NCHU Course Outline

Course Name	(中) 工程數學(三)(2328)
	(Eng.) Engineering Mathematics (III)
Offering Dept	Department of Electrical Engineering
Course Type	Required			Credits	3	Teacher	HSU, SHUN-PIN
Department	Department of Electrical Engineering / Undergraduate			Language	Chinese	Semester	2025-FALL
Course Description	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
Prerequisites

Relevance of Course Objectives and Core Learning Outcomes(%)			Teaching and Assessment Methods for Course Objectives
Course Objectives	Competency Indicators	Ratio(%)	Teaching Methods	Assessment Methods
Introduce the concepts of probability and how it can be applied to solve engineering problems	1.ability to apply knowledge of mathematics, science, and electrical engineering 2.ability to analyze, design, and integrate electrical engineering systems 3.ability to plan and use technical skills in research projects and various electrical engineering practices 4.ability to collect data, think independently, solve problems, and innovate	25 20 25 20	Exercises Lecturing	Quiz
Course Content and Homework/Schedule/Tests Schedule
Week Course Content Week 1 Combinatorial Analysis (I) Week 2 Combinatorial Analysis(II) Week 3 Axioms of Probability Week 4 Conditional Probability and Independence Week 5 Definition of Random Variables and expectation Week 6 Discrete Probability Distributions I Week 7 Discrete Probability Distributions II Week 8 Quiz and Midterm Exam Week 9 Continuous Probability Distributions Week 10 Jointly Distributed Random Variables Week 11 Properties of Expectation Week 12 Variance, Covariance and Correlation Week 13 Moment Generating Functions Week 14 Inequalities & Weak Law of Large Number Week 15 Week and Strong Law of Large Number, Central Limit Theorem Week 16 Quiz and Final Exam Independent study (Bertrand's paradox, Secretary problem) Independent study (Prison's problem, Catalan number) self-directed learning
Evaluation
Quiz 1/3 Midterm Exam 1/3 Final Exam 1/3
Textbook & other References
A First Course in Probability, 9th edition, by Sheldon Ross Pearson Education, Inc.(book agent in Taiwan (TEL) 04-2241-3551)
Teaching Aids & Teacher's Website
https://sites.google.com/view/signals-system-engineering-lab/course-info/probability
Office Hours
Thu. 10am-12pm
Sustainable Development Goals, SDGs(Link URL)
include experience courses：N

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Update Date, year/month/day：None	Printed Date, year/month/day：2026 / 8 / 12
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