數(shù)學博士培養(yǎng)方案（英文版）

EducationalPlanforAcademicPhDCandidates

Discipline:Mathematics

Disciplinecode:0701

I.Objectives

a．NurtureseniortalentslovingthemotherlandandsupportingtheleadershipoftheCPC,abidingbythedisciplineandlaw,possessinggoodconduct,obeyingacademicnorms,havingrigorousandrealisticscientificattitudeandenterprisingspirittowardslearning,engagedinresearchingofmathematicaltheoryandapplications;

b.Masterbroadandsolidmathematicalfoundationtheory,havesystematicandin-depthexpertise,familiarwiththeinternationalpresentsituationandadvancedresearchprojectsandprogressintherelatedmajors;

c.Obtainthewholeprocessofscientificresearchtraininginrelatedmajors,possesscapabilitytoconductindependentlyscientificresearch,teaching,orotherpracticalworkability.Makecreativeachievementsinrelatedworkofthefield,qualifieddoctoralthesisachievingtherequirementsoftheuniversity;

d.Atleastmasteroneforeignlanguage,proficiencyinreadingandunderstandingforeignliteraturerelatedtothissubjectinthefield.Possesscapabilitytousetheforeignlanguagetowriteacademicpapersindependentlyandtoconductacademiccommunicationinforeignlanguageatinternationalconferences.

II.Sub-disciplineandResearchDirections

Sub-discipline

Code

ResearchDirections

PureMathematics

070101

Fractalgeometry

Geometryandtopology

Algebra

Functionalanalysis

ComputationalMathematics

070102

Numericalmethodsfordifferentialequationsandapplica-tions

Intelligentcomputingandimageprocessing

Mesoscopicmodelingandsimulationofnonlinearsystems

ProbabilityandMathematicalStatistics

070103

Stochasticanalysis

Stochasticdynamicalsystems

Mathematicalstatistics

AppliedMathematics

070104

Partialdifferentialequationsandapplications

Harmonicanalysisanditsapplications

Dynamicalsystemsandapplications

OperationalResearchandControlTheory

070105

Theoryandmethodforoptimization

Controltheoryanditsapplications

III.Educational

Duration

Thenormativetimeforfull-timePhDstudentsis3-5years.ThedurationforMD-PhDstudentsis4-6years.

IV.CreditsRequirement

CreditsforcommonPhDstudentswithMasterdegree≥29.CreditsforMD-PHDanddirectPHDstudents≥53.

Category

MD-PhDanddirectPhDstudents

CommonPhDstudents

Totalcredits

≥53

≥29

Coursescredits

≥34credits,(includingcreditsforadvanced

orinternationalcourses≥6)

Compulsorypubliccourses≥9credits:

Studyontheoryandpracticeof

C

hinese

characteristics

:2credits

ChineseMarxism:2credits

DialecticsofNature:1credit

Foreignlanguageforpostgraduatestudents:2credits

Englishthesiswriting:2credits

Optionalpubliccourses≥1credit

≥10credits

(includingcreditsforadvancedorinternationalcourses≥2)

Compulsorypubliccourses≥4credits:

ChineseMarxism:2credits

Englishthesiswriting:2credits

Disciplinebasiccoursesandprofessionalcourses≥24credits:

1st-leveldisciplinebasiccourses:8credits(compulsory)

2nd-leveldisciplinebasiccourses:4credits(restrictedoptional)

Professionalcoursesforpostgraduatestudents:4credits(optional)

Cross1st-leveldisciplinecourses:4credits(optional)

ProfessionalcourseforPhDstudents:4credits(optional)

Cross1st-leveldisciplinecourses:2credits(optional)

ProfessionalcourseforPhDstudents:4credits(optional)

Nocreditformake-upcoursesandotheroptionalcourses,gradesonly.

Research

≥19credits

Literaturereviewandthesisproposal:1credit

≥19credits

Literaturereviewandthesisproposal:1credit

ParticipationininternationalacademicconferencesorinternationalacademicconferenceheldinChina,andpapersubmission:1credit

ParticipationininternationalacademicconferencesorinternationalacademicconferenceheldinChina,andpapersubmission:1credit

Dissertationinterimprogressreport:1credit

Dissertationinterimprogressreport:1credit

Academicpaperpublication:1credit

Academicpaperpublication:1credit

Doctoraldissertation:15credits

Doctoraldissertation:15credits

Remark:EducationplanforstudentswithanequivalenteducationlevelisinaccordancewiththeeducationplanforMD-PhDanddirectPhDstudents.Coursesexemptionwillbegranteduponfindingconformitywiththecourseexemptionprovision.

V.CourseCurriculumandCreditsAllotment

Courses

Coursecode

Coursename

Hours

Credits

Season

Department

Notes

Degreecourses

Compulsorypubliccourses

408.602

DialecticsofNature

18

1

Spring/

Autumn

CollegeofMarxism

Compulsory

≥6credits(atthepostgraduatephase)

408.601

Studyontheoryandpracticeof

C

hinese

characteristics

36

2

Spring/

Autumn

CollegeofMarxism

411.500

Foreignlanguage(English)

32

2

Autumn,

Spring

Schoolofforeignlanguages

Optionalpubliccourses

1

408.810

ChineseMarxism

36

2

Autumn

CollegeofMarxism

CompulsoryforPhDstudents≥4credits

411.800

Englishthesiswriting

24

2

Autumn

Schoolofforeignlanguages

1st-leveldisciplinebasiccourses

011.520

FunctionalAnalysis(advanced)

64

4

Autumn

SchoolofMathematicsandStatistics

Compulsory≥8credits(atthepostgraduatephase)

011.521

Topology(advanced)

64

4

Autumn

SchoolofMathematicsandStatistics

011.522

Algebra(advanced)

64

4

Autumn

SchoolofMathematicsandStatistics

011.523

AdvancedProbabilityTheory(advanced)

64

4

Autumn

SchoolofMathematicsandStatistics

011.524

AdvancedNumericalAnalysis(advanced)

64

4

Autumn

SchoolofMathematicsandStatistics

011.532

AdvancedMathematicalStatistics

64

4

Autumn

SchoolofMathematicsandStatistics

2nd-leveldisciplinebasiccourses

011.528

PartialDifferentialEquations(advanced)

64

4

Spring

SchoolofMathematicsandStatistics

Restrictedoptional≥4credits(atthepostgraduatephase)

011.529

MeasureTheory

64

4

Autumn

SchoolofMathematicsandStatistics

011.530

GeneralizedFunctionsandSobolevSpaces(advanced)

64

4

Autumn

SchoolofMathematicsandStatistics

011.519

ComplexAnalysis

64

4

Spring

SchoolofMathematicsandStatistics

011.517

TopicsofAbstractAlgebra

64

4

Spring

SchoolofMathematicsandStatistics

011.518

AnIntroductiontoDifferentialManifold

64

4

Spring

SchoolofMathematicsandStatistics

011.531

OperationsResearchTheory,ModelandMethod

64

4

Spring

SchoolofMathematicsandStatistics

011.533

TheModernNumericalMethodsforDifferentialEquations

64

4

Autumn

SchoolofMathematicsandStatistics

011.536

StochasticProcess(international)

64

4

Spring

SchoolofMathematicsandStatistics

011.537

Stochasticanalysis

64

4

Spring

SchoolofMathematicsandStatistics

professionalcoursesforpostgraduatestudents

011.534

SemigroupsofLinearOperatorsandEvolutionEquations

(international)

64

4

Autumn

SchoolofMathematicsandStatistics

≥4credits(atthepostgraduatephase)

011.535

MethodsofModernMathematicalPhysics

64

4

Autumn

SchoolofMathematicsandStatistics

011.605

Stochasticdifferentialequation

64

4

Autumn

SchoolofMathematicsandStatistics

011.606

Calculusofvariation

64

4

Autumn

SchoolofMathematicsandStatistics

ProfessionalcourseforPhDstudents

011.800

FractalGeometry

64

4

Spring/

Autumn

SchoolofMathematicsandStatistics

≥4credits

011.801

NumberTheoryandArithmetic

64

4

Spring/

Autumn

SchoolofMathematicsandStatistics

011.814

StochasticDynamicalSystems(international)

64

4

Spring/

Autumn

SchoolofMathematicsandStatistics

011.803

DynamicalSystems

(international)

64

4

Spring/

Autumn

SchoolofMathematicsandStatistics

011.804

NonlinearEvolutionalEquations

64

4

Spring/

Autumn

SchoolofMathematicsandStatistics

011.805

InfiniteDimensionalDynamicalSystems

64

4

Spring/

Autumn

SchoolofMathematicsandStatistics

011.806

HarmonicAnalysis

64

4

Spring/

Autumn

SchoolofMathematicsandStatistics

011.807

NumericalMethodsforDelaySystemsandTheirTheory(international)

64

4

Spring/

Autumn

SchoolofMathematicsandStatistics

011.808

TheoryofComputationalMethodsforEvolutionEquations

64

4

Spring/

Autumn

SchoolofMathematicsandStatistics

011.809

ApproximationandComputation

64

4

Spring/

Autumn

SchoolofMathematicsandStatistics

011.810

ModelingandsimulationoflatticeBoltzmannmethod

64

4

Spring/

Autumn

SchoolofMathematicsandStatistics

011.811

BasicTheoryofOptimalControl

64

4

Spring/

Autumn

SchoolofMathematicsandStatistics

011.812

MathematicalControlTheory(international)

64

4

Spring/

Autumn

SchoolofMathematicsandStatistics

011.817

Thetheoryofinvariantmanifold

(international)

64

4

Spring/

Autumn

SchoolofMathematicsandStatistics

011.818

Stochasticfiniteelementmethod

64

4

Spring/

Autumn

SchoolofMathematicsandStatistics

011.819

NumericalmethodsforStochasticpartialdifferentialequations(international)

64

4

Spring/

Autumn

SchoolofMathematicsandStatistics

011.820

Perturbationtheoryofrandomsystems(international)

64

4

Spring/

Autumn

SchoolofMathematicsandStatistics

Cross1st-leveldisciplinecourses

CompulsoryforPhDstudents≥2credits

Non-

degreecourses

Make-upcourses

1.FunctionsofRealVariables

FunctionalAnalysis

PartialDifferentialEquations

GeneralTopology

SchoolofMathematicsandStatistics

CompulsoryforNon-MathematicalandNon-Statisticalmajorundergraduates

Research

650.801

Literaturereviewandthesisproposal(PhD)

1

SchoolofMathematicsandStatistics

650.802

ParticipationininternationalacademicconferencesorinternationalacademicconferenceheldinChina,andpapersubmission(PhD)

1

650.803

Dissertationinterimprogressreport(PhD)

1

650.804

Academicpaperpublication(PhD)

1

650.805

Doctoraldissertation(PhD)

15

650.501

Literaturereviewandthesisproposal(MD)

1

650.502

AcademicReportinacademicconferences(MD)

1

650.503

DegreeDissertation(MD)

10

Remark:pleasemarktheadvancedinternationalcoursesafterthecoursename.

VI.SpecificRequirementsforPhDCandidatesEducation

TheeducationmodeforPhDstudentsemploysthesupervisor-responsiblesystem,byestablishingthesupervisor-headedinstructiongroup.ThesupervisorisresponsibleforthecultivationandassessmentofthePhDcandidates.

RestrictionofCross1st-leveldisciplinecourses

(1)Cross1st-leveldisciplinecoursesrefertotheotherpostgraduatecoursesinthesamelevel.Studentsarerequiredtoattendclassandtaketheexaminationofthecourse.

(2)Cross1st-leveldisciplinecoursesselectedshouldbedifferentfromthe