國立中興大學教學大綱

課程名稱	(中) 工程數學(三)(2328)
	(Eng.) Engineering Mathematics (III)
開課單位	電機系
課程類別	必修	學分	3	授課教師	許舜斌
選課單位	電機系 / 學士班	授課使用語言	中文	英文/EMI		開課學期	1141
課程簡述	This course introduces the fundamental concepts of probability theory and its applications. Probability is the mathematical framework for modeling uncertainty and making informed decisions in a wide range of fields, including statistics, finance, engineering, and the natural sciences. The course will cover the following topics: Basic Probability Concepts: Sample spaces, events, probability axioms, complement rule, addition rule, conditional probability. Discrete Probability Distributions: Probability mass functions, cumulative distribution functions, expected value, variance, common discrete distributions (e.g., Bernoulli, Binomial, Poisson). Continuous Probability Distributions: Probability density functions, cumulative distribution functions, expected value, variance, common continuous distributions (e.g., uniform, normal, exponential). Joint Probability Distributions: Joint PMFs and PDFs, marginal and conditional distributions, independence. Transformations of Random Variables: Functions of random variables, distribution of sums and differences. Law of Large Numbers and Central Limit Theorem: Convergence in probability, weak law of large numbers, central limit theorem. Statistical Applications: Probability in statistical inference, hypothesis testing, confidence intervals. Simulation and Monte Carlo Methods: Using random numbers to solve practical problems. This course typically requires a solid foundation in basic algebra and mathematical reasoning. Some courses may have additional prerequisites in calculus
先修課程名稱						課程含自主學習	Y

課程與核心能力關聯配比(%)

課程目標之教學方法與評量方法

課程目標

核心能力

配比(%)

教學方法

評量方法

Introduce the concepts of probability
and how it can be applied to solve engineering problems

1.運用數學、科學及電機工程知識之能力

2.分析、設計與系統整合之能力

3.執行電機工程實務所需之技術與能力

4.資料蒐集、獨立思考、解決問題及研究創新之能力

習作

講授

測驗

授課內容(單元名稱與內容、習作/每週授課、考試進度-共16週加自主學習)

週次	授課內容
第1週	Combinatorial Analysis (I)
第2週	Combinatorial Analysis(II)
第3週	Axioms of Probability
第4週	Conditional Probability and Independence
第5週	Definition of Random Variables and expectation
第6週	Discrete Probability Distributions I
第7週	Discrete Probability Distributions II
第8週	Quiz and Midterm Exam
第9週	Continuous Probability Distributions
第10週	Jointly Distributed Random Variables
第11週	Properties of Expectation
第12週	Variance, Covariance and Correlation
第13週	Moment Generating Functions
第14週	Inequalities & Weak Law of Large Number
第15週	Week and Strong Law of Large Number, Central Limit Theorem
第16週	Quiz and Final Exam Independent study (Bertrand's paradox, Secretary problem) Independent study (Prison's problem, Catalan number)
自主學習內容

學習評量方式

Quiz 1/3
Midterm Exam 1/3
Final Exam 1/3

教科書＆參考書目(書名、作者、書局、代理商、說明)

A First Course in Probability, 9th edition, by Sheldon Ross
Pearson Education, Inc.(book agent in Taiwan (TEL) 04-2241-3551)

課程教材（教師個人網址請列在本校內之網址）

https://sites.google.com/view/signals-system-engineering-lab/course-info/probability

課程輔導時間

Thu. 10am-12pm

聯合國全球永續發展目標(連結網址)

提供體驗課程：N

請尊重智慧財產權及性別平等意識，不得非法影印他人著作。
更新日期西元年/月/日：無	列印日期西元年/月/日：2025 / 7 / 04
MyTB教科書訂購平台：http://www.mytb.com.tw/