PhD in Mathematics

The PhD in Mathematics (PhD 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 PhD 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.

The objectives of the PhD 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.

Upon successful completion of the PhD in Mathematics, a graduate will be able to:

Demonstrate and critically analyse 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 judgements.
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 behaviour 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.

The structure and requirements for the PhD in Earth Sciences program for candidates with a Master’s degree and those with only a Bachelor’s degree are detailed below.

Candidates with a Master’s Degree

Overall Program Structure

The PhD in Mathematics consists of a minimum 60 credit hours, distributed as follows: 24 credit hours of coursework, 36 credit hours of PhD Dissertation and two zero credit PhD 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 PhD Research Dissertation	36
Total	60

Program Requirements

Students seeking the degree of PhD in Mathematics must successfully complete a minimum 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 seven 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 approval of the Main Advisor and the Program Coordinator, up to two electives (6 credits) may be taken from outside the student’s department and chosen from the list below, if these courses support the student’s dissertation topic.

Course	Department	Area of Interest
AERO 701 Nonlinear Structural Dynamics	Aerospace Engineering	Applications of Dynamical Systems in Engineering.
AERO 703 Numerical Methods in Aerofluids	Aerospace Engineering	Applications of numerical methods in Aerospace Engineering.
ECCE 732 Machine Learning and Applications	Electrical and Computer Engineering	Applications of machine learning in solving mathematical problems are increasing recently.
ECCE 738 High Performance Computing	Electrical and Computer Engineering	To teach math students HPC in solving numerically challenging problems.
ECCE 742 Adv. Conc. in Stoch. Proc., Detection, and Estimation Theory	Electrical and Computer Engineering	Relevant to research in stochastic processes.
ECCE 753 Computational Prototyping of Dynamical Systems	Electrical and Computer Engineering	Of interest to Industrial and Applied Math students.
ECCE 754 Computational Prototyping of Partial Differential Equations	Electrical and Computer Engineering	Of interest to Industrial and Applied Math students, involving differential equations.
ESMA 710 Times Series Analysis Modeling and Prediction	Engineering Systems and Management	Supporting the department’s research on time-series analysis.
ESMA 720 Advanced Production and Operations Management	Engineering Systems and Management	Relevant to students in operation research.
ESMA 721 Stochastic Processes and Applications	Engineering Systems and Management	Relevant to research in stochastic processes.
ESMA 730 Complex Network Analysis	Engineering Systems and Management	Of interest to Industrial and Applied Math students.
MEEN 703 Linear and Nonlinear Finite Element Methods	Mechanical Engineering	A course on numerical methods that can be important to Applied Math or Scientific Computing students.
MEEN 721 Computational Fluid Mechanics	Mechanical Engineering	Of interest to Industrial and Applied Math students.
MEEN 722 Non-Newtonian Fluid Dynamics	Mechanical Engineering	Of interest to Industrial and Applied Math students.
PHYS 701 Advanced Computational Physics	Physics	Of interest to Mathematical Physics students.
PHYS 702 Advanced Quantum Mechanics	Physics	Of interest to Mathematical Physics students.

SCIE 799 PhD Research Dissertation (36 credit hours)

Students must complete a Dissertation that involves creative, research-oriented work within the field of mathematics, under 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 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.

Study Plan

A typical study plan for students enrolled in the PhD in Mathematics is shown below.

Typical Study Plan for Full-Time Students
	Semester 1	Semester 2
Year 1	SCIE 701 Research Methods Science Elective Course 1 Elective Course 2 Elective Course 3	Elective Course 4 Elective Course 5 Elective Course 6 SCIE 799 PhD Research Dissertation
Year 2	Elective Course 7 SCIE 795 PhD Written Qualifying Examination SCIE 799 Research Dissertation in Science	SCIE 702 Research Seminar I SCIE 796 PhD Research Proposal Examination SCIE 799 Research Dissertation in Science
Year 3	SCIE 799 PhD Research Dissertation	SCIE 703 Research Seminar II SCIE 799 PhD Research Dissertation
Year 4	SCIE 799 PhD Research Dissertation	SCIE 799 PhD Research Dissertation PhD Research Dissertation Examination

Candidates with only a Bachelor’s Degree

Overall Program Structure

Students with only a Bachelor’s degree must enroll on full-time basis. The PhD in Mathematics consists of a minimum 72 credit hours, distributed as follows: 36 credit hours of coursework, 36 credit hours of PhD Dissertation and two zero credit PhD Seminar courses. The components of the program are summarized in the table below:

Program Component	Credit Hours
Core Courses	12
Technical Electives	24
SCIE 702 PhD Research Seminar I	0
SCIE 703 PhD Research Seminar II	0
SCIE 795 PhD Written Qualifying Exam	0
SCIE 796 PhD Research Proposal Exam	0
PhD Research Dissertation	36
Total	72

All the courses that the students will take are at PhD level. The students will only be able to attempt SCIE 795 PhD Written Qualifying Exam (WQE) after successfully completing a minimum of 27 credits of formal coursework.

Typical Study Plan

All courses in the study plan are 3 credit hours each. PhD Research Seminar I & II are zero credit each.

Typical Study Plan for Full-Time Students

Semester 1

Semester 2

Year 1

SCIE 701 Research Methods in Science

Core Course 1

Core Course 2

Core Course 3

Technical Elective 1

Technical Elective 2

Technical Elective 3

Year 2

Technical Elective 4

Technical Elective 5