"Time Series Analysis is one of the specialized subject courses of the Department of Probability and Statistics. It mainly teaches students theory and practices on analysis and modeling of correlated data, and basic knowledge of stationary time series. It focuses on time domain models, but also give introduction to frequency domain concepts. "

This course focuses on standard nonparametric procedures useful for the analysis of experimental data. One-sample, two-sample, and multiple sample rank test and their power are covered. Goodness-of-fit tests, contingency table test are also covered. It also includes some modorn nonparametric techniques such as nonparametric distribution estimation, nonparametric regression, functional data analysises. Theories are are emphasized, such as U-statistics, power function, and asymptotic relative efficiency are introduced, but the applications are not completely neglected, some applications such as gene set enrichment analysis are also included.

Ordinary Differential Equations is a basic course for mathematical students. In this course, the students will learn the basic knowledge of ordinary differential equations, including how to solve some simple equations, the existence and uniqueness for Cauchy problem, boundary value problems as well as the theory of linear differential equations.

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The course teaches student using the SAS system with an easy starting attitude, it includes SAS programming, data management, reporting and graphics, basic statistical analysis techniques. The course will also introduce R, another statistical software. R is especially suitable for programming statistical algorithms, and it is one of the most prefered developement and computing tools used by statisticians.

This Course aims at guiding students to describing and modelling non-determinative iphenomenons mathematically, and provides chances for students to practice Set Theory,Calculus and Advanced Algebra.

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Higher algebra is an important basic course in mathematics and applied mathematics, mathematics and applied mathematics. Its main contents include two parts: polynomial theory and linear algebra. The purpose of this course is to make students master the basic knowledge and system algebra and abstract strict algebraic method for subsequent courses such as algebra, differential equations, probability theory and mathematical statistics, functional analysis, calculation methods to provide necessary algebraic knowledge, but also provide a training for further study all the courses of mathematics and Applied Mathematics needed for abstract thinking ability. Higher algebra is to continue and improve the high school algebra. Through the course of teaching, to enable students to deepen the understanding of high school algebra.

Mathematical analysis is one of the most important courses for the students who wish to study the mathematics and related subjects. The course mainly includes the theory of Riemann integrals and the theory of series. The course is a basis for Mathematical analysis and for many courses such as differential equations; differential geometry, functions of one complex variable; real analysis, probability; basic physics, etc. The course provides the training for the mathematical thinking and skills.

Mathematical Statitics is a basic course with wide application, it mainly focuses on the analysis of randon sample and other data set, including how to effectively collect data, parameter estimation , hypothesis testing, linear model and statistical design. The purpose is to let the students to understand elementary ststistica concepts and ideas, to study the most commonly used statistical methods and to solve some practical problems, and to establish the way of statistical thinking.

The course is one of the important branches of mathematical statistics. It is the subject of studying how to effectively draw out a sample for collecting data and how to interference and analysize all kinds of indexes of the collectivity. This course is ready to systematically introduce simple random sampling, unequal probability sampling, stratified sampling, multistage sampling, cluster sampling, systematic sampling, two-phase resampling and their corresponding statistical inference methods, and also to discuss some popular problems in the sampling applications. The techniques have broadly been applied in natural sciences and social sciences.

Applied regression analysis is the courese that blends theory and applications effectively. Through the study during the course, it is required for students to know the theory and methods of regression analysis and can explain the analysis result practically. As the mean while, it is required for students to learn some statistic software to solve the questions.

"Combinatorics is a core course for all majors in the School of Mathematical Sciences, while it is also useful for students in (theoretical) computer science, logic, linguistics, philosophy, EE, chemistry, biology, physics, etc. Topics shall include (varying by instructors): Generating functions, enumeration methods, Polya`s theorem, combinatorial designs,Ramsey theory, fundamental graph theory, extremal graphs, special enumerating sequences, the probabilistic method, etc."

Functional analysis plays increasing role in applied and pure mathematics. This course will familiarize the student with basic concepts, principles and methods of functional analysis and its application. This course is suitable for a one-semester course meeting three hours per week.

"Functions of Real Variables" is a basic course for all undergruaduate students in School of Mathematical Sciences, which concentrates the Lebesgue thoery of measure and integral, and provides the knowledge and training of modern analysis for students.

Geometry and its exercise class of School of Mathematical Sciences, PKU (As part of all undergraduate students of our department and Yuanpei experimental class of undergraduates) open the first door of the geometry curriculum. It is one of the most important basic courses in our department. Important task of the course is to charge with the cultivation of students` geometric thinking and to enhance the quality of students` geometry. This lesson mainly introduces the theory of analytic geometry of space and the basic idea of geometry properly, such as geometric in-variants, relations between groups and geometry. Curves in the space, the geometric properties of surfaces and in-variants are discussed in algebraic methods such that graphics and equations linked. Topics include vector algebra, plane and a straight line, the common surface, coordinate transformation, simplification of the quadratic equation and its properties, orthogonal transformation and affine transformation, projectile plane and projectile transformations. Therefore, the lesson is not only the extension and expansion of plane analytic geometry knowledge, but also lays a solid foundation for student diversity in undergraduate calculus, physics and other courses.

The course consists of nine chapters divided into three parts. The first part contains three chapters that provide some preliminary results on matrix theory and multivariate normal and related distributions. Various linear models are also introduced through real examples in this part. The second part consists of two chapters on statistical inference of linear models, including parameter estimation, hypotheses testing, confidence intervals, and prediction. In the third part, the methodologies are applied to various linear models, such as the linear regression model, the analysis of variance model, the analysis of covariance model, the variance components model, and the mixed effect model. The course will emphasize the statistical and geometric motivation for the methods, the practical application of the methods, the implementation by Statistical software, and the interpretation of the results.

This course will introduce the basic knowledge of Sobolev spaces used in Partial Differential Equations. Based on Sobolev spaces, the well-posedness problems such as existence, uniqueness and regularity for weak solutions of linear partial differential equations of second order will be investigated. These linear partial differential equations include linear elliptic partial differential equations, linear parabolic partial differential equations and linear hyperbolic partial differential equations. The aim is to help students understand the elementary theory and modern methods of linearpartial differential equations.

Applied regression analysis is the courese that blends theory and applications effectively. Through the study during the course, it is required for students to know the theory and methods of regression analysis and can explain the analysis result practically. As the mean while, it is required for students to learn some statistic software to solve the questions.

After taking this course, students can learn the basic knowledge about computational statistics and learn how to generate random numbers. They know how to test if the random variables come from some distribution or not. They know how to do statistical simulations using generated random numbers. EM and MCMC algorithms are also introduced in this class.