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Functional Analysis

4

72

/

Real Analysis

4

72

/

Foundation of Probability Theory

4

72

/

Differential Geometry

4

72

/

Abstract Algebra

4

72

/

Partial Differential Equations

4

72

1

/

Algebraic Topology

4

72

/

Complex Analysis

4

72

/

Nonlinear Functional Analysis

4

72

2

/

Stochastic Processes

4

72

/

Numerical Methods of Partial differential Equations

4

72

/

Basics of Control Theory

4

72

/

Foundation of Modern Analysis

3

54

/

/

Selected Topics in Functional Analysis

3

54

/

/

Variational Methods and Applications

3

54

/

/

Function Spaces and Partial Differential equations

3

54

/

/

Elliptic Equations

3

54

/

/

Introduction to Dynamical Systems

3

54

/

/

Hamiltonian Systems

3

54

/

/

Introduction to BifurcationTheory and its Applications to Biomathematics

3

54

/

/

Commutative Algebra

3

54

/

/

Representation Theory of Groups

3

54

/

/

Algebraic Graph Theory

3

54

/

/

Model Theory

3

54

/

/

Digital Image Processing and Analysis

3

54

/

/

Data Mining

3

54

/

/

Artificial Intelligence

3

54

/

/

Graph theory with Applications

3

54

/

/

Mathematical Models and Their Applications

3

54

/

/

Optimization theory and algorithm

3

54

/

/

Finite Element Method

3

54

/

/

Spectral Methods

3

54

/

/

Computational Fluid Dynamics (CFD)

3

54

/

/

Symplectic Geometry and Contact Geometry

3

54

/

/

Differential Topology

3

54

/

/

Riemannian Geometry

3

54

/

/

Lie groups and Lie algebras

3

54

/

/

Stochstic Differential Equations

3

54

/

/

Probability Limit Theory

3

54

/

/

Stochastic Calculus for Finance

3

54

/

/

Levy Processes

3

54

/

/

Homological Algebra

2

36

/

/

Representation Theory of Algebras

2

36

/

/

Analysis and Geometry on Metric Spaces

2

36

/

/

Representation Theory of Finite Groups

2

36

/

/

Rings and Algebras

2

36

/

/

Elliptic Curves

2

36

/

/

Approximation Theory of Functions

2

36

/

/

Wavelets and Splines

2

36

/

/

Singular Integral Operators

2

36

/

/

Littlewood-Paley

Littlewood-Paley Theory

2

36

/

/

Hardy

Theory and Application of Real Hardy Spaces

2

36

/

/

(1)

Function Spaces and Their Applications (1)

2

36

/

/

(2)

Function Spaces and Their Applications (2)

2

36

/

/

Spherical Harmonics

2

36

/

/

Orthogonal Polynomials

2

36

/

/

Entire Functions

2

36

/

/

H^p

H^p Spaces Complex Variable Theory

2

36

/

/

Foundation of Modern Partial Differential Equations

2

36

/

/

Viscosity Solutions

2

36

/

/

System of Partial Differential Equations

2

36

/

/

Nonlinear Evolutional Equations

2

36

/

/

Mathematical Problems in Image Process

2

36

/

/

Mathematical Theory and Computational Methods of Inverse Problems

2

36

/

/

Foundation of Bifurcation Theory

2

36

/

/

Qualitative Theory of Differential Equations

2

36

/

/

Submanifolds and Minimal Submanifolds

2

36

/

/

Multilinear Algebra

2

36

/

/

Markov Processes

2

36

/

/

Interacting Particle Systems

2

36

/

/

Queueing Theory

2

36

/

/

Markov Chains and Applications

2

36

/

/

Branching Processes

2

36

/

/

Large Deviation Principle

2

36

/

/

Random and Graphs

2

36

/

/

Functional Inequalities and Applications

2

36

/

/

Ergodic Theory of Markov Processes

2

36

/

/

Stochastic Control Theory

2

36

/

/

Majorizing Inequalities

2

36

/

/

Foundation of Matrix Theory

2

36

/

/

Matrix Computation

2

36

/

/

Model Theory

2

36

/

/

Recursive Theory

2

36

/

/

Axiom Set Theory

2

36

/

/

Stochastic Processes and Interactional Fields

2

36

/

/

Stochastic Financial Models

2

36

/

/

Stochastic Analysis

2

36

/

/

Coupling and Applications

2

36

/

/

Advanced Markov Chains

2

36

/

/

Measure-Valued Processes

2

36

/

/

Random Walk in Random Environment

2

36

/

/

Limit Properties of Branching Processes

2

36

/

/

Statistical Inference for Stochastic Processes

2

36

/

/

Diffusion Processes and Elementary Stochastic Calculus

2

36

/

/

Linear Statistical Model

2

36

/

/

Errors-in-Variables Model

2

36

/

/

Generalized Linear Models

2

36

/

/

Genetics

2

36

/

/

Mathematical Ecology

2

36

/

/

Factor Space Theory

2

36

/

/

Induction to Fuzzy Sets

2

36

/

/

Optimal Control Theory

2

36

/

/

Adaptive Control

2

36

/

/

System Identification

2

36

/

/

Intelligence Control

2

36

/

/

Computer Control Project

2

36

/

/

Parallel Computing

2

36

/

/

Unix

Unix Operating System

2

36

/

/

Methods of Scientific Computing

2

36

/

/

Seminar of Selected Papers

2

36

/

/

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Symplectic Geometry and Symplectic Topology (I)

2

36

/

5

1

2

1

Functional Analysis

72

4

Baire Banach-SteinhausHahn-Banach

1.

2.

3.

4.

5.

6.

7.

1. Baire

2. Banach-Steinhaus

3.

4.

5.

1. Hahn-Banach

2.

3.

Banach

1.

2.

3.

W. Rudin, Functional Analysis, Second Edition.

K. Yosida, Functional Analysis, Sixth Edition.

Real Analysis

72

4

EuclidLebesgue

Lebesgue

Lebesgue Lebesgue LebesgueRadon-Nikodym FubiniHausedorff RadonRadon Haar

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,,Minkowski, L^p, Hilbert,Hahn,, Radon-Nikodym FubiniTonelli

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2. Hausdorff

3. Radon Riesz

4. Lusins

5. Radon

6. Haar

1. G. B. Folland, Real Analysis, Second Edition, 1999.

2. R. L. Wheeden, Antoni Zygmund, Measure and Integral, 1977

3. W. Rudin, Real and Complex Analysis, Third Edition, 2004

4. H.L. Royden, Real Analysis, Second Edition, 1968.

Foundation of Probability Theory

:72

4

,

:

1

2

3

1

2

3

4

1

2

3

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1 Fubini

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3

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2

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4 Kolmogorov

1

2

3

4

1

2

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Foundations of modern probability O. Kallenberg

ProbabilityA.N. Shiryayev

Probability-Theory and ExamplesR. Durrett

Probability Theory: an Analytical ViewD.W. Stroock

A Course in the Theory of Stochastic ProcessesA.D. Wentzell

Brownian Motion and Martingales in AnalysisR. Durrett

Gibbs Measures and Phase TransitionsH.O. Georgii

Interacting Partical SystemsT.M. Liggett

Theory of Phase TransitionsY.G. Sinai

PercolationF.R. Grimmett

Differential Geometry

72

4

1

2

3 Whitney

4 Frobenius

1

2

3

1

2 Pfaff

3

4 StokesStokes

Stokes

1

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Abstract Algebra

72

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6

7

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1. Thomas W. Hungerford, Algebra , GTM 73.

2. Michael Artin, Algebra.

,.

: Partial Differential equations

:72

4

Sobolev

Sobolev

1

2

3 Sobolev

4

5

1

2

3

4

5

6 Hopf

7

1

2

3

4

1

2

3

1

2

3

4

5

1

2

3

.

.

1. L. C. Evans, Partial Differential Equations (2nd edition), Graduate Studies in Mathematics, vol. 19, American Mathematical Society, Providence, Rhode Island, 2010.

2. G. M. Lieberman, Second Order Parabolic Differential Equations, World Scientific Publish- ing, Singapore, 1996.

3.2014.

4.2003.

5.2003.

6.1997.

Algebraic Topology

1

4

1

2

18

1

2

3 Mayer-Vietoris

4 M-V

5 BrouwerJordan

6

7

8

9 Eilenberg-Steenrod

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5 Kronecker

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5

Poincare

Poincare

1. J.W. Vick. Homology Theory. New York and London: Academic Press, 1973

2. M.J. Greenberg, J.R. Harper. Algebraic Topology. Benjaming-Cummings, 1981

3. James R. Munkres, Elements of Algebraic Topology, Addison-Wesley Publishing Company

30%40%

Nonlinear Functional Analysis

72

4

FrchetGteaux

Brouwer

Leray-Schauder

A-proper

Minmax

1. , ,, , , 2004

2. , . 1985

3. K. Deimling, Nonlinear Functional Analysis, Springer-Verlag, 1985;

4. L. Nirenberg, Topics in Nonlinear Functional Analysis, AMS, 2001

5. K.C. Chang, Methods in Nonlinear Analysis, Springer-Verlag, 2005.

Stochastic Processes

72

4

1.1

1.2

1.3

2.1

2.2

2.3

2.4

2.5

3.1

3.2

3.3

3.4

4.1

4.2

4.3

4.4

4.5

5.1

5.2

5.3

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6.1

6.2

6.3

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7.2

7.3

7.4

1. (2010): . , .

2. (1996): ()., .

3.Chen, M.F. (2004): From Markov Chains to Non-Equilibrium Particle Systems. 2nd Ed. World Sci., River Edge, NJ.

4. Chen, M.F. (2004): Eigenvalues, Inequality and Ergodic Theory. Springer, New York.

5. Ethier, S.N. and Kurtz, T.G. (1986): MarkovProcesses: Characterization and Convergence. Wiley, New York.

6. Ikeda, N. and Watanabe, S. (1989): Stochastic Differential Equations and Diffusion Processes. 2nd Ed. North-Holland, Amsterdam; Kodansha, Tokyo.

7. Sharpe, M. (1988): General Theory of Markov Processes. Academic Press, New York.

Numerical Methods of Partial differential Equations

: 54

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2. Morton, Mayers: Numerical Solution of Partial Differential Equations, Cambridge University Press, (, )

3. ()

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:

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Foundation of Control Theory

72

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1

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2

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7

7.1

7.2

7.3Fourier

7.4

1. 2010.

2. Wonham W. M., Linear Multivariable Control: A Geometric Approach, 2nd edition, Springer-Verlag, 1979.()

Complex Analysis

54

3

1. .

2. , Riemann.

3. .

4.

5 .$H^p$ Fourier .

6 ..

1.

2.

3. Cauchy

4.

1.

2.

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3.

4.

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3.

4. Dirichlet Green

5.

6.

HpFourier

1. Hp

2. Hp

3. FourierFourier

1.

2.

1., . . : , 1995

2... . . : , 1957

3. , , . .:,1989

4. . . : , 1999

5. []Dieter Gaier . . . : ,1992

6. , . . : , 1993

7. M. Andersson. Topics in Complex Analysis}.: , 2005

8. V.Ahlfors. Complex Analysis (Third Edition).:,2004

9. John B. Conway. Functions of One Complex Variable. Springer-Verlag,

New York Heidelberg Berlin, 1978 2nd. Edition,

10. P. L. Duren, Theory of H$^{p}$-Spaces.} Academic Press, New York, 1997

11. W. Rudin. Real and Complex Analysis.Third edition. McGraw-Hill Publishing,

New Delhi, 1987

12. E. M. Stein and R. Shakarchi. Complex Analysis,Princeton Lectures in Analysis II.

Princeton Univ. Press, Princeton. 2003

13. E. M. Stein and G. Weiss. Real and Complex Analysis . China Machina Press,

Beijing. 2004

Foundation of Modern Analysis

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3

Fourier

PoissonFourierSchwartzHilbertRiesz

1.

2. Hardy-Littlewood

3.

4.

Fourier

1. FourierL^1

2. FourierL^2

3. Fourier

Schwartz

1. Schwartz

2.

3.

1. R^n

2. R^{n+1}_+

3.

1. Hilbert

2. Riesz

3. Calderon-Zygmund

4. Fourier

. 2. 2013.

1. E. M. Stein. Harmonic Analysis: Real Varial Methods, Orthogonality, and Oscillatory Integrals. Princeton Univ. Press, Princeton, 1993.

2. E. M. Stein and G. Weiss. Introduction to Fourier Analysis on Euclidean Spaces. Princeton Univ. Press, Princeton, 1971.

3. Modern Fourier Analysis. 2nd Edi., Graduate Texts in Math. 250, Springer-Verlag, Berlin, 2008.

II

II

Selected Topics in Functional Analysis II

54

3

()

, .

, .

, , , , , Hilbert-Schmidt,

1.

2. Cayley

3.

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2.

3. Stone

,,

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2. ,(),

: Variational Methods and Applications

54

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1

1 Banach

2 Sobolev

2

1

2 p-Laplace

4

3

1

2

3 Sobolev

4 Minimax

1 Minmax

2 Mountain Pass

3 Mountain Pass

Paul H. Rabinowitz :Minimax methods in critical point theory with applications to differential equations.

Michael Struwe :Variational methods. Applications to nonlinear partial differential equations and Hamiltonian systems.

Michel Willem: Minimax Methods.

: Function Spaces and Partial Differential equations

: 54

3

BesovTriebel-LizorkinMorrey-Campanato

BesovTriebel-LizorkinMorrey-Campanato

BesovTriebel-LizorkinMorrey-Campanato

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3 SobolevHolder

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4 Morrey-Campanato

1. H. Bahouri, J.-Y. Chemin and R. Danchin, Fourier analysis and nonlinear partial differential equations, Grundlehren der Mathematischen Wissenschaften 343, Springer, 2011

2. R. Danchin, Fourier Analysis Methods for PDE's

3. P.G. Lemarie-Rieusset, Recent development in the Navier-Stokes problem, volume 431 of Chapman & Hall, 2002

4. L. Sivestre and V. Vicol, Hlder continuity for a drift-diffusion equation with pressure, Ann. I. H. Poincar AN 29 (2012), 637652

5. H. Triebel, Theory of function spaces, Monographs in Mathematics, v.78 Birkhuser Verlag, 1983.

Introduction to Dynamical Systems

54

3

SmaleAnosov

1.1

1.2

1.3

2.1

2.2

2.3

2.4Hartman-Grobman

2.5

SmaleAnosov

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3.2 Smale

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4.1

4.2

4.3

4.4

4.5

4.6

5.1

5.2

5.3

5.4

1. , , 2014

2. ,

3. Introduction to the Modern Theory of Dynamical Systems, Cambridge University Press, ;

4. Differential Equations, Dynamical Systems &An Introduction to Chaos, Academic Press

5. Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer-New York.

Hamiltonian systems

: 54

3

1

2

1

2

3

4

1

2

3

4

5

6 -

7

1

2

3

4

Lectures on Hamiltonian systems, J. Moser

Introduction to Hamiltonian Dynamical Systems and the N-Body Problem,K. Meyer and G.Halland D. Offin

Hamiltonian Dynamical Systems and Applications, W. Craig

Mathematical Methods of Classical Mechanics, V.I. Arnold

Introduction to bifurcation theory and its applications in biology mathematics

54

3

Hopf BT

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2

3

4

5

1

2

3 Hopf

4

5 Poincare

6 BT

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2

1

2 Hopf

3 BT

1, , , ,

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2Chow, S. N., Li, C. Z. & Wang, D. Normal Formsand Bifurcation of Planar Vector Fields (Cambridge University Press)1994.

Commutative Algebra

54

3

NoetherianArtinDedekind

Jacobson

1.

2. Jacobson

3.

Nakayama

1.

2.

3. Hom

4.

5.

6.

1.

2.

3.

4.

5.

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2.

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HilbertNoetherian

1. Hilbert

2. Noetherian

3.

4.

1. M.F.Atiyah and I.G.Macdonald, Introduction to commutative algebra, Addison-Wesley, 1969.

2. M.Reid, Undergraduate commutative algebra, Cambridge University Press, 1995.

3. J.Rotman, Advanced modern algebra, Higher Education Press (English reprint), 2004.

4. D.Eisenbud, Commutative algebra with a view toward algebraic geometry, Springer-Verlag, New York, 1995.

Representation Theory of Groups

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3

ArtinBrauer

SchurMaschke

1.

2.

3.

4. Maschke

1.

2.

3.

4.

5.

FrobeiusMackey

1.

2.

3.

YoungFrobenius

1.

2. GL(2), SL(2)

ArtinBrauer

ArtinBrauer

1. Artin

2. Brauer

Peter-Weylbranching law

1.

2.

3. Peter-Weyl

4.

5. SUSO

1. Jean-Pierre Serre, Linear representations of finite groups, GTM 42.

2. William Fulton, Joe Harris, Representation theory, a first course. GTM 129.

3. Michael Artin, Algebra (second edition), Addison Wesley.

:

: Algebraic Graph Theory

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: 3

():

():,

:. , . .

: .

: ; ; ; Tutte ;; ; ; .

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3.

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7.

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:

:; Krein ; P-Q-; .

1.

2.

3. Krein

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5. P-Q-

6.

7.

:, .

:.

:

1. E. Bannai and T. Ito, Algebraic Combinatorics I : Association Scheme,Benjamin.

2. N. Biggs, Algebra graph theory, Cambridge university press, 1993.

3. A. Brouwer, A. Cohen and A. Neumaier, Distance-regular graphs, Springer-Verlag, Berlin, Heidelberg, 1989.

4. A. Brouwer and W. Haemers, Spectra of graphs, Springer, 2011.

5. C. Godsil and G. Rodsil, Algebra graph theory, Springer, 2004.

6. C. Godsil, Algebraic Combinatorics, Chapman and Hall, New York, 1993.

: ; , , .

:

Model Theory

54

3

1. First order logic (summary)

2. Compactness and nonstandard analysis

3. Quantifier elimination and its applications in DLO, DAG, ACF, DCF

4. Realizing and Omitting types

Compactness compactness

5. Saturated/Homogeneous model

type /types

6. IndiscerniblesParis-Harrington Theorem

Pari-Harrington

Classification theory, introduction

Morleys Categoricity Theorem

o-minimal theory

Forking

Algebraic independence

Stable theory

Simple theory

Unstable theory

Recent developments in model theory

1-6

1. Model Theory: An Introduction, by David Marker. Springer, 2003.

2. Model Theory, by C.C. Chang and H.J. Keisler. Elsevier, 3rd ed., 1990.

Digital Image Processing and Analysis

54

3

3

3

6

6

3

3

3

6

3

3

3

3

3

48

1

2

3

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4

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2

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2

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[1] Rafael C. Gonzalez, Richard E. Woods, DigitalImage ProcessingSecond Edition2008.

[2] Rafael C. Gonzalez, Richard E. Woods, Steven L. Eddins, DigitalImage Processing Using MATLAB2009.

[3] KENNETH R. CASTLEMAN, Digital Image Processing, , 2003.

[4] 2009.

[5] 2013.

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Data Mining

54

3

1.

2.

3.

1.

2.

3.

4.

1.

2.

3.

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7.

8.

9.

1.

2.

3.

4.

5.

6.

7.

8.

9.

1.

2.

3.

4.

5.

6.

1.

2.

3.

4.

5.

6.

[1] 2012.7

[2] Jiawe Han Micheline Kamber Jian PeiData Miningconcepts and techniques, Third Edition, Elsevier Inc., 2012.

[3] 2006

[4] 2003

:

:Artificial Intelligence

: 54

3

:

:

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[1] 2006

[2] Artificial Intelligence: A Guide to Intelligent Systems, Second EditionMichael NegnevitskyPearson Education, 2005

[3]Artificial Intelligence: Structures and Strategies for Complex Problem Solving6th Edition()George F.LugerAddison Wesley

[4](6)2010

:

:

Graph theory with applications

54

3

Hamilton

1.1

1.2

1.3

1.4

1.5

1.6

1.7

2.1

2.2

2.3

2.4 Cayley

2.5

3.1

3.2

3.3

Euler Hamilton

4.1 Euler

4.2 Hamilton

4.3

4.4

5.1

5.2

:

Mathematical Models and Their Application

:48

:3

:

:, , ,

:

Continuous Population Models for Single Species

1.1 Continuous Growth Models

1.2 Insect Outbreak Model: Spruce Budworm

1.3 Delay Models

1.4 Linear Analysis of Delay Population Models: Periodic Solutions

Discrete Population Models for a Single Species

2.1 Introduction: Simple Models

2.2 Cobwebbing: A Graphical Procedure of Solution

2.3 Discrete Logistic-Type Model: Chaos

2.4 Stability, Periodic Solutions and Bifurcations

Models for Interacting Populations

3.1 PredatorPrey Models: LotkaVolterra Systems

3.2 Complexity and Stability

3.3 Realistic PredatorPrey Models

Temperature-Dependent Sex Determination (TSD)

4.1 Biological Introduction and Historical Asides on the Crocodilia

4.2 Nesting Assumptions and Simple Population Model

4.3 Age-Structured Population Model for Crocodilia

4.4 Density-Dependent Age-Structured Model Equations

Modelling the Dynamics of Marital Interaction: Divorce Prediction

and Marriage Repair

5.1 Psychological Background and Data: Gottman and Levenson Methodology

5.2 Marital Typology and Modelling Motivation

5.3 Modelling Strategy and the Model Equations

5.4 Steady States and Stability

Reaction Kinetics

6.1 Enzyme Kinetics: Basic Enzyme Reaction

6.2 Transient Time Estimates and Nondimensionalisation

6.3 MichaelisMenten Quasi-Steady State Analysis

6.4 Suicide Substrate Kinetics

Biological Oscillators and Switches

7.1 Motivation, Brief History and Background

7.2 Feedback Control Mechanisms

7.3 Oscillators and Switches with Two or More Species

BZ Oscillating Reactions

8.1 Belousov Reaction and the FieldKorosNoyes (FKN) Model

8.2 Linear Stability Analysis of the FKN Model and Existence of Limit Cycle Solutions

8.3 Nonlocal Stability of the FKN Model

Perturbed and Coupled Oscillators and Black Holes

9.1 Phase Resetting in Oscillators

9.2 Phase Resetting Curves

9.3 Black Holes

Dynamics of Infectious Diseases

10.1 Historical Aside on Epidemics

10.2 Simple Epidemic Models and Practical Applications

10.3 Modelling Venereal Diseases

10.4 Multi-Group Model for Gonorrhea and Its Control.

10.5 AIDS: Modelling the Transmission Dynamics

Reaction Diffusion, Chemotaxis, and Nonlocal Mechanisms

11.1 Simple Random Walk and Derivation of the Diffusion Equation

11.2 Reaction Diffusion Equations

11.3 Models for Animal Dispersal

11.4 Chemotaxis

Oscillator-GeneratedWave Phenomena

12.1 BelousovZhabotinskii Reaction Kinematic Waves

12.2 Central Pattern Generator: Experimental Facts in the Swimming of Fish

12.3 Mathematical Model for the Central Pattern Generator

BiologicalWaves: Single-Species Models

13.1 Background and the Travelling Waveform

13.2 FisherKolmogoroff Equation and Propagating Wave Solutions

13.3 Asymptotic Solution and Stability of Wave front Solutions of the FisherKolmogoroff Equation . .

13.4 Density-Dependent Diffusion-Reaction Diffusion Models and Some Exact Solutions

Use and Abuse of Fractals

14.1 Fractals: Basic Concepts and Biological Relevance

14.2 Examples of Fractals and Their Generation

14.3 Fractal Dimension: Concepts and Methods of Calculation

14.4 Fractals or Space-Filling?

:

:

Mathematical Biology (third edition) , Murray JD, Springer.

1.

2.

3.Applied Nonlinear Dynamical Systems and Chaos, Stephen Wiggins, Springer

:

:

Finite Element Method

: 54

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1. Zhiming Chen, Haijun Wu , Selected Topics in Finite Element Methods, Science Press, Beijing, 2010

2. Brenner S. C., The Mathematical Theory of Finite Element Methods, Springer, 2010.

:

:

Spectral Methods

: 54

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: MATLABFORTRAN

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5.JacobiJacobi

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4. KDV

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3. Galerkin

4. Poisson

:

1.

2. Laguerre-Hermite

3. Stokes

4. Navier-Stokes

5.

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: +

()()

1. Jie Shen and Tao Tang, Spectral and High-Order Methods with Applications, Science Press, Beijing, 2006

2. Jie Shen, Tao Tang and Lilian Wang, Spectral Methods: Algorithms, Analysis and Applications, Springer, 2011

3. Lloyd N. Trefethen, Spectral Methods in Matlab, SIAM,Philadelphia, 2000

:

:

Computationall Fluid Dynamics (CFD)

: 54

: 3

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Symplectic Geometry and Contact Geometry

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Hofer-Zehnder Hofer , FloerGromov-Witten

J 1997

Ana Cannas da Silva Lectures on Symplectic Geometry

LNM(1764), Springer-VerlagBerlin 2001.

D.McDuff and D.Salamon, Introduction to Symplectic Topology,

Clarendon PressOxford 1998.

D.McDuff and D.Salamon, J-curves and Symplectic Topology,

(AMS)Colloquium Publications( Vol.52), Providence, Rhode Island 2004

H.Hofer and E.Zehnder Symplectic Invariants and Hamiltonian Dynamics

Birkhauser Advanced Texts: Verlag Basel.Springer-Verlag Berlin 1994.

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Differential Topology

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J. Milnor, Topology from a differential viewpoint, University of Virginia Press.

V. Guillemin, A. Pollack, Differential Topology, Prentice Hall, Inc.

M. Hirsch, Differential Topology, Springer.

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Lie Groups, Lie Algebras, and Their RepresentationV.S. VaradarajanSpringer-VerlagWorld Publishing CorporationBeijingChina1984

1998

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Differentiial Geometry , Lie Groups, and Symmetric Spaces, S. Helgason, Academic, New York, 1978

Introduction to Lie Algebras and Representation Theory, J. E. Humphreys, Springer-Verlag, New York Berlin, Heidelberg , 1972

30%40%

Branching Processes

54

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Branching Processes, K.B. Athreya and P.E. Ney

The Theory of Branching Processes T.E. Harris

IntroductoryLecturesonFluctuationofLevyProcesswithApplication,A.E.Kyprianou

SpatialBranchingProcesses,RandomSnakesandPartialDifferentialEquations,

Jean-Franois,LeGall

Levy Processes

54

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Introductory Lectures on Fluctuation of Levy Process with Application, A.E. Kyprianou

Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance,

G. Samorodnitsky and M.Taqqu

Levy Processes and Infinitely Divisible Law, K. Sato

Levy Processes and Stochastic Calculus, D. Applebaum

Levy Processes: Theory and Applications, E. Banrdorff and Thomas Mikosch

Foundations of modern probability O. Kallenberg

A Course in the Theory of Stochastic ProcessesA.D. Wentzell

Brownian Motion and Stochastic CalculusI. Karatzas et al et al

Stochastic Differential Equations and Diffusion ProcessesN. Ikeda et al

Measure-valued Branching Processes, Zenghu Li

Stochastic Differential Equations

54

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Stochastic Differential Equations B. Oksendal

Harnack Inequalities for Stochastic Partial Differential Equations Feng-Yu Wang

Brownian Motion and Stochastic CalculusI. Karatzas et al

Stochastic Differential Equations and Diffusion ProcessesN. Ikeda et al

Stochastic calculus for finance

54

3

Markov

Black-Scholes

1. Steven E. Shreve, Stochastic calculus for finance, Springer, 2004.

2. M. Steele, Stochastic Calculus and Financial Applications. Springer, 2000.

3. A. Etheridge, A Course in Financial Calculus. Cambridge Univ Press, 2002

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Ringes and Algebras

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Elliptic Curves

, , , , zeta, Galois,

(Approximation Theory of Functions)

Jackson Berstein N-

(Wavelets and Splines)

Fourier

(Singular Integral Operators)

Littlewood-Paley (Littlewood-Paley Theory)

Littlewood-Paley Littlewood-Paley Littlewood-Paley

Hardy (Theory and Application of Real Hardy Spaces)

HardyBMOC-Z

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FourierCaldern-ZygmundLpHardyBMO

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1HardyBesovTriebelLittlewood-PaleyT(1)Heisenberg

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, H^P, , Taylor, H^P, , H^PH^P, Corona

(Modern Partial Differential Equation Basis)

(Viscosity Solutions)

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L2, Schauder, Lp

Nonlinear Evolutional Equations

Mathematical Problems in Image Process

Mathematical Theory and Computational Methods of Inverse Problems

(Foundation of Bifurcation Theory )

HopfPoincare Hilbert 16;

(Qualitative Theory of Differential Equations)

Poincare-BendixsonHopf

(Submanifolds and Minimal Submanifolds)

, KaehlerBochner

(Multilinear Algebra)

(Majorization)

(Foundation of Matrix Theory)

M-

Matrix Computations

(LU, QR, SVD)QRLanczosJacobi.

(Model Theory)

(Recursive Theory)

(Axiom Set Theory)

ZF Forcing

(Markov Processes)

FellerHunt,

(Stochastic Calculus)

,

(Probability Limit Theory)

(Interacting Particle Systems)

FKG

(Random Walks in Random Environments)

annealedquenched0-1

(Linear Statistical Model)

BLUE

(Large Sample Statistical Inference)

(Errors-in-Variables Model)

Generalized Linear Models

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(Factor Spaces Theory)

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Adaptive Control

System Identification

Intelligence Control

Computer Control Project

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Unix (Unix Operating System)

UnixLinuxShellUnixCUnixUnixUnix

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