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上海大学 数学专业攻读硕士学位研究生培养方案

上海大学 /2013-04-20

 

数学专业攻读硕士学位研究生
 
一、培养目标
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,对硕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.身心健康。
3.了解本研究方向的发展趋势,掌握其主攻方向的基本知识,学好本方向的基础课程,对本方向的研究课题和重要文献有系统的了解。具有独立从事科学研究工作的能力和创新能力。
二、学习年限和学分
硕士研究生的学习年限为三年(其中应用数学专业为两年半),在职硕士研究生的学习年限可延长至三年半或四年。
三、主要研究方向
1.解析数论及其应用
2.有限群论
3.矩阵代数及其表示
4.分析及其应用
5.偏微分方程
6.几何分析与凸体理论
7.奇异摄动理论与渐近分析
8.分层理论与非线性偏微分方程
9.变分不等方程与优化控制
10.分支理论的应用及数值方法
11.偏微分方程的边值问题和反问题
12.动力系统及其应用
13.连续介质力学中的数学理论与方法
14.数学建模与工业中的数学反问题
15.数值代数与并行算法
16.偏微分方程数值方法
17.数值逼近与计算几何
18.小波分析与反问题
19.分歧与混沌的理论和算法
20.分数阶微分方程数值解
21.计算流体力学
22.计算分子生物学
23.孤立子理论与可积系统
24.数学规划理论与算法
25.锥优化和内点算法及其应用
26.非线性整数规划理论与算法
27.随机模型与智能算法
28.机器学习与生物信息
29.非线性动力系统与控制
30.组合最优化及应用
31.保险理论与金融数学
32.图论及其应用
四、课程设置及学分要求
1.课程设置(见附表)
2.课程学分要求:课程学分要求达到48学分及以上。
3.要求在攻读硕士学位期间在国外重要期刊或国内核心刊物上发表论文一篇以上。
五、硕博连读资格考试
申请硕博连读的学生需通过资格考试,资格考试通常一年举行两次,时间安排与学校博士生入学考试同步。其他按照上海大学有关文件执行。
六、培养计划的制定
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。
七、论文工作
1.在修满规定学分后,可申请进入论文课题研究,但在开题报告前应递交相关的综述报告。
2.开题报告一般在第二学年第一学期进行,选题应根据专业特点,着重选择对于科学研究和经济建设有应用价值的课题。课题要具有先进性,课题份量和难易程度要适当,并尽量结合国家、部委和上海市的科研任务选题。开题报告应在3000字以上,包括发展现状、选题意义、研究内容、进度安排以及预期成果等。
3.开题报告应组织3名及以上高级职称教师进行评审,为公开性报告。
4.在论文阶段的中期,进行阶段检查和中期考核,对离进度要求偏差较大者,应采取相应措施。
5.在完成论文并经2名高级职称教师双盲评审通过后,组织校内外专家评审答辩。论文答辩通过后,并至少在国外重要期刊或国内核心期刊上发表与学位论文有关的学术论文一篇后才可申请硕士学位。
 
 


 

数学专业硕士研究生课程设置

 
课程编号
课程名称
学时
学分
开课
学期
备注
 
 
 
 
 
 
 
政治
理论课
001000701
科学社会主义理论与实践
30
2
1
 
001000702
自然辩证法
45
3
2
第一
外国语
001000704
公共英语
100
3
1,2
 
011000701
专业英语
40
2
4
专业
基础课
专业课
011000702
泛函分析
40
4
1
根据专业任选三门
011101701
现代分析基础
40
4
1
011101702
近代分析基础
40
4
1
011101703
一般拓扑学
40
4
1
011101704
代数学
40
4
1,2
011101705
现代偏微分方程
40
4
2
011101706
数值代数
40
4
1,2
011101707
逼近论及其算法
40
4
1,2
011101708
数学规划
40
4
1
011101709
应用随机过程
40
4
1,2
 
 
 

 
 
 
 
 
 
 
 
 
 
 

 
 
 
 
 
 
文献
阅读
研讨课
 
 
 
 
 
 
 
 
 
 
文献
阅读
研讨课
 
011101901
拟线性双曲型偏微分方程
40
4
3
 
 
 
 
根据专业任选六门
 
 
 
 
 
 
 
 
 
 
 
 
根据专业任选六门
 
011101902
凸体的Brunn-Minkowski理论
40
4
2
011101903
空间理论基础
40
4
2
011101904
高等矩阵代数
40
4
2
011101905
群论概论
40
4
3
011101906
微分流形初步
40
4
3
011101907
非线性方程组迭代解法
40
4
2
011101908
最优化理论与方法
40
4
3
011101909
不适定问题的解法
40
4
3
011101910
非线性逼近的理论与方法
40
4
3
011101928
矩阵计算
40
4
3
011101911
孤立子理论与可积系统
40
4
3
011101912
二阶椭圆型偏微分方程
40
4
2
011101913
微分方程数值解法
40
4
3
011101914
分数阶微分方程数值解法
40
4
2
011101915
分歧和混沌的数值解法
40
4
3
011101916
布朗运动与随机流系统
40
4
2
011101917
全局最优化
40
4
2
011101918
锥优化和内点算法及其应用
40
4
2
011101919
组合最优化与计算复杂性
40
4
2
011101920
随机模型
40
4
3
011101921
复杂网络——理论与应用
40
4
2
011101922
整数规划
40
4
3
011101923
图论及其应用
40
4
3
011101924
渐进分析和计算机代数
40
4
2
011101925
非线性偏微分方程
40
4
2
011101927
应用数学专题选讲
40
4
3
学术
研讨课
 
 
 
2
 
 

 


 

Cultivation Plan for Master’s Degree of Mathematics
 
1.Cultivation aim
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.
 
2.Duration of the Program
The program is scheduled for 3 years for full-time students, and can be extended to 3 and a half years or 4 years for in-service students.
 
3.Main Orientations of Research
01. Number Theory and Its Applications
02. Theory of Finite Group
03. Matrix Algebra and Its Representations
04. Analysis and Its Applications
05. Partial Differential Equations
06. Geometric Analysis and Convex Body Theory
07. Singular Perturbation and Asymptotic Analysis
08. Stratification Theory and Nonlinear Partial Differential Equation
09. Variational Inequality and Optimal Control
10. Application and Numerical Method of Bifurcation
11. Boundary Value Problems and Inverse Problems in Partial Differential Equations
12. Dynamic System and Its Applications
13. Mathematical Theory and Methods in Continuum Mechanics
14. Mathematical Modeling and Inverse Problems in Industry
15. Numerical Algebra and Parallel Algorithms
16. Numerical Methods for Partial Differential Equations
17. Approximation and Computational Geometry
18. Wavelet Analysis and Inverse Problems
19. Theory and Algorithm of Bifurcation and Chaos
20. Numerical methods for Fractional Differential Equations
21. Computational Fluid Mechanics
22. Computational Molecular Biology
23. Soliton Theory and Integrable System
24. Theory and Algorithm of Mathematical Programming
25. Conic Optimization and Interior-Point Methods and Applications
26. Theory and Algorithm of Nonlinear Integer Programming
27. Stochastic Model and Intelligent Algorithm
28. Machine Learning and Biological Information
29. Nonlinear Dynamic System and Cybernetics
30. Combinatorial Optimization and Application
31. Actuarial Theory and Financial Mathematics
32. Graph Theory with Applications
 
4.Curricular and Credit Hour Requirements
4.1 Curricular (as listed below)
4.2 Credit Hour Requirements: At least 48 credit hours.
4.3 Students are required participate in at least 5 academic seminars, and publish at least one article in key foreign journal or national core journal.
 
5.Qualification exam for consecutive master and doctor program
Students applying for consecutive master and doctor program should pass the qualification exams on a twice-a-year basis, which coincide with doctor enrollment exams. As for the other requirements, they are subject to the regulations specified in the relevant SU documents.
 
6.Setting Cultivation Plan
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.
 
7.Thesis
7.1 After completing the stipulated credit points, postgraduates embark on thesis research, but they are to submit relevant comprehensive report prior to the preliminary conference.
7.2 The preliminary conference is scheduled to take place in the first term of the second academic year. The theme should evolve around scientific research and economic construction in light of the characteristics of the specialty with applied value. The theme should be up-to-date, and achievable through adequate efforts. It's well advisable to link the theme with scientific undertakings of the country, the ministries and Shanghai Municipality. The preliminary lecture covers the quo status of development, the impact of the theme, research content, timetable and expected result.
7.3 The preliminary lecture is to be assessed by at least three teachers with senior academic titles on an open basis.
7.4 Midway through the thesis, stage check-up and mid-term assessment are conducted. Given great deviation from the schedule, appropriate measures should be taken accordingly.
7.5 The theses, upon completion, are examined and approved in the form of dual sampling appraisals by two teachers with senior academic titles before assessment being made by experts both from and outside the university. After the thesis is approved, a degree-related academic article published in foreign key journals or domestic core journals is prerequisite to the acquisition of master's degree.
 
 
 
Curriculum
 

Category
Course number
Course name
Period
Credit
Term
Remarks
Academic degree courses
Political theoretical course
001000701
Scientific Socialist Theory and Practice
30
2
1
 
001000702
Dialectics of Nature
45
3
2
 
First foreign language
001000704
Public English
100
3
1,2
 
011000701
Specialty English
40
2
4
 
Basic and specialty courses
011000702
Functional Analysis
40
4
1
Choose three courses according to specialty
011101701
Introduction for Modern Analysis
40
4
1
011101702
Fundament of Advance Analysis
40
4
1
011101703
General Topology
40
4
1
011101704
Algebra
40
4
1, 2
011101705
Modern Methods in Partial Differential Equations
40
4
2
011101706
Numerical Algebra
40
4
1, 2
011101707
Approximation Theory and Algorithms
40
4
1, 2
011101708
Mathematical Programming
40
4
1
011101709
Applied Stochastic Processes
40
4
1, 2
Required Courses
Literature reading seminar
011101901
Quasilinear Hyperbolic Partial Differential Equations
40
4
3
 
 
 
 
Choose six courses according to specialty
 
 
 
 
 
 
 
Choose six courses according to specialty
011101902
Convex Bodies: The Brunn-Minkowski Theory
40
4
2
011101903
Introduction to Spaces Theory
40
4
2
011101904
Advanced Matrix Algebra
40
4
2
011101905
The Theory of Group
40
4
3
011101906
Introduction of Differential Manifold
40
4
3
011101907
Iterative Solution of Nonlinear Equations
40
4
2
011101908
Theory and Method of Optimization
40
4
3
011101909
Methods of Ill-Posed Problems
40
4
3
011101910
Theory and Method of Non-linear Approximation
40
4
3
011101911
Soliton Theory and Integrable System
40
4
3
011101912
2nd Order Elliptic Partial Differential Equations
40
4
2
011101913
Numerical Methodsfor Differential Equations
40
4
3
011101914
Numerical Methods for Fractional Differential Equations
40
4
2
011101915
Numerical Methods for Bifurcation and Chaos
40
4
3
011101916
Brownien Motion and Stochastic Flow System
40
4
2
011101917
Global Optimization
40
4
2
011101918
Conic Optimization and Interior-Point Methods and Applications
40
4
2
011101919
Combinatorial Optimization and Computational Complexity
40
4
2
011101920
Stochastic Models
40
4
3
011101921
Complex Networks——Theories and Applications
40
4
2
011101922
Integer Programming
40
4
3
011101923
Graph Theory and Its Applications
40
4
3
Seminars
 
 
 
2
 
 

 
 
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