1. 
CourseWork (Minimum of 18
credits) 

The student must
complete a coursework in accordance to the scheme described in (a), (b), and
(c) below. The minimum number of combined credits is
18. 
a) 
Basic Courses*: (06 credits)


The student must
take each of the six courses listed below (each course is three credits), and
pass each with a grade of B or better provided such a course or its equivalent
had not been taken before to complete a Master or an undergraduate degree
requirements. 

0410501 
Algebra I 
0410510 
Analysis
I 
0410512 
Complex Analysis
I 
0410513 
Ordinary Differential
Equations 
0410515 
Functional
Analysis 
0410525 
General
Topology  


If a student needs to take more than two
courses from the list above, then only 6 credit hours will be awarded toward the
fulfillment of the coursework requirement.

If a student
has already taken all the courses listed above to complete a Master’s or an
undergraduate degree requirements, then the student may include in the program
of study 500Level mathematics courses other than those listed above. However,
the student must pass any such course with a grade of B or better in order to
count toward the coursework requirements; and the maximum number of credits
awarded shall not exceed six.

b) 
600Level Courses: (9 credits or
more) 

The student must take at least three (3) of the 600Level
courses listed below (each course is three credits) that are offered by the
department of Mathematics and Computer Science.
0410  601 
Algebra 
0410  603 
Ring Theory 
0410  606 
Group
Theory 
0410  608 
Advanced Topics in
Algebra 
0410  610 
Measure and Integration
Theory 
0410  610 
Complex
Analysis 
0410  614 
Operator Theory 
0410  615 
Functional
Analysis 
0410  616 
qAnalysis 
0410  617 
Methods of Mathematical Physics 
0410  618 
Advanced Topics in Analysis 
0410  623 
Advanced Topics in Applied
Mathematics 
0410  625 
Topology 
0410  626 
Algebraic
Topology 
0410  635 
Advanced Topics in Geometry and
Topology 
0410  636 
Graph Theory 
0410  637 
Theory of Linear
Programming 
0410  638 
Advanced Topics in Discrete
Mathematics 
0410  650 
Approximation and
Optimization 
0410  661 
Numerical Solution of Partial
Differential Equations 
0410  668 
Advanced Topics in Numerical
Mathematics  
c) 
Graduate Courses from Outside
Mathematics Graduate Program: (06credits) 

With the consent and encouragement of the program committee,
a student may include in the program of study up to 6 credit hours from 500 or
600Level courses offered by other graduate programs within Kuwait
University. 
2. 
Qualifying
Examination 

The student must submit to the College of Graduate Studies a
request to sit the Ph.D. qualifying examination. The request must be made just
before or soon after the student completed the coursework requirement with a
GPA not less than 3.00 out of scale A = 4.00.
The qualifying examination structure for the Ph.D. program
comprises three written examinations that are administered on three consecutive
workweeks. Each examination is fourhour long and covers a specific area of
mathematics. The student must choose the three area from the following four
areas:
1. Algebra
2. Real
Analysis
3. Differential
Equations
4. Numerical
Analysis
The student passes the qualifying examination by passing all
three examinations. Each exam will be graded in two categories, Ph.D. Level
Pass, Ph.D. Level Fail. The student must achieve Ph.D. Level Pass on each
examination in order to remain in the Ph.D. program.
The examinations will cover materials specified in the
existing syllabi that are available with the Director of the Graduate Studies
Programs of the department of Mathematics and Computer Science. Should the
student fail any examination, there will be only one additional chance to pass
that examination, which the student must take in the same subject area. The
student should make the second attempt no later than the next regular
semester. 
3. 
Major
Topic 

After the approval
of the Ph.D. dissertation proposal, the academic supervisor will decide on a
topic in the general field in which the student is writing a dissertation. The
topic is referred to as "Major Topic." The Major Topic may be supportive of the
planned dissertation topic, but should not have a narrow focus. The specific
and exact goal of the Major Topic is to provide the student with a good
understanding of how his or her work fits into a larger picture. Therefore, one
expects the student to have an overview of the Major Topic's subject and his or
her area of study and become familiar with all important work that has been done
in both, and identify the particular problem(s) he or she proposes to work
on.
Within one year of the selection of the Major Topic the
student must submit a written report and give an oral presentation. The graduate
program committee will form a committee of at least three members with
the academic supervisor as the chair. This committee is in charge of studying
the written report and coordinating the oral presentation. The written report
should include

A discussion of the relevant
literature,

The common or the critical methodology
involved in the subject of the Major Topic, and

A clear explanation of how the planed
dissertation fits into the subject of the major
topic.
The oral presentation is public and should
emphasize

Particular problems the student attacked in
relation to the dissertation, and some partial results,
and

How the dissertation will relate to the Major
Topic's subject.
Questions and suggestions from the
committee will follow the presentation. In order to pass, the committee must be
convinced that the topic is genuine and the student is engaged in a meaningful
research that is going to lead to a Ph.D. dissertation. Should the student fail,
there will be one additional chance only to pass, otherwise the student is
removed from the Ph.D. program. The second attempt must be made within a
period of six months. 
4. 
Oral Defense of the
Dissertation 

After the student had completed the coursework requirement,
passed the qualifying examination, completed the Major Topic and had written the
dissertation, the advisor should notify the program committee that the student
is ready for the final oral defense. The College of Graduate Studies, in
consultation with the Program Committee and the supervisor will select a
suitable external examiner. Copies of the dissertation will be sent to the
external examiner at least one month before the scheduled date of the final oral
defense. If the report of the external examiner is positive then the final oral
defense proceeds as scheduled. 