课程详述

COURSE SPECIFICATION

以下课程信息可能根据实际授课需要或在课程检讨之后产生变动。如对课程有任何疑问，请联

系授课教师。

The course information as follows may be subject to change, either during the session because of unforeseen

circumstances, or following review of the course at the end of the session. Queries about the course should be

directed to the course instructor.

课程名称 Course Title

概率论 Probability Theory

授课院系

Originating Department

数学系 Department of Mathematics

课程编号

Course Code

MA215

课程学分 Credit Value

课程类别

Course Type

专业选修课 Major Elective Courses

授课学期

Semester

秋季 Fall

授课语言

Teaching Language

英文 English

授课教师、所属学系、联系方

式（如属团队授课，请列明其

他授课教师）

Instructor(s), Affiliation&

Contact

（For team teaching, please list

all instructors）

陈安岳，教授，数学系

科研教学服务中心 701-09 室

chenay@sustc.edu.cn

0755-8801-8688

CHEN Anyue, Professor, Department of Mathematics

Rm.701-09, Service Centre of Scientific Research and Teaching Bldg.

chenay@sustc.edu.cn

0755-8801-8688

实验员/助教、所属学系、联系

方式

Tutor/TA(s), Contact

无 NA / 待公布 To be announced

10.

选课人数限额(可不填)

Maximum Enrolment

（Optional）

授课方式

Delivery Method

讲授

Lectures

习题/辅导/讨论

Tutorials

实验/实习

Lab/Practical

其它(请具体注明)

Other（Please specify）

总学时

Total

11.

学时数

Credit Hours

12.

先修课程、其它学习要求

Pre-requisites or Other

Academic Requirements

数学分析 II 或者高等数学（下）

Mathematical Analysis II or Calculus A II

13.

后续课程、其它学习规划

Courses for which this course

is a pre-requisite

MA314 应用随机过程

MA314 Applied Stochastic Processes

14.

其它要求修读本课程的学系

Cross-listing Dept.

教学大纲及教学日历 SYLLABUS

15.

教学目标 Course Objectives

To introduce the basic concepts in probability theory which forms the basis for all applications of probability and statistics, and for

further probability and statistical theory including, in particular, stochastic processes. Also to introduce the basic probability methods

and techniques with a strong emphasis on applying these standard methods and techniques appropriately and with clear

interpretation. The emphasis is on applications. The basic teaching goal is to grasp the basic concepts regarding random variables,

random vectors, functions of random variables, expectation , variances, covariance, and central limit theorems and the related

important conclusions and theorems and to study their extensive applications in many fields. The basic aim is to teach students to

handle the basic theory and fundamental methods and technologies for random phenomenon, to train students' scientific thinking and

problem analysis and problem solving skills, and to lay a good foundation for the subsequent courses in modern probability theory.

本课程介绍概率论的最基本概念，它们组成了概率和统计的应用基石。本课程也为进一步学习其他概率和统计课程,例如随

机过程，打下良好的基础。本课程还重点介绍了一些基本的概率方法和技巧，且强调它们的实际应用及概率解释。基本教

学目标是掌握关于随机变量,随机向量,随机变量的函数,期望,方差、协方差,和中心极限定理及相关重要结论和定理,研究他们

在许多领域广泛应用。基本目标是教会学生处理随机现象的基本理论和基本方法技巧,培养学生的科学思维和分析解决问题

的能力,并为后续课程打下良好的现代概率论基础。

16.

预达学习成果 Learning Outcomes

After completing this course, students should master the basic concepts and methods in probability theory. After learning this

course, the students should be familiar with a range of methods and techniques for solving real life problems of the probabilistic

nature. In particular, after learning this course, the students should be able

1．to master the basic knowledge, deeply to understand and master the nature of the definitions, theorems, probability laws,

principles and formulae. After the study, the students should be able not only to remember the above concepts and the basic

probability laws including conditions and conclusions, but also deeply to understand the basic principles and ideas of probability

theory.;

2．to master the basic skills and be able to compute expectations and probabilities according to law and formula correctly;

3．to train the ability of thinking and to enhance the ability to do research regarding random variables;

4．to improve the ability of solving practical problems. After learning this course, students should be able to use the learned

knowledge to establish a suitable probability model and to solve the life related mathematical problems.

完成本课程后,学生应掌握概率论的基本概念和方法，熟悉各种概率方法和技巧，并能解决现实生活提出的问题，了解其概

率特性。特别是,在学习本课程后,学生应该能够

1.掌握基本知识,深入理解和掌握定义,定理,原则和公式本质。学习后,学生应该能够不仅记住概念和基本概率方法, 同时也能

深刻理解概率论的基本原理和理念。

2.掌握基本技能,并能根据概率规律和公式正确计算期望和概率

3.培养思维能力，提高对事物的观察，比较,和概括的能力。

4.提高解决实际问题的能力。学习本课程后,学生应该能够使用学到的知识对实际问题建立合理的概率模型，从而解决相关

的数学问题。

17.

课程内容及教学日历（如授课语言以英文为主，则课程内容介绍可以用英文；如团队教学或模块教学，教学日历须注明

主讲人）

Course Contents (in Parts/Chapters/Sections/Weeks. Please notify name of instructor for course section(s), if

this is a team teaching or module course.)

Ch1. Introduction (3 hours): Introduction; Baby Set Theory; Combinatorial Methods; Binomial Coefficients; Binomial Theorems.

Ch2. Probability Measure (5 hours): Sample Spaces; Events; The Probability of an Event; Some Rules of Probability; Conditional

Probability; Independent Events; Bayes’ Theorem.

Ch3: Random Variables (10 hours): Random Variables; Probability Distributions; Discrete Random Variables; Probability Mass

Functions; Binomial Random Variable; Poisson Random Variable; Other Discrete Random Variables; Continuous Random Variables;

Probability Density Functions; Exponential Distributions; Normal Distributions; Gamma Distributions; Some Other Commonly Used

Continuous Distributions; Function of a single random variable; Transformations; cdf methods.

Ch4: Random Vectors (8 hours): Multivariate Random Variables; Joint, Marginal and Conditional Distribution Functions;

Independent Random Variables; Bivariate Normal Distributions; Multivariate Normal Distributions.

Ch5: Mathematical Expectations (10 hours): The Expected Value of a Random Variable; The Basic Properties of Expectations; The

Variance of a Random Variable; Moments; Covariance and Correlation of Random Vectors.

Ch6: Functions of Random Variables (8 hours): Basic Concepts; Property of Expectation of Function of Random Variables;

Distribution Function Techniques; Transformation Technique for One Variable; Transformation Technique for Several Variables;

Generating Function Technique; Sum and Ratio of Two Random Variables,; the Moment Generating Functions: properties and

Applications.

Ch7 : Limit Theorems and Distributions Derived from the Normal Distribution (4 hours): The Law of Large Numbers, The Central

Limit Theorems; Chi-Square Distribution, The T- and F- Distributions; The Sample Mean, The Sample Variance.

18.

教材及其它参考资料 Textbook and Supplementary Readings

Required : Rice, J.A., Mathematical Statistics and Data Analysis, Duxbury Press.

Recommended:

1. Douglas G. Kelly, Introduction to Probability, Macmillan Publishing Company, 1994, ISBN 0-02-363145-7

2 Sheldon Ross , A First Course in Probability, 4

Ed, Macmillan Publishing Company, 1994, ISBN 0-02-403872-5

课程评估 ASSESSMENT

19.

评估形式

Type of

Assessment

评估时间

Time

占考试总成绩百分比

% of final

score

违纪处罚

Penalty

备注

Notes

出勤 Attendance

课堂表现

Class

Performance

小测验

Quiz

课程项目 Projects

平时作业

Assignments

25%

期中考试

Mid-Term Test

25%

期末考试

Final Exam

2 hours

50%

期末报告

Final

Presentation

其它（可根据需要

改写以上评估方

式）

Others (The

above may be

modified as

necessary)

20.

记分方式 GRADING SYSTEM

 A. 十三级等级制 Letter Grading

 B. 二级记分制（通过/不通过） Pass/Fail Grading

课程审批 REVIEW AND APPROVAL

21.

本课程设置已经过以下责任人/委员会审议通过

This Course has been approved by the following person or committee of authority