Curriculum

Course

Introduce

Core courses

The Course of Functional Analysis

1. nonlinear operators in infinity dimensional normed linear spaces

2. the basic theory of topology linear spaces

3. Frechet-derivative and Gateaux-derivative of nonlinear operators.

4. topology degree theory and its applications

5. Variational methods and its applications

Elements of Algebra

The content of the course should cover the following chapters:

Chapter 1 Groups.

It includes the related definitions and properties of groups, cyclic groups, normal subgroups, quotient groups, homomorphism theorems, direct sums, and decompositions, etc.

Chapter 2 Rings.

It includes the related definitions and properties of rings, ideas, quotient rings, and homomorphism theorems, etc.

Chapter 3 Modules.

It includes the related definitions and properties of modules, free modules, and projective modules, etc.

Specialized courses

Stochastic Process

Stochastic process is the quantitative description of the dynamic relationship between a series of random events. It is an important tool in various fields of natural science, engineering and social sciences. The theory of stochastic processes has been widely used in weather forecast, statistical physics, astrophysics, mathematical economics, population theory, reliability and computer science etc. The main contents include some typical point process, stochastic differential equation and martingale theory. Through the course of learning to enable students to masterthe basic theory and research method of stochastic process.

Foundations of Probability Theory

Based on the measure theory, the basic concepts such as distribution function, probability measure, and conditional expectation and so on are introduced systematically. Independence of random variables and various convergence modes of random variable sequence, random series and law of large numbers are discussed in detail. Chief analytical weapons, namely Fourier and Laplace transforms are discussed. On this basis, the classical probability theory "problem center" is introduced, mainly including Liapounov's theorem, Lindeberg-Feller theorem and ramifications of the central limit theorem.

Advanced Mathematical Statistics

This course includes basic concepts of statistical decision theory, Unbiased estimation, admissible estimation, equivalent estimation, Bayes estimation, minimax estimation, large sample estimation, interval estimation, optimalities of estimator and so on relative estimation theory. And also discusses the optimization of hypothesis test, large sample test and the least-squares estimation problem in linear model.

Optional courses

Actuarial science

Actuarial science is using the principle of mathematics, probability statistics and a variety of financial models to analyze all kinds of risk factors in the insurance industry forecasts. It is a basic skill sets actuarial science, risk analysis for the integration of an insurance professional course. Main content is divided into two parts: life insurance actuarial theory, non-life insurance actuarial theory. Life insurance actuarial interest part mainly introduces the theory and function of life insurance actuarial science basic knowledge; Non-life insurance actuarial part mainly introduce how to according to the insurance accident frequency and loss magnitude to determine insurance rates and risk liability reserve funds. These theoretical knowledge for students engaged in insurance work in the future to lay the solid foundation of the mathematical actuarial basis.

Mathematical Finance science

Mathematical finance is to use mathematical tools of finance theory and the phenomenon of research and analysis, establish the corresponding mathematical model, through theoretical analysis and numerical calculation, etc., to find inner financial behaviors and to guide the practice. The main content of this course include: asset pricing theory, the optimal portfolio theory and algorithms, options on futures pricing theory and the analysis of financial products.

Statistical methods for multivariate data analysis

In this course, most of the ordinary multivariate methods will be introduced, including their theory and applications. The theory of multivariate normal distribution and linear statistical models is the base of many multivariate methods. They will be introduced before the multivariate methods. The basic knowledge of matrix algebra and mathematical statistics is necessary for the studying of this course. We will review the basic results of matrix algebra and mathematical statistics in the beginning of the course.

Time series analysis

In this course, some basic concepts may first be introduced, such as time series, stationary process, autocorrelation function, spectra etc. The linear time series model is a main topic of the course, we will discuss it in detail, with emphasis on the estimation of the model parameters. Spectrum analysis is another important topic of the course; we will focus on the spectral estimation with parametric and non-parametric methods. It is also emphasized to practice with real time series data via using statistical packages (such as R).

Nonparametric statistics

In contrast to the situation in parametric statistics where we usually assume that the underlying distribution belongs to a family indexed by a few real parameters, nonparametric statistics deals with problems where hardly anything is known about the underlying distribution. Nonparametric statistical methods, and also be called distribution-free methods, do not rely on parameter estimates or precise assumptions about the distributions of variables. As their title suggests, these tests do not make numerous or stringent assumptions about the population. In addition, most non- parametric tests may be used with non-numerical data, and it is for this reason that many of them are often referred to as "ranking tests" or "order tests."

Statistical Computation

Statistical Computation is a young but rapidly maturing subject in Statistics Research, it is the combination of mathematical statistics, computational mathematics and computer science . The main task of Statistical Computation is to discuss the basic method and principle in statistical calculation , it mainly presents the error and data analysis, the production and test of random number, the random simulation methods, MCMC algorithm, , EM algorithm and so on

Regression Analysis

The course introduces the statistic regularity systematically between variables with correlativity . The main contents include: the linear regression analysis, the multivariate linear regression analysis,the regression diagnosis, the quantitative method with qualitative variables, the unbiased estimation in multivariate linear regression model ,nonlinear regression model and so on.

Mathematical methods for data processing

This course introduces some currently commonly used methods in the application of ocean random data analysis - spectral estimation, linear systems analysis, linear mean square estimation, signal EMD and Hilbert spectral analysis, principal component analysis and orthogonal function decomposition, wavelet analysis and marine random statistical analysis of variables and their extremes.

Practical Extreme Value Statistical Methods

This course introduces some practical extreme value statistical analysis methods，with the expectation that students can learn to set up a probability model for the observed extreme values that satisfy some basic conditions and are based on a sample size.The contents of this course include：univariate extreme value theory, statistical inference of extreme value distribution，the extreme value distribution theory of time series，multivariate extreme value theory.

Statistical reference

This course introduces the methods of SVM pattern recognition，the main ideas of SVM regression analysis，the theory of machine learning problems and the application of SVM.The contents include：linear SVM pattern recognition, nonlinear SVM pattern recognition, SVM regression analysis, further reflection of SVM methods, statistical learning theory, the application of SVM method.

Linear models

Linear models are kinds of statistical models. It includes linear regression models, ANOVA, covariance analysis models, linear mixed effects models and etc. Linear models can be used to approximate description many problems such as in biology, medicine, economics, management, geology, meteorology, agriculture, industry, engineering & technology and so forth. Linear models have become one of the most widely used models in modern statistics. This course systematically introduces the basic theory of linear models and methods.