Wednesday, March 26, 2008

Course description 7

24. Western Economics

Short description of macro and mecro economics.

25. Finite Element Method

Short description, small deformation non-linear solid mechanics problems, non-linear quasi-harmonic field problems. Iterative techniques, Ritz-Galerkin approximation, error estimates, piecewise polynomial apaces - the Finite Element Method.

26. Computer Application Technology VB

Short description , basis concepts , overview of computers and programming , algorithm, data type, expression type, parameter passing among functions, local and global variables and the recursive programming . Design Using VB, variables and basic types, arrays and pointers, functions, algorithms, tools for large programs, specialized tools and techniques.

27. Elementary Number Theory

Short description, Integral the most basic property. Sums of higher powers and fermat’s last theorem. Divisibility and the greatest common divisor, linear equations, factorization and the fundamental theorem of arithmetic, congruences, powers, and Fermat’s little theorem, computing kth roots, Roots.

28. Computer Graphics

Short description, overview of graphics systems, geometric transformations. Two-dimensional viewing, three-dimensional viewing, three-dimensional object representations, visible-surface detection nethods, color models and color applications, computer animation, etc..

29. Spectral Method Numerical Analysis

Short description ,Chebyshev difierentiation matrices, Chebyshev difrentiation by FFT, Clenshaw curtis quadrature, complex arithmetic, eigenvalue problems, finite difference methods. GauSS quadrature, Laplace and Poisson problems, nonlinear problems, spectral accuraecy.

30.The website design

Short description and introduce various website design software. For example, Dreamweaver, ASP, JSP, FrontPage, HTML, JavaScript, VBScript.

Course description 6

19. Matrix Theory

Matrix analysis, general linear systems, special linear systems, linear space and linear transformation, orthogonalization and least squares. The unsymmetric eigenvalue problem, the symmetric eigenvalue problem. Iterative methods for linear systems, reductions and transformations. Methods for the dominant eigenvalue. Methods for the subdominant eigenvalue. Inverse iteration. Jacobi's methods, Givens and Householder's methods. Eigensystem of a symmetric tridiagonal matrix. The LR and QR algorithms. Extensions of Jacobi's method, extension of Givens' and Householder's methods. QR Algorithm for Hessenberg matrices. SOR method and related methods.

20. Visual C++

Short description ,basic facilities. Design using C++, variables and basic types, library types, arrays and pointers, functions, algorithms, tools for large programs, specialized tools and techniques.

21. Partial Differential Equations

Short description, basics of functional analysis. Lax-Milgram lemma, Sobolev spaces, Galerkin methods, the finite element method, basic features, convergence analysis for 1D problems. Error control, a-priori and a-posteriori analysis. Advection-diffusion problems. Stabilization techniques, Galerkin Generalized schemes for boundary layer problems. Parabolic problems. Space-time approximations with finite elements and finite differences. Hyperbolic (convection) problems. conservative finite difference schemes for scalar problems. Continuous and discontinuous finite elements.

22. MATLAB 2

Short description , mainstream areas of image processing. intensity transformations, linear and nonlinear spatial filtering, filtering in the frequency domain, image restoration and registration, color image processing, image data compression, morphological image processing, image segmentation, region and boundary representation and description, and object recognition. Solve image processing problems using MATLAB and IPT functions. New function was written and documented , implement new image processing software solutions.

23.The information science and foundation

Short description, entropy,relative entropy and mutual information, entropy rates of stochastic process, channel capacity, differential entropy, the Gaussian channel, information theory, coding, channel coding theorem.

Course description 5

15. Methods of Optimizations

General outline ,basic definitions, linear programming, maximize and minimize problems. Decision making under uncertainty and decision making with multiple objectives. Linear programming and related topics, the simplex algorithm. One-variable case, descent methods, analysis of quadratic objective functions, quadratic-fitting algorithms, nelder-meade algorithm and simulated annealing, constrained minimization.

16. Discrete Mathematics ,

Short description. Digital logic, set theory, proposition logic, conditional statements , valid andinvalid arguments ,graphics, predicate logic, the logic of quantified statements, two classical theorems, algorithms, sequences, mathematical induction, sets, set theory and axion system. Relation function, chain and ring, tree, binomial theorem, Euler graph and Homulton graph.

17. Numerical Analysis

Short . description ,mathematical preliminaries, Taylor’s Theorm, orders of convergence ,computer arithmetic, floating-point numbers and errors, stable and unstable computations conditioning. Solution of nonlinear equations, bisection (Interval Halving Method, Newton’s Method, Secant Method), fixed points. and functional iteration,computing roots of polynomials. Homotopy and continuation methods. Solving systems of linear equations, matrix algebra, LU and Cholesky factorizations, pivoting and constructing an algorithm,norms and the analysis of errors, neumann Series and iterative refinement,analysis of roundoff error in the Gaussian algorithm. Selected topics in numerical linear algebra, QR-algorithm of francis for the eigenvalue problem,approximating functions, Hermite interpolation, spline interpolation,Taylor series,interpolatlon in higher dimensions,continued fractions, adaptive approximation, Gaussian quadrature, Romberg integration,Bernoulli polynomials and the Euler-Maclaurin formula,numeriral solution ot ordinary differential equations. Runge-Kutta methods, multistep methods,boundary-value problems,linear differential equations.

18.Data structure

Short description, programming languages, object oriented programming, basic concepts and experiences. Advanced concepts and techniques, multi-threaded programming, basic mathematical techniques, recurrence equations, algorithm analysis. Fundamental algorithms and data structures, lists, queues, stacks, search and sorting, binary trees. Advanced algorithms and data structures, specialized tree data structures, tree search, graphs, search, order.

Tuesday, March 25, 2008

Course description 4

11. Probability & Statistics
Short description, sample space and axiomatic definition of a probability measure. Probabilistic models of the real line. Conditional probability and independence. Random variables and probability distributions. Main discrete and continuous random variables. Expectation, moments and characteristic functions. Independence of random variables. Multidimensional gaussian laws. Different kinds of convergence of sequences of random variables. Law of Large Numbers and Central Limit Theorem.
12. Mathematical Modeling
Short description, Modeling process , Modeling Change , the elementary grade model, stability model. simulation modeling, discrete probabilistic modeling, graphs of functions as modeling and examples.

13. Matlab 1
Short description, introduction to the fundamentals of MATLAB functions and programming, the class proceeds to address the mainstream areas of image processing. Compiler, a new function was written and documented, M-files, code optimization. Cell arrays and structure, visualizing data and function, notebook, M-functions, generating and plotting image histograms etc..
14. Database Management System
Short description, brief introduction to data models and formal languages for databases , how to develop server-side and client-side database applications and analyze business intelligence data. All of the brand-new features, Reporting Services, Integration Services, Notification Services, and Service Broker, create custom management scripts with SQLCMD, and improve performance with SQL Profiler, relation data theories, database design. Using SQL both as a query and data manipulation language, designing and querying databases, Entity-Relationship.

Course description 3

8. Analytical Mathematics (Calculus)
Short description, basics of logic and set theory. Real numbers numerical sequences and series,cartesian coordinates. Differential and integral calculus for real functions of several variables, limits, continuity, partial derivatives, gradient, differential, implicit functions and Parametric curves, curvilinear integrals of scalar fields. Multiple integrals, parametric surfaces and surface integrals, differential forms and conservative fields. Gauss, Green, and Stokes theorems. Sequences and series of functions, pointwise and uniform convergences. Fourier series of periodic functions. Euler formula. Real functions, derivatives and differentiation rules, properties of differentiable functions on intervals, searching maxima and minima, differential. Taylor polynomial and Taylor formula. Convex functions, qualitative study of the graph of a function. Riemann proper integral. Fundamental Theorem of Calculus. Integration methods. Cauchy problem, existence and uniqueness, continuous dependence on data, regularity and extension of the solution. Qualitative study of solutions to first order differential equations. phase space, stability analysis in the linear case and in the nonlinear case, Discrete dynamical systems, graphical and qualitative analysis, equilibria and periodic orbits, stability criteria, bifurcation, logistic growth, chaotic phenomena. Analytic functions. Functional analysis. Distributions. Fourier transform, Laplace transform and Z transform.
9. C-Programming Language
Short description , basis concepts , overview of computers and programming , algorithm, data type, expression type, parameter passing among functions, local and global variables and the recursive programming.
10. Ordinary Differential Equations
First order equations, explicit first order equations. The linear differential equation. Implicit first order differential equations, complex differential equations, the higher differential equation power series expansions, upper and lower solutions. Maximal and minimal integrals.

Course description 2

5. Linear Algebra
Polynomial, matrices , binomial ,linear spaces, linear transformations, λ-matrix. Euclid space . Determinant of a square matrix and its properties. Rank of a matrix, inverse matrix, linear systems of equations. Eigenvalues and eigenvectors of a matrix, matrix similitude and diagonal form of a real symmetric matrix. Orthogonal matrix and their basic properties, vector spaces linear dependence and linear independence. Bases and dimension. Linear maps . Matrices related to a linear map, rank and nullity theorem, analytic geometry. Geometric vectors and their algebra. Chauchy-Schwartz Theorem. Straight lines and planes in the space. Parallelism and orthogonality properties. Matrices and determinants. Methods for solving linear systems. Eigenvalues and eigenvectors. Matrix diagonalization. canonical forms.
6.Analytic geometry
Basis concepts of vector and coordinate, locus and equation, plane and space, space line, cylindercal surface, conical surface, revolve surface and quadratic surface. Planar and spatial vectors. Vector space and scalar product. Straight lines and planes. Parallelism and orthogonality. Linear applications. Changes of planar and spatial coordinates. Polar coordinates. Conic sections and quadric surfaces, qualitative study of the graph of a function.
7. General Physics
Short description ,the electric field and magnetic field, electromagnetics, vibrate and undulate, quantum physics.

Course description 1

1.Fundamental Mathematics & Geometry
Basis concepts,equation and systems of equations, function, complex number, inequation, ordered series of numbers, permutation, combination and binomial formula, analytic functions. Functional analysis, vector, space, camber.
2.Fundamental Chemistry
Basis concepts, elements and compounds, chemical formula, mole, simple reactions, stoichiometry. Atomic structure, nucleus, molecules and electrons. The electronic structure of atoms and the periodic system. The chemical bond, ionic bonding, crystal structure and properties of ionic compounds, description of the gaseous state by the ideal-gas equation of state and of solids and liquids by phase diagrams. Chemical thermodynamics, first and second principles of thermodynamics. Application to the calculation of the heat, spontaneity and equilibrium conditions of chemical reactions. The molecular collision model of chemical reactions. Parameters affecting reaction rates. Catalysts, reactions and equilibria in aqueous solutions. Acids, bases and acid-base equilibria . Autoprotolysis of water and the pH. Red-ox reactions. Electrochemical cells, electromotive force, electrolysis.
3. Fundamental Physics
Short description , basis concepts of mechanical vibration and the mechanical wave, thermodynamics, electromagnetics, optics etc..
4. Computer Science
Short description, Introduction to the structure of operating systems with reference to Windows 98, processes description and Microsoft office .Introductory concepts of TCP/IP, Internet. multi-media technique and MPC ,HTML , memory management and virtual memory ,memory and I/O devices interfacing, etc..

Diploma and Degree Certificate

Diploma and Degree Certificate
(English copy)
This is to certify that xxxxxxxxxxxxxxx , born in Xinjiang Province,Oct.1 x ,198 x has studied for 5 years from Sep.2001 to July 2006 in the institute of Mathematics and System Science majoring in Information and Computing Science, has completed all the courses prescribed in the Teaching Programme,and has passed all the exams necessary for graduation from Xinjiang University. Having fulfilled the requirements stipulated by the Academic Degree Regulations of the People’s Republic of China, he is awarded the degree of Bachelor of Science.
Xinjiang University
Registered Certificate No: xxxxxxxxxxxxxxxxxxxxx

Monday, March 24, 2008

Sample honor certificate!

Honor Certificate

(English copy)

This is to certify that Mr. xxx a undergraduate student in our Institute of Mathematics & System Science , received eight times scholarship for excellent students , which only students among the top five percent are entitled to.

Xinjiang University


Registered Certificate No: xxx


aaa zzz ), male, born in October, 19 xx , majoring in the Applied Chemistry of XINJIANG UNIVERSITY and having completed 4 years study from September, 200 1 to July, 200 6 , is graduated. He is now awarded Degree of Bachelor of Science according to the Regulation of Degree in people’s Republic of China.

Chairman, Degree Committee: ANNIWAER AMUTI


DATE OF ISSUE: July 1, 200 6

Certificated serial No: bbb

The sample certificate of diploma 1.



This is to certify that xxx xxx ), male, born in October, 1982, has studied Applied Chemistry in XINJIANG UNIVERSITY from September 2000 to July 2005.Upon completing and being qualified for all the required courses of the 4 years undergraduate program, he is granted graduation.



Certificated serial No: xxxxx




Information & Computing Science

Mathematics & System Science Institute

830046, Xinjiang University


Phone : +86 991 xxx

E-mail : xxxxxx @ xxxx .com


An energetic, multi-lingual, self-motivated, disciplined, team working student.


2004/07-2004/08: taught mathematics (Algebra, Geometry), Physics to middle school students in Atush.

2005/01-2005/07: taught English at Ultash School in Urumqi, on weekends.

Currently, teaching English at Atlan Language Training Center in Urumqi.


2001/09-2006/07 BSc in Mathematics, Xinjiang University, P.R.China

Major: Information & Computing Science ( currently final year student)


2001-2002 School year, scholarship for excellent students, Xinjiang University.

2002-2003 School year, scholarship for excellent students, Xinjiang University.

2003-2004 School year, excellent student award of Xinjiang University

Second awards in English speaking contest, Xinjiang University.


Operating System: Windows 9x, 2000, XP.

Programming: C, VB, VC++, Foxpro, SQL, Matlab

Environment: Microsoft Office


Mother tongue: Uighur

Fluent: in English, Chinese (writing, reading, speaking, listening)


Honest, hardworking, conscientious, humorous, popular with fellow students


Music, reading, hiking, backpacking, basketball, guitar, piano, astronomy

Computer Skills!

Dear Professors:

Here I would like to state which programming languages I master. They are as follows:

1. Matlab: I took one semester of Matlab course and I am taking Signal Processing course in Matlab this semester. We did all the computer experiments of Numerical Analysis and Optimization and Numerical Solutions of PDEs in Matlab, and that is the main computational tool that our department has been using. I would say that is the main tool that I master.

2. C programming language

3. VB

4. VC++

5. Foxpro / SQL

6. Maple / Mathematica

7. Latex

Those are the programming languages that I took and also good at.

I hope that will give you some information about my computer skills.

Sincerely yours,


( xxx , Chinese transliteration)



This is to certify that Mr. xxx ( xxx , Chinese Transliteration) has been enrolled as an undergraduate student at Institute of Mathematics and System Science of Xinjiang University during the period off September, 2001-June 2006. He is currently final year student in our department.


Professor of Mathematics

Information & Computing Science

Mathematics & System Science Institute

830046, Xinjiang University


Tel : +86 991 8580377

Fax: +86 991 8580377

E-mail : xxx

Application for Scholarship !!!

Dear Sir / Madam,

Here I have sent my application for Master s studies in your esteemed institute. Along with my application, I express my desire to be considered as a candidate for scholarship. Since the economical problem is the major issue to study in high living standard environment for me, such as xxx , even if I have the strong competence. The scholarship would be the great reward and encouragement to me for further academic studies. I will show the benefit of scholarship with my strong academic records if I have the chance among the scholarship receivers.

Hope you kindly consider me for the possible candidate and hope to hear encouraging feedback.

Sincerely yours,


Statement of Purpose

November 19, 200 7

Dear Admission Committee:

I am very keen to study in your International Master Programme in Bioinformatics in the coming year. I am currently a final year student majoring in Information and Computing Scie n ce in the Mathematics and System Science Department here at Xinjiang University in China.

I am interested in mathematics and biology, especially in biomathematics. Here in Xinjiang I have been studying computational mathematics, and for my bachelor’s thesis I am currently learning about iterative methods in numerical analysis. I would like to study at Chalmers because I am interested in the research done at the Mathematical Statistics and Finite Element Method Centers, and because these centers present research opportunities unavailable in China . I have read the work of Professor Peter Jagers, Stig Larsson, Claes Johnson and would hope to be one of those distinguished professors students in the not too distant future. I have heard a lot about Chalmers and its study environment from my brother, xxx , who has already completed one of your Master s programs . After finishing my Master studies, I plan to pursue PhD studies.

The reason why I eagerly hope to pursue a Master degree in Bioinformatics is that in my homeland, we have a lot of traditional Uyghur medicine which has more than one thousand years of history, and has been scientifically proven to be useful. During a visit to a local hospital , which was full of patients, I was deeply impressed by the curing power of those traditional medicine s . Then, all of a sudden, an idea came to my mind that I would one day do some research on these medicine s and try to understand how they work. In order to realize my dream, I must have better understanding of biological structures. I think Bioinformatics is the right choice, since I studied Information and Computing Science ( in other words , Computational Math), and I can combine what I have learned with what I am going to learn while they are fresh in my mind.

As far as my past academic performance is concerned, I have confidence to do the program well and to finish it successfully. I hope that you will consider me as a possible candidate of the program and give me a chance to achieve my goals.

Sincerely yours,


( xxx , Chinese transliteration)

Sample recommendation letter 6.

Letter of reference

To Whom It May Concern:

I am very pleased to write this letter of reference for xxx , who has been studying Information and Computing Science in our department since 2001.

As the assistant head of Institute of Mathematics and System Science and her former teacher in “ Analytical Mathematics (Calculus) ”, I have ample opportunity to observe her in many ways and believe that she is one of the most promising students possessing a great-untapped potential. Her tenacity and steadiness in her academic pursuits brought her professional proficiency. Unusually extensive courses she selected to study certainly indicate that she has a broad range of knowledge in many subjects.

She distinguished herself not only in the grades she earned but also in her ability to work independently and creatively. She is a person full of ideas, always brings up stimulating questions and original comments, showing profound insights into her major.

Worthy of mentioning is her English proficiency. She already owns the ability of speaking English fluently, writing and translating English freely into Chinese and Uighur. Here Uighur students study Chinese, we don’t require them to study English. As I know, she started to learn English at her early ages with the help of her tutor and then studied completely by herself (very few do that). Before attending this University, she already reached the level which we require Chinese students to have in order to get their diploma, which shows that she can master language quite quickly. Also she is skillful in getting wanted information through English mathematical literature so that she can be familiar with the development of her major in time.

I strongly recommend her for admission to your program with the belief that you will find your investment in this promising student very worthwhile.



Professor of Mathematics

Mathematics & System Science Institute
830046, Xinjiang University

Tel: +86 991


Sample recommendation letter 5.

Letter of Reference

To whom it may concern,

I deem it a great pleasure to recommend Mr. xxx for admission to your International Master s Program in Scientific Computing. He has proven himself as an excellent student not only in his major classes but also in other subjects such as English and Chinese.

Although Mr. xxx is not my direct student, I have known him personally for years. He has a very good background on mathematics. During our conversation, he impressed me a lot by bringing up profound and stimulating questions. Also he displayed an impressive capability in grasping specialized knowledge, absorbing new content from new material, and applying professional principles to the solution of practical problems. In addition to computational mathematics, he also has shown an interest in our institute s minor degree program Computer Application. He has studied a wide range of courses such as Analytical Mathematics (Calculus), Linear Algebra, Analytical Geometry, Numerical Analysis, Matlab, Probability and Statistics, Mathematical Modeling, Ordinary and Partial Differential Equations, Discrete Mathematics, Matrix Theory, VB and C programming Language, which together lay for him a broad and solid foundation and make him a qualified student. Aside from his intellectual ability, he has had additional energy to participate in many nonacademic activities such as sports and fine arts.

In my assessment, he is academically prepared and ready for education at your institute s higher level. I believe he will produce outstanding work in your department there as he has done here.



Professor of Mathematics

Mathematics & System Science Institute

830046, Xinjiang University


Tel: +86 991 xxx

Mobile:+86 991 xxx

Email: xxx

Sample recommendation letter 4.

Dear Sir or Madam:

I take great pleasure in recommending xxx one of my most favorite students and my Undergraduate Assistant researcher for one year, for admission into your distinguished graduate program of Organic Chemistry

I selected him to participate in me research group as Undergraduate Assistant research because I found out his analytical and potential research abilities when I taught him in the course of “Environmental Chemistry”. During under my instruction, I found that he has learned solid knowledge not only Chemistry, but also in the fields of Physics and mathematics and he often came up with creative ideas. Unlike some other students and research member, he studied not to just pass the exam but to really improve his knowledge and expertise. In the research group, he found out that Congo Red can be fabricated Thin Film under hot distilled water Solution, and he proposed that synthesized compound according to relation between gas nature and compound absorption, but my lab real condition can not support his idea.

In my close contact with him in and out of the classroom, I was deeply impressed with his real sprit of scientific research and his insight into problems confronting him and from my colleagues and his work. I know that Mr. xxx possesses a great untapped potential. He is one of the most outstanding students that I have ever taught. In his performance of duties, he has displayed a high sense of responsibility and always helped others whenever he could. In many extracurricular activities, he has played a major role and shown richful experience.

He often talks with me about his ideal to become a chemist. To help quench his thirst for knowledge, I have lent many of my own books to him in his self study program. He has much more engrossed in doing independent research than preparing for exams, but his grades still keep him ranked among the top 1% of his class. I think he is a very intelligent young fellow.

According to my observation, Mr. xxx is so enthusiastic, reliable and responsible that I have full confidence upon hi potential in academic studies and advancement .At present, He is studying xxx , it demonstrated my comment. Therefore, I support his application without reservation. I am very confident that you will find him a competent student and find your assistance to him worthwhile. Your favorable consideration of his application will be much appreciated.

Yours Sincerely,


Doctor (graduated in ddd )


Institute of chemistry and chemical Engineering in XJU

Home: Email:



Sample recommendation letter 3.

Dear XXX,

It is my great pleasure to recommend to you yyy as a worthy candidate for admission to your graduate school. Being his faculty advisor, I have known him for quite well for about 2 years, first as an undergraduate student who is taught in accordance with his aptitude and later as my research assistant.

yyy began his undergraduate studies in September of 2001 and I became acquainted with him when I came to work as a Communication Theory teacher in the Xin Jiang University.

In my close contact with him in and out of the classroom, I was deeply impressed with his real sprit of scientific research and his insight into problems confronting him and from my colleages and his work. I know that yyy possesses a great untapped potential. He is one of the most outstanding students that I have ever taught. In his performance of duties, he has displayed a high sense of responsibility and always helped others whenever he could. In many extracarricular activities, he has played a major role and shown richful experience.

I recommend him most enthusiastically. Any assistance you could render to his application for admission and assistantship would be highly appreciated. If you need further information regarding this promissing young student, please do not hesitate to contact me.

Sincerely yours

Sample recommendation letter 2.

Dear xxx :

I would like to recommend one of my best students yyy for the graduate program in your department.

I selected him to study in our department in 2001 because of his outstanding performance in our national college entrance exams and his excellent study records in high school. Served as a Chairman in department of computer science and technology , I have known him very well for about 3 years. He has very strong desire for knowledge and has shown strong and constant interest in his major field. His understanding and insight into his academic fields are very impressive.

Being an undergraduate student who was taught in accordance with his aptitude, he joined to a student research group when he was a sophomore Since then he has done a lot of productive work as a research assistant. During the past several year s, he has led a "Hi-Tech" group and completed many projects in collaboration with other departments and companies. It is fair to say that he did very well in extrac u rricular activities and won several awards. In dealing with his fellow students, Mr. yyy always showed his willingness to help others and was highly respected by them. But as much as he enjoyed all these activities, he never let them interfere with his academic studies and maintained a top level in all of his courses as a result of his devotion to study and intelligent nature.

Although he is proud of what he has achieved, he does not feel contented, and is eager to continue his studies in order to realize his potential. In my opinion, Mr. yyy has sound academic background and great potential for research work. I strongly recommend his admission and believe that he will produce outstanding work in your university as he did in ours. Any further information about Mr. yyy will be immediately furnished if required.

If I can be of further assistance, I can be reached at

Sincerely yours,