph.D. Thesis would be evaluated by at least two Ph.D. experts from technologically/ academically advanced foreign countries and two local experts in addition to one internal examiner.

Board of Examiners for PhD Defence 

Board of Examiners for PhD Defence will be as follows: 

•           Dean of Faculty 

•           Head of Department 

•           Supervisor 

•           Internal Examiner 

•           Two Local Experts 

Research Paper 

Acceptance/publication of at least one research paper in an HEC-approved “X” category journal is a requirement for the award of Ph.D. degree. 

Plagiarism Test  

The Plagiarism Test would be conducted on the thesis before its submission to the two foreign experts. 

Duration of PhD Programme

• The minimum period for completion of PhD requirements shall be three years from the date of registration, and the maximum period shall be seven years.  Copy of PhD Thesis to HEC 
• A copy of Ph.D. thesis (both hard and soft) would be submitted to HEC for record in Ph.D. Country Directory and for attestation of the PhD degree by the HEC in future. 

Conduct of PhD Programme 

• There would be at least 3 relevant full time Ph.D. Faculty members in the Department of Mathematics to launch the Ph.D. programme. 
• The maximum number of Ph.D. students under the supervision of a full time faculty member would be five. 

 Brief Description of Ph.D. Degree Requirement

 To complete Ph.D. degree Programme, a candidate must

a.         Complete 18 credit-hours course work.

b.         Qualify Comprehensive Examination.

c.         Present the 1^st Seminar in 4^th or 5^th Semester of Ph.D and 2^nd Seminar in 6^th Semester.

d.        Attend a workshop on Computer Tools for Mathematics or MATH 692 Research Methodology.

e.         Deliver a pre-submission seminar prior to submission of Ph.D thesis.

f.          Prepare a PhD thesis of 18 credit hours comprising at least 100 pages.

g.         Meet other requirements as per rules and regulations and prescribed procedure of NUML and HEC minimum criteria for Ph.D. Programme for award of Ph.D. degree.

Doctor of Philosophy (Ph.D.) Degree Scheme of Studies

•  Students can take at least one course and at the most four courses in one semester from the list given below.
• Students cannot opt for any course from the given list if he/she has studied that course in M.Phil /MS (Mathematics) Programme