PhD In Mathematics

The Ph.D. in Mathematics (Ph.D. MATH) builds on Khalifa University’s internationally leading research activity in science, engineering, and medicine. It supports the University’s alignment with the Abu Dhabi Economic Vision 2030 plan through the provision of internationally excellent education and student experience in Mathematics, producing highly skilled science professionals capable of transferring state-of-the-art technologies to priority sectors of industry, business, and government. The aim of the Ph.D. in Mathematics program is to produce graduates who are able to conduct independent research in Mathematics at the highest levels of originality and quality. The degree will be awarded to students who demonstrate a range of advanced knowledge and skills at the forefront of Mathematics and who complete an independent investigation of a novel specialist topic in order to present a dissertation addressing a problem in cutting-edge research. Candidates for the degree will be supervised by teams of experienced researchers.

Overall Program Structure

The Ph.D. in Mathematics consists of a minimum of 60 credit hours, distributed as follows: 24 credit hours of coursework, and 36 credit hours of Ph.D. Dissertation and two zero credit Ph.D. Seminar courses. The components of the program are summarized in the table below:

Program Component - Credit Hours

• SCIE 701 Research Methods Science - 3
• SCIE 702 Research Seminar I - 0
• SCIE 703 Research Seminar II - 0
• Program Electives - 21
• SCIE 799 Ph.D. Research Dissertation - 36
• Total - 60

Program Requirements

Students seeking the degree of Ph.D. in Mathematics must successfully complete a minimum of 60 credit hours as specified in the program requirements detailed below, with a minimum CGPA of 3.0. Course selection should be made in consultation with the student’s Main Advisor.

Program Core (3 credit hours)

Students must complete the following core courses:

• SCIE 701 Research Methods Science
• SCIE 702 Research Seminar I (0 credits)
• SCIE 703 Research Seminar II (0 credits)

Program Electives (21 credit hours)

Students must complete a total of six elective courses (21 credits). Program electives are listed below:

• MATH 701 Combinatorial Analysis
• MATH 702 Functional Analysis.
• MATH 703 Finance and Stochastic Calculus
• MATH 704 Matrix Computation
• MATH 705 Mechanics of interacting particle
• MATH 706 Modern Statistical Prediction and Data Mining
• MATH 707 Nonlinear Optimization.
• MATH 708 Partial Differential Equations
• MATH 709 Probability and Stochastic Processes
• MATH 710 Selected topics in group theory
• MATH 711 Selected topics in high-dimensional statistics
• MATH 717 Methods of Mathematical Physics
• MATH 777 Mathematical Models for Biology & Epidemiology
• MATH 787 Mathematical Imaging

Subject to the approval of the Main Advisor and the Program Coordinator, up to two electives (6 credits) may be taken from outside the student’s department, if these courses support the student’s dissertation topic.

SCIE 799 Ph.D. Research Dissertation (36 credit hours)

Students must complete a Dissertation that involves creative, research-oriented work within the field of Mathematics, under the direct supervision of a full-time faculty advisor from the Mathematics Department, and at least one other full-time faculty who acts as a co-advisor. The outcome of the research should demonstrate the synthesis of information into knowledge in a form that may be used by others. The research findings must be documented in a formal dissertation and defended successfully in a viva voce examination.

Objectives

The objectives of the Ph.D. in Mathematics program are to produce graduates who have the ability to:

• Synthesize and critically evaluate complex current knowledge in the Mathematical sciences in order to plan and implement new and creative approaches so as to generate new knowledge and solve research challenges with effective dissemination of the results to a variety of audiences;
• Work to the highest professional and ethical standards in an area of Mathematical sciences and develop their individual academic, professional, and career skills; and
• Keep abreast of the latest developments in Mathematics that contribute to the advancement of knowledge for the benefit of society.

Outcomes

Upon successful completion of the Ph.D. in Mathematics, a graduate will be able to:

• Demonstrate and critically analyze comprehensive, deep, and overarching knowledge that is at the frontier of recent developments in Mathematical sciences.
• Conduct and defend original independent research that creates significant new knowledge in Mathematical sciences of publishable quality that leads to scholarly articles or other intellectual outputs.
• Analyse and critically evaluate the uses and limitations of diverse methodologies and techniques for solving problems in Mathematical research, leading to informed and valid judgments.
• Select and deploy advanced experimental and related skills to investigate and solve complex problems in Mathematical research.
• Communicate effectively and professionally, in written and oral forms as appropriate, the major tenets of areas of Mathematics and their individual specializations to a variety of audiences.
• Demonstrate a commitment to safe, responsible, and ethical behavior in all research and professional activities.
• Reflect upon their role(s) in their research specialization and in the wider research community to ensure that they take responsibility for their own development and that of peer groups and networks.