Recruiting about 10-13 very promising Ph.D. candidates and very excellent 10 master candidates from elite universities in China every year, the program cultivates top talents with solid academic background, a wide range of knowledge and vision, comprehensive and practical ability, and a strong social responsibility.
The program offers more than 30 professionally-related courses such as Theories and Methods for Optimization, Parallel Computation II, Partial Differential Equations, Hyperbolic Partial Differential Equations, Computational Fluid Dynamics, Operation Research, Functional Analysis II, Stochastic Simulation Methods, Fluid Mechanics II, Finite Element Method II, Applied PDE, Convex Optimization, Topics in Stochastic Modeling and Simulations, Selected Multilevel Algorithms and Randomized Algorithms, Computational Systems Biology, Finite Difference Method II, Boundary Integral Method, Structure-Preserving Discretization and Multi-scale Solution Methods for Differential Forms and Equations, Mathematics of Data, Spectral Methods, etc. All doctoral students should take three required compulsory courses (at least one from Theories and Methods for Optimization, Parallel Computation II) and eight elective professionally-related courses based on their individual background and research interest. They should also attend academic lectures at least six times every semester. Master students should take three compulsory courses and six elective professionally-related courses based on their individual background and research interest, and attend at least four times every semester. All graduate students must take part in teaching to get 2 credits. This can be fulfilled by serving as a teaching assistant (TA).
Students in the doctoral degree program should pass the qualifying examination before the end of the sixth semester. One subject of the qualifying examination is Computational Methods, the other is chosen, at the discretion of their supervisor, from the subjects Analysis, Algebra, Differential Equation, Probability, Digital Signal Processing, Algorithm and Data Structure, Introduction to Theoretical Computer Science. With successful pass of these two exams, the student is eligible to work towards the Ph.D. degree and enters into the research stage. If failed, students may take qualifying exams repeatedly before the sixth semester. Those students who failed three times can apply for the program of Master of Science, or drop off the program. With approval of the application and the successful completion of the requirement, the student can receive a degree of Master of Science at the end of the eighth semester. On the other hand, master candidates can also apply for the doctoral program if they pass the qualifying exams during the period of Master program, and their course credits can be counted in the Ph.D. program.
Based on his/her interest in the research fields, students discuss with their advisor on the selection of the topic for the Ph.D. dissertations after passing the qualifying exam. At the end of the sixth semester, the student should make an oral presentation to brief the research plan to his/her thesis committee. A written proposal needs to be submitted to the thesis committee before giving an oral presentation.
A Ph.D. student is required to give a pre-defense of the dissertation work to the defense committee, six months before the final defense. A student who fails the pre-defense may apply for an extension of study.
During their study, the doctoral candidates are required to publish at least one paper in a SCI-indexed journal (or 1 paper in a SSCI journal, or 2 papers in EI journals). The published research paper has to be a part of dissertation. In light of lengthy waiting period, a paper being accepted by the time of graduation is deemed as publication. This requirement can be waived for students who have tried to challenge the difficulty problems and have made a substantial progress in research. In this case, the advisor should submit a petition to the academic degrees committee of SMS for approval.
A Ph.D. dissertation is anonymously reviewed by five experts including at least two experts outside Peking University in the same discipline, and is voted for the approval to give the defense. The defense is scheduled when all 5 reviews are positive. If 2 or more reviews are negative, the procedure is terminated. If only one negative review is received, the sixth review will be sent to an expert in the field. Depending on the outcome of the sixth review, a defense will be held if the outcome is positive, and will be terminated otherwise. The defense committee usually consists of 5 professors, with at least 2 from outside PKU. The supervisor cannot serve on the defense committee. A two-thirds-majority of the committee votes will determine whether the defense is successful or not.
Graduate students in the Master program also have to defense their thesis, in a similar procedure with a lighter standard. For example, the defense committee is consists of three faculty members.
It normally takes 5 years for a bachelor to obtain a Ph.D. degree. For students who have already had a degree of MS, the expected duration is 3 to 4 years. The master program normally takes 3 years.