# Statistics

### 1. Program Description

The Statistics is a subject of data collection, data analysis, prediction and control, and so on, it is widely used in fields such as natural science, engineering, finance, economics, technology, insurance. The undergraduate program of Statistics in Nanjing Normal University aims to cultivate students’ abilities, which is adapted to Jiangsu and the national economic and social development needs of high quality in theory and application research on statistic science.

Successful graduates of this program are expected to have a solid statistic foundation, master the basic idea of statistic methods, and creative spirit. After graduation from this program, the students should become high-level professional with certain international vision, and have the practical operation ability which they engaged in scientific research, technology development, etc. In addition, most of them should be graduate students in high-level university and research institutions both at home and abroad.

### 2. Program Duration and Credit

This is a four-year undergraduate program, which can be completed within a minimum of three years and a maximum of seven years.

A total of 161 credits are required upon the completion of the program.

### 3. Curriculum

Three modules of courses are offered for the program: Basic Curriculum, Essential Curriculum, and Elective Curriculum. The Basic and Essential curricula are compulsory for a Bachelor’s degree.

The Elective Curriculum in the list includes extended disciplinary courses offered by the school into which an individual student is admitted, as well as cross disciplinary courses offered by other schools. Students can choose the extended and cross disciplinary courses according to their personal interests and career plans; however, credits should be approved by the School.

(1) Basic Curriculum

 Course Code Course Credit Semester Remark 100701062110 Mathematical Analysis(Ⅰ)* 7 1 100701062111 Advanced Algebra (Ⅰ)* 6 1 100701062112 Analytic Geometry 3 1 100701062113 Mathematical Analysis (Ⅱ)* 7 2 100701062201 Mathematical Analysis(Ⅲ)* 7 3 100701062202 Advanced Algebra (Ⅱ)* 6 2 100701062203 Mathematical program introduction and discussion 2 1 Including 2 practice credit

(2) Essential Curriculum

 Course Code Course Credit Semester Remark 100712063001 Probability Theory * 3 3 100701063001 Ordinary Differential Equations 3 3 100712063002 Mathematical Statistics* 4 4 100712063003 Sampling Survey 3 4 100712063004 Actuarial Science of Insurance 3 4 100712063005 Applied Stochastic Processes* 3 4 100712063006 Application Regression Analysis 3 5 Including 1 practice credit 100712063007 SAS and Statistical Analysis 4 5 Including 1 practice credit 100701063006 Real Variable Function 3 5 100712063008 Analysis of Time Series* 3 6 Including 0.5 practice credit 100712063009 Multivariate Statistical Analysis* 4 6 Including 0.5 practice credit 100201154010 World Economy 2 7 100712063010 Graduation Practice 2 8 Including 2 practice credit 100701063011 Graduation Thesis 4 8 Including 4 practice credit

(3) Elective Curriculum

 Course Code Course Credit Semester Remark 100701063004 Functions of Complex Variable 3 4 100010072101 College Physics B（1） 3 100010072102 College Physics B（2） 2 100010072103 College Physics Experiments 1（1） 0.5 Including 0.5 practice credit 100010072104 College Physics Experiments 1（2） 0.5 Including 0.5   practice credit 100712164001 The Principle of Accounting 3 2 100010191003 Programming in C 4 Including 1 practice credit 100701194003 Database Developing Language 3 Including 1 practice credit 100712064002 Non-parametric Statistics 3 6 Including 0.5 practice credit 100712064003 Options and Futures Pricing Theory 3 6 Including 1 practice credit 100701063019 Operations Research 3 5 100701064009 Research of Mathematical Analysis 3 7 100701064005 Research on Advanced Algebra 3 7 100712064004 Risk Theory 2 5 100712064008 Statistical Modeling and Data Analysis 3 6 Including 1 practice credit 100712064007 Statistical computation 3 6 Including 0.5 practice credit 100701064014 Some Topics in Modern Statistics methods 2 7 Including 0.5 practice credit 100203063001 Econometrics 4 6 Including 1.5   practice credit 100203064003 Financial Statistics Analysis 3 6 100701064003 Algebra 4 7 100701064013 Modern  Analyse 4 7 100712064001 Foundations of Measure and Probability 4 7

Note: 1. Odd-number semesters are the fall semesters and even-number semesters are the spring semesters in each academic year.

2. The asterisk * marks a core course.

### 4. Core Courses and Introductions

100701062110      Mathematical Analysis()      (7 cr.)

Prerequisites:

This course mainly introduces the theory of completeness of real numbers, the differential calculus of one-variable function and its applications. The main contents of Mathematical Analysis (Ⅰ) are as follows: sets of real numbers and functions, limits of number sequence, limits of a function, continuities of the function, derivatives and differentiations, mean value theorems of differentiation and their applications, and the theory of completeness of real numbers, and so on. The teaching of this course not only pays attention to integral introduction of its basic principles and major methods, but also emphasizes the abilities of abstract, logic and calculation.

The teaching of this course will make the students to correctly understand the basic concepts of Mathematical Analysis, to master the basic theories and basic techniques of Mathematical Analysis, to improve the ability of abstract thinking and strictly logical reasoning. To cultivate the students to have the ability to perform mathematical calculations and apply mathematics.

100701062113      Mathematical Analysis ()     (7 cr.)

Prerequisites:

This course introduces the integral calculus of one-variable function, the theory of series, and their applications. The main contents of Principles of Mathematical Analysis(Ⅱ) are as follows: indefinite integral, definite integral, some applications of definite integral, improper integral, series of number terms, sequence of functions and series of function terms, power series, Fourier series. The teaching of this course not only pays attention to integral introduction of its basic principles and major methods, but also emphasizes the abilities of abstract, logic and calculation.

The teaching of this course will make the students to obtain an integrated knowledge of the integral calculus of one-variable function, the theory of series, and their applications. Students can master the methods and basic theories to study the analysis properties of one-variable function.

100701062201      Mathematical Analysis()    (7 cr.)

Prerequisites:

This course introduces the calculus differential and integral calculus of function of many variables and their applications. The main contents of Principles of Mathematical Analysis (Ⅲ) are as follows: limits and continuities of function of many variables, the differential calculus of multivariable function, implicit function theorems and their applications, integral depending on parameters, curvilinear integral and surface integral, multiple integral, the theory of field. The teaching of this course not only pays attention to integral introduction of its basic principles and major methods, but also emphasizes the abilities of abstract, logic and calculation.

The teaching of this course will make the students to obtain an integrated knowledge of the differential-integral calculus of function of many variables, and their applications. Students can master the methods and basic theories to study the analysis properties of function of many variables.

100701062111     Advanced Algebra ()    (6 cr.)

Prerequisites:

This textbook is designed to teach the university mathematics student the basics of the subject of linear algebra. The text has two goals: to teach the fundamental concepts and techniques of matrix algebra and abstract vector spaces, and to teach the techniques associated with understanding the definitions and theorems forming a coherent area of mathematics. So there is an emphasis on worked examples of nontrivial size and on proving theorems carefully.

(1) The basic theory of the polynomials over the number fields. (2) The properties of the determinants and some computing skills, Cramer’s rule. (3) The basic concept of system of linear equations and Gaussian elimination. (4) The operations of matrices, the determinant and rank of matrices multiplication, and the inverse of the matrix, the block of matrices, elementary matrix. (5) The basic theory of quadratic form, the properties and applications of the positive definite quadratic forms.

100701062202      Advanced Algebra ()      (6 cr.)

Prerequisites:

This textbook is designed to teach the university mathematics student the basics of the subject of linear algebra. The text has two goals: to teach the fundamental concepts and techniques of matrix algebra and abstract vector spaces, and to teach the techniques associated with understanding the definitions and theorems forming a coherent area of mathematics. So there is an emphasis on worked examples of nontrivial size and on proving theorems carefully.

(1) The concepts and theory of linear spaces and linear mappings. (2) The properties of operations of linear transformations, the definitions and computings of eigenvalues, eigenvectors, and characteristic polynomials. (3) The basic properties of Euclidean spaces, orthogonal bases, and Schmidt orthogonalization method, the definitions of the least squares method and the unitary spaces.

100712063001       Probability Theory      (3.00 cr.)

Prerequisites:

Through learning, students are required to grasp the basic concepts, theories and methods of probability theory, learn how to processing method of random phenomena, master the basic ability to use probability method to solve practical problems and make a good foundation for the study on some subsequent professional statistics courses.

Probability theory mainly introduces the mathematical theories and methods of statistical regularity of random phenomena, such as events and probability, random variables and their distributions, random vectors and their distributions, numerical characteristics and characteristic functions of random variables, law of large numbers and the central limit theorem and so on. Axiomatic definition of probability, the definitions of random variable, the distributions of random variable, numerical characteristics and characteristic functions of random variables and law of large numbers will be highlighted.

100712063002      Mathematical Statistics      (4.00 cr.)

Prerequisites:

Trough the study of the course, students are required to master the basic concepts, basic theories and methods of mathematical statistics, learn to use common statistical methods to solve some practical problems, and lay a good foundation for the follow-up courses.

Mathematical statistics is based on the Probability theory, which is a discipline about the collection, organization and analysis of the data. The main contents of this course are the basic concepts, statistics and distribution; parameter estimation, including point estimation, the evaluation criteria, sufficience and completeness, interval estimation; hypothesis test, including the basic concepts, hypothesis test about mean and variance, goodness-of-fit test of distribution function, test of independence, optimal test, other methods of hypothesis test; analysis of variance (ANOVA), including one-way ANOVA, two-way ANOVA; Bayesian statistics, including the estimation of Bayesian priori distribution and posterior distribution, Bayesian estimation, Bayesian inference.

100712063005      Applied Stochastic Processes   (3.00 cr.)

Prerequisites:

Stochastic processes is an important branch in the field of modern probability theory, through the study of the course of stochastic processes can further improve the mathematical ability of students' understanding the phenomenon of stochastic , preliminary master the control capacity of stochastic system ; through the study of this course, students have a preliminary knowledge ability to read the relevant literature. Basic requirements: students are required to understand the basic concepts and methods of stochastic processes, familiar with the basic theory of several stochastic processes, and can use them to solve some simple practical problems.

As one of the important branches of modern probability theory, the stochastic process theory provides us rich theoretical guidance and practical methods to explore the stochastic phenomena in the real world. Along with the progress of the society, more and more people need to understand and even to use the stochastic process theory in practice. The stochastic process theory is not only essential for professional experts in probability and statistics, but also for many others in mathematics, natural science, technology, economy, management, and even for researchers in social science. This course focuses on teaching students the basic concept, ideas and methods of the stochastic process theory. In this course we introduces the theories, methods and applications of the important processes such as Poisson process, renewal process, Markov chain, Martingale, Brown motion and stochastic integral. Students with higher mathematics and elementary probability theory can master the main content of the course without difficulties.

100712063008       Analysis of Time Series       (3.00 cr.)

Prerequisites:

The key goal of the course Analysis of Time Series is to make the students master the basic concepts and models of time series, the modeling procedure and forecasting methods.

Analysis of time series introduces the main theories and methods of time series analysis. The main contents include the basic concepts of time series; The three basic models of time series analysis: AR model, MA model and ARMA model; The modeling process of ARMA model: preliminary identification, parameter estimation, model order determination and model testing; Stationary time series prediction: linear prediction and conditional expectation prediction; Non-stationary time series models: ARIMA model, ARMA model with a trend and seasonal ARIMA model. The teaching of each of methods not only pays attention to the introduction of the basic theory, but also focuses on practicing by using the statistical software.

100712063009    Multivariate Statistical Analysis     (4.00 cr.)

Prerequisites:

Through this course, students learn the fundamental methods and theory of multivariate statistical analysis and develop the ability of using the method of multivariate statistical analysis and software to deal with practical problem.

This course mainly introduces the inferential methods of multivariate normal population and the method of multivariate analysis. The main contents of Multivariate Statistical Analysis are as follows: the theory and methods of multivariate normal population, discriminant analysis, cluster analysis, principal component analysis, factor analysis, correspondence analysis, canonical correlation analysis and partial least square methods. The teaching of this course not only pays attention to the introduction of multivariate statistical method and its statistical ideas，but also emphasizes the abilities of theory analysis and software computations.

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