OVERVIEW
OBJECTIVES
OUTCOMES
STRUCTURE & REQUIREMENTS
OVERVIEW
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.
OBJECTIVES
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.
OUTCOMES
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.
STRUCTURE & REQUIREMENTS
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
|