为了更好地贯彻党和国家的教育方针，教育要“面向现代化、面向世界、面向未来”的要求，培养德、智、体全面发展的教学、科研和适应国家经济建设和社会发展需要的高级专门人才，对博士生培养基本要求如下：

1．较好地掌握马克思主义的基本原理，坚持党的基本路线，热爱祖国，遵纪守法，品德优良，学风严谨，具有较强的事业心和献身精神，积极为社会主义现代化建设服务。

2．在本门学科上掌握坚实宽广的基础理论和系统深入的专门知识，具有独立从事科学研究工作的能力和创新能力，在科学或专门技术上作出创造性的成果。

3．身体健康。

4．本学科以数学研究发展的前沿问题为主要研究方向，培养坚实的基础理论和广泛的实际应用技术以及先进的计算机分析手段、具有独立从事科学研究工作能力、在研究或应用方面具有解决实际问题能力的高级科技人才，使本学科得到新的发展，为国家的经济建设和社会发展服务。

1．博士研究生的学习年限一般为三年。

2．硕、博连读研究生的学习年限为四年半至五年。

3．在职博士生的学习年限可相应延长，一般最多不超过六年。

1．解析数论及其应用

2．有限群论

3．矩阵代数及其表示

4．空间理论及其应用

5．几何分析与凸体理论

6．非线性偏微分方程

7．非线性科学和复杂系统行为

8．偏微分方程数值解

9．孤立子理论与可积系统

10．变分不等式及优化控制

11．矩阵计算与并行算法

12．数值有理逼近及应用

13．守恒型方程组及其数值方法

14．反问题和不适定问题的理论与算法

15．计算分子生物学

16．数学规划

17．随机模型与智能算法

18．动力系统与混沌控制

19．图论与组合最优化

20．生物信息和复杂网络

1．课程设置（见附表）

2．课程学分要求：课程学分要求达到16学分及以上。

3．要求在攻读博士学位期间在公开学术讨论会报告1次，在国内核心刊物或国际学术刊物上发表与本学科相关的论文两篇以上，其中至少有一篇被收入三大检索。发表的论文中至少有一篇是第一作者，其余可以是除导师以外排名第一。

研究生入学后，在导师的指导下，完成培养计划的制定，并报学院（学科）学位分委员会批准，在入学后一个月内报研究生部。博士生课程学习要求在第一学年内结束。

1．开题报告

(1) 选题：论文的研究课题应与本专业的前沿研究相关或者来自本专业相关的国民经济建设中的重要应用问题。

(2) 条件：应当修满规定的16学分以上，并提交2篇文献研读报告或者学术讨论报告。

(3) 要求：在入学一年内(专职博士生)或两年内(在职博士生)或三年内(硕博连读生)完成8000字以上的开题报告。内容包括文献综述、选题意义、研究目标、难点与特点、预期成果和可能的创新点等部分。引用文献不少于50篇。

(4) 评审：组织5名以上一级学科高级职称（含4名教授）的教师听取开题报告并进行评议，评议通过后方可开题。

2．阶段报告

在论文课题研究中期，在与开题报告相似的范围内，对论文进展情况进行阶段性报告和考核，以保证论文按进度完成。

3．论文工作、答辩及学位：按学校相关要求执行。

 

 

 

 

 

 

 

 

 

In order to better follow the education policy of CCP and the state that “Education should face the modernization, face the world and face the future”, cultivate high-ranking special personnel who is suitable for teaching, scientific research, the state’s economic construction and social development, give everyone the best opportunities to grow morally, intellectually and physically, to lay down the following requirements for master’s degree applicants:

1.1 Better master basic Marxism principles, insist CCP’ s basic lines, love our motherland, follow disciplines and obey laws, have good moralities, have a cautious study style, have a pretty strong ambition and a self-devotion spirit, active to serve socialism modernization.

1.2 Healthy

1.3 Know the development tendency, research task and important materials systematically, and master the basic knowledge and courses of this program, with the ability and creativity of independent scientific researching.

1) Study period for doctorial degree applicant is 3 years.

2) Study period for post-doctorial degree applicant is 4.5-5 years.

3) Study period for doctorial degree applicant on-the-job is 4-6 years.

1) Analytic Number Theory and Its Application

2) Theory of Finite Groups

3) Matrix Algebra and Its Representations

4) Space Theory and Its Application

5) Geometric Analysis and Convex Body Theory

6) Nonlinear Partial Differential Equations

7) Nonlinear Science and Complex System Behavior

8) Numerical Methods of Nonlinear Partial Differential Equations

9) Soliton Theory and Integrable System

10) Variational Inequality and Optimal Control

11) Matrix Computation and Parallel Algorithm

12) Numerical Rational Approximation and Applications

13) Conservation Equation and Its Numerical Methods

14) Theory and Algorithm for Inverse Problem and Ill-posed Problem

15) Computational Molecular Biology

16) Mathematical Programming

17) Stochastic Model and Intelligent Algorithm

18) Dynamic System and Chaotic Control

19) Graph Theory and Combinatorial Optimization

20) Biological Information and Complex Networks

4.1 Curricular (as listed below)

4.2 Credit Hour Requirements : At least 16 credit hours.

4.3 Students are required to report at least once at public academic seminars, publish at least 2 theses on key foreign journal or national core journals, at least one of which included into the three main searches. (Being the first author of at least one of the thesis and second to the supervisor of the others.)

The cultivation plan shall be made under the instruction of the tutor and submitted to the academic committee of the college. Within one month after the enrollment, the plan is required submitted to the Graduate Department. Courses of doctorial degree are required to be finished within the first academic year.

6.1 demonstration report

6.1.1 The choice of thesis 

The question that thesis discusses is relevant with advanced research belonging to the same specialty or the question comes from important application problems of civil economic construction relevant with the same specialty.

6.1.2Qualifications  

Doctorial degree applicants are required to finish regulated over 16 credit hours and submit 2 literature reading reports or academic discuss reports.

6.1.3Requirements   

Full-time doctorial degree applicants are required to finish a demonstration report of more than 8000 words within one year after the enrollment, doctorial degree applicants on-the-job are required to finish the report within 2 years and post-doctorial degree applicants are required to finish the report within 3 years. The report should include literature summary, the meaning of the thesis, research aim, difficulties, features, expected results, possible innovations, etc. The number of quoted literatures should be at least 50.

6.1.4 Check and approve 

A group of above 7 first-rate subject high–ranking teachers (including 4 professors) should listen to the demonstration report and give their comments, the open-thesis can only be begun after the pass of the check.

6.2 Period report  

At the middle of thesis research and composing period, reports and checks aiming at doctorial thesis performance are required in a scope similar with the demonstration report scope. If the warp is rather big, a yellow card warning will be given.

6.3 Thesis process, oral defense of dissertation and the conference of academic degree should be carried out according to the relevant requirements of Shanghai University.