数学专业攻读硕士学位研究生培养方案92483012.doc

数学专业攻读硕士学位研究生培 养 方 案一、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类 别课程编号课程名称学时学分开课学期备注学位课政治理论课001000701科学社会主义理论与实践3021001000702自然辩证法4532第一外国语001000704公共英语10031,2011000701专业英语4024专业基础课专业课011000702泛函分析4041根据专业任选三门011101701现代分析基础4041011101702近代分析基础4041011101703一般拓扑学4041011101704代数学4041,2011101705现代偏微分方程4042011101706数值代数4041,2011101707逼近论及其算法4041,2011101708数学规划4041011101709应用随机过程4041,2必修课必修课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4043根据专业任选六门根据专业任选六门011101902凸体的Brunn-Minkowski理论4042011101903空间理论基础4042011101904高等矩阵代数4042011101905群论概论4043011101906微分流形初步4043011101907非线性方程组迭代解法4042011101908最优化理论与方法4043011101909不适定问题的解法4043011101910非线性逼近的理论与方法4043011101928矩阵计算4043011101911孤立子理论与可积系统4043011101912二阶椭圆型偏微分方程4042011101913微分方程数值解法4043011101914分数阶微分方程数值解法4042011101915分歧和混沌的数值解法4043011101916布朗运动与随机流系统4042011101917全局最优化4042011101918锥优化和内点算法及其应用4042011101919组合最优化与计算复杂性4042011101920随机模型4043011101921复杂网络理论与应用4042011101922整数规划4043011101923图论及其应用4043011101924渐进分析和计算机代数4042011101925非线性偏微分方程4042011101927应用数学专题选讲4043学术研讨课2Cultivation Plan for Masters Degree of Mathematics1Cultivation aimIn 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 states economic construction and social development, give everyone the best opportunities to grow morally, intellectually and physically, to lay down the following requirements for masters 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 Healthy1.3 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.2Duration 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.3Main Orientations of Research01. Number Theory and Its Applications02. Theory of Finite Group03. Matrix Algebra and Its Representations04. Analysis and Its Applications05. Partial Differential Equations06. Geometric Analysis and Convex Body Theory07. Singular Perturbation and Asymptotic Analysis08. Stratification Theory and Nonlinear Partial Differential Equation09. Variational Inequality and Optimal Control10. Application and Numerical Method of Bifurcation11. Boundary Value Problems and Inverse Problems in Partial Differential Equations12. Dynamic System and Its Applications13. Mathematical Theory and Methods in Continuum Mechanics14. Mathematical Modeling and Inverse Problems in Industry15. Numerical Algebra and Parallel Algorithms16. Numerical Methods for Partial Differential Equations17. Approximation and Computational Geometry18. Wavelet Analysis and Inverse Problems19. Theory and Algorithm of Bifurcation and Chaos20. Numerical methods for Fractional Differential Equations21. Computational Fluid Mechanics22. Computational Molecular Biology23. Soliton Theory and Integrable System24. Theory and Algorithm of Mathematical Programming25. Conic Optimization and Interior-Point Methods and Applications26. Theory and Algorithm of Nonlinear Integer Programming 27. Stochastic Model and Intelligent Algorithm28. Machine Learning and Biological Information29. Nonlinear Dynamic System and Cybernetics30. Combinatorial Optimization and Application31. Actuarial Theory and Financial Mathematics32. Graph Theory with Applications4Curricular and Credit Hour Requirements4.1 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.5Qualification exam for consecutive master and doctor programStudents 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.6Setting Cultivation PlanThe 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.7Thesis7.1 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. Its 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 masters degree.CurriculumCategoryCourse numberCourse namePeriodCreditTerm RemarksAcademic degree coursesPolitical theoretical course001000701Scientific Socialist Theory and Practice3021001000702Dialectics of Nature4532First foreign language001000704Public English10031,2011000701Specialty English4024Basic and specialty courses011000702Functional Analysis4041Choose three courses according to specialty011101701Introduction for Modern Analysis4041011101702Fundament of Advance Analysis4041011101703General Topology4041011101704Algebra4041, 2011101705Modern Methods in Partial Differential Equations4042011101706Numerical Algebra4041, 2011101707Approximation Theory and Algorithms4041, 2011101708Mathematical Programming4041011101709Applied Stochastic Processes4041, 2Required CoursesLiterature reading seminar011101901Quasilinear Hyperbolic Partial Differential Equations4043Choose six courses according to specialtyChoose six courses according to specialty011101902Convex Bodies: The Brunn-Minkowski Theory4042011101903Introduction to Spaces Theory4042011101904Advanced Matrix Algebra4042011101905The Theory of Group404301