Applied Mathematics and Computational Science Program
The Applied Mathematics and Computational Sciences (AMCS) program trains students in constructing mathematical and computational models of real-world problems.
The program in AMCS includes five tracks, each of which leads to a frontier of applied and computational mathematics. The five track areas are:
- Partial Differential Equations (PDEs)
- Geometric Modeling and Scientific Visualization (GMSV)
- Information Science (IS)
- Modeling and Numerical Simulation (MNS)
- Computational Geoscience (CG)
Three degree programs are offered: the MS degree without thesis, the MS degree with thesis, and the PhD degree.
The Core course requirements for all students in the AMCS program are:
- Numerical Optimization (AMCS 211) or Linear and Nonlinear Optimization (AMCS 212)
- Numerical Linear Algebra (AMCS 251)
- Numerical Analysis of Differential Equations (AMCS 252)
- Applied Partial Differential Equations I (AMCS 231)
- Probability and Random Processes (AMCS 241)
The Immersion courses in each AMCS track are as follows:
Partial Differential Equations- Stochastic Differential Equations (AMCS 236)
- Applied Partial Differential Equations II (AMCS 331)
- Mathematical Modeling (AMCS 332)
- Hyperbolic Conservation Laws and Godunov-type Methods (AMCS 333)
- Mathematical Fluid Dynamics (AMCS 334)
- Scientific Visualization (AMCS 247)
- Computer Graphics (AMCS 248)
- Geometric Modeling (AMCS 272)
- GPU and GPGPU Programming (AMCS 380)
- Machine Learning (AMCS 229)
- Information Networks (AMCS 337)
- Computational Methods in Data Mining (AMCS 340)
- Advanced Topics in Data Management (AMCS 341)
- Stochastic Differential Equations (AMCS 236)
- Scientific Visualization (AMCS 247)
- Stochastic Methods in Engineering (AMCS 308)
- Computational Science and Engineering (AMCS 330)
- Mathematical Modeling (AMCS 332)
- Computational Methods in Data Mining (AMCS 340)
CG track students must take 3 of the following ErSE courses:
- Geophysical Fluid Dynamics I (ErSE 201)
- Geophysical Continuum Mechanics (ErSE 203)
- Seismology I (ErSE 210)
- Global Geophysics (ErSE 211)
- Inverse Problems and Data Assimilation (ErSE 216)
- Data Analysis in Geosciences (ErSE 253)
- Seismic Imaging (ErSE 260)
- Multiphase Flows in Porous Media (ErSE 305)
- Stochastic Methods in Engineering (AMCS 308)
- High Performance Computing I (AMCS 311)
- Computational Science and Engineering (AMCS 330)
- Applied Partial Differential Equations II (AMCS 331)
Master of Science Degree
Each MS degree student will be assigned an academic advisor who will assist the student in planning his/her program of study.
MS degree without thesis
The MS without thesis is usually a one year program. Typically, this will involve 4 courses each in the fall and spring semesters, and 6 credits of summer research or coursework. The degree requirements for the MS without thesis are:
- Complete the five core courses
- Complete three immersion courses in a chosen track
- Complete one cognate course from outside the AMCS program
- Complete 3 additional credits (coursework or directed research), for a total of 30 credits (minimum).
- Write a short technical report and give a scientific presentation.
The last requirement may be fulfilled by, for instance, a course research project presentation and report.
MS degree with thesis
The MS degree with thesis is typically a 3-4 semester program. The degree requirements for the MS with thesis are:
- Complete the five core courses
- Complete three immersion courses in a chosen track
- Complete one cognate course from outside the AMCS program
- Complete 9 additional credits (including at least 6 MS thesis credits), for a total of 36 credits minimum.
- Complete 12 credits of AMCS 297 (MS Thesis), present the thesis at a public seminar followed by an examination, and obtain approval signatures of the thesis committee.,
The MS thesis must involve research under the supervision of a KAUST faculty member. Typically, students in this program will complete their coursework during the first year, although additional courses may be taken during the second year.
By the end of the student’s first year at KAUST, the student must find an advisor. By the end of the third semester, the student is required to form a committee including the advisor and two other faculty, one outside of the AMCS program. This committee must read and approve the thesis.
Doctor of Philosophy Degree
Ph.D. students must first satisfy the coursework requirements for the M.S. program, take at least 6 additional credits of 300-level coursework, pass qualifying examinations, and conduct original research culminating in a doctoral dissertation. Ph.D. coursework in AMCS is designed to ensure that graduates are equipped to lead multidisciplinary research in which they are required to communicate in the language of and understand the intellectual culture of each contributing discipline—from formulation, to mathematical technique, to computational implementation, to analysis and interpretation of results.
Completing the Ph.D. program generally takes 3 additional years beyond the completion of the M.S. program requirements. The Ph.D. requirements are described in greater detail below.
A faculty advisor is either immediately designated (in the case of a student being recruited by a specific faculty member) or temporarily assigned (in the case of KAUST fellowship students); in the latter case, the student is expected to identify a research advisor by (at the latest) the end of the first year.
There are two phases and associated milestones for PhD students: (i) a qualification phase with a candidacy milestone and (ii) a dissertation phase with a final defense milestone.
The Ph.D. program consists of the following requirements:- Coursework and comprehensive exam.
- Acceptance to candidacy.
- Doctoral thesis and final examination.
Coursework Requirements
Students pursuing a Ph.D. must first satisfy the coursework requirements for the M.S. program.
For students admitted to the program after obtaining a Master’s degree elsewhere, some or all of these requirements may be waived, at the discretion of the student’s advisor and with the approval of the dean.
All Ph.D. students must complete at least an additional 6 credits of 300-level coursework.
For most students admitted to the Ph.D. program, an advisor will already have been identified. If not, an interim advisor will be assigned. In any case, the student must identify a research advisor by the end of the first year.
Comprehensive Exam
The comprehensive exam covers material from the students Masters and PhD coursework. The student will be provided a list of examination topics in advance.
The possible outcomes of the exam are: pass, fail, or fail with possibility of retake. In the case of a retake, the student must retake and pass the exam within 3 months of the date of the first exam.
The exam is administered by an examination committee, which does not include the student’s advisor. The committee may waive the exam based on the student’s preparation and performance.
Admission to Candidacy
To be admitted to candidacy, the student must:- Complete the coursework requirements and pass the comprehensive exam (unless waived).
- Identify an advisor and form a supervisory committee.
- Present a doctoral research proposal and obtain approval of the supervisory committee.
Supervisory Committee
The supervisory committee is formed by the student under the guidance of the advisor. The committee is chaired by the advisor, and must include at least three other faculty, one of whom must be external to the program.
The committee may additionally include one or more appropriate persons external to KAUST. The committee must meet at least once annually (as arranged by the student) with the student to discuss the student’s progress. The supervisor and two other committee members must be designated as readers.
Doctoral Candidacy Exam
The doctoral candidacy exam tests the student's preparedness to pursue thesis research. It is a public oral presentation of a research proposal, together with questioning by the advisory committee. The student must submit a written research proposal to the committee two weeks prior to the exam.
The committee shall consist of a minimum of three KAUST faculty members, one of whom must be external to the degree program. The candidate must convince the committee that the chosen research area is suitable and demonstrate an appropriate breadth of knowledge in the chosen area. The committee should decide if there is a thesis topic in the area and whether the candidate is capable of completing such a thesis.
There are four possible outcomes: pass, conditional pass, failure with retake permitted, and failure. Passing the qualification phase is achieved by acceptance of all committee members of the written proposal and a positive vote of all but, at most, one member of the oral exam. If more than one member casts a negative vote, one retake of the oral defense is permitted if the entire committee agrees.
A conditional pass involves conditions (e.g., another course in a perceived area of weakness) imposed by the committee, with the conditional status removed when the conditions have been met. Each student is expected to complete the candidacy exam by the end of the second year.
Thesis and Final Examination
The student must schedule the final examination after completion of the doctoral research (including completion of 60 credits of AMCS 397) and writing of the thesis. This examination will be a defense of the doctoral thesis and a test of the candidate’s knowledge in the specialized field of research.
The format of the examination will be a public seminar presented by the candidate, with an open question period, followed by a private examination by the final examination committee. The final examination committee shall consist of a minimum of four members, one of whom should be a KAUST faculty member external to the degree program and one of whom should be external to KAUST (holding a faculty position or equivalent position at another institution, with approval by both the faculty research advisor and division dean). The only requirement for commonality with the proposal examination committee is the research advisor, although it is expected that other members will carry forward to the dissertation committee.
Passing the dissertation phase is achieved by acceptance of all committee members of the written dissertation, with a minimum of a positive vote of all but, at most, one member of the oral defense. If more than one member casts a negative vote, one retake of the oral defense is permitted if the entire committee agrees.
A fifth non-voting KAUST faculty member, appointed by the division dean, shall serve as a faculty monitor to ensure that the established protocol is followed, and the required forms are completed.