NCHU Course Outline
Course Name (中) 應用數學方法(一)(6595)
(Eng.) Methods of Applied Mathematics (I)
Offering Dept Department of Applied Mathematics
Course Type Elective Credits 3 Teacher 陳齊康
Department Department of Applied Mathematics / Graduate Language Chinese 英文/EMI Semester 2025-FALL
Course Description The course covers the statistical learning methods for data analysis
Prerequisites
self-directed learning in the course Y
Relevance of Course Objectives and Core Learning Outcomes(%) Teaching and Assessment Methods for Course Objectives
Course Objectives Competency Indicators Ratio(%) Teaching Methods Assessment Methods
To understand the statistical learning methods and acquire the skills of data analysis using R.
1.Mathematical Thinking and Logic
7.Literature Review
50
50
Lecturing
Oral Presentation
Attendance
Assignment
Written Presentation
Course Content and Homework/Schedule/Tests Schedule
Week Course Content
Week 1 Using R language
Week 2 Using R language
Week 3 Multivariate normal distribution
Week 4 Least square (LS) regression
Week 5 Maximum likelihood (ML) regression
Week 6 GCV, AIC: Best subset regression
Week 7 Stepwise regression
Week 8 L2-norm regularized (ridge) regression (RR)
Week 9 Adaptive weighted ridge regression (AWRR)
Week 10 Polynomial regression; Basis function and data transformation
Week 11 Ridge regression with the (spline) basis expansion
Week 12 Additive model (I) with the RR
Week 13 Additive model (II) with the AWRR
Week 14 Smoothing spline (I)
Week 15 Smoothing spline (II)
Week 16 Final reports Self-learning (Additive model estimated by the backfitting algorithm)
Assignment: homework problems + learning experience report Self-learning (Additive model estimated by the stagewise regression (boosting))
Assignment: homework problems + learning experience report
self-directed
learning

Evaluation
Class attendance and homework assignments: 45%
Final report: 45%
Self-learning: 10%
The grade system is tentative and subject to modification.
Textbook & other References
The elements of statistical learning by Hastie et al.
Distributed optimization and statistical learning via the alternating direction method of multipliers by Boyd et al.
Teaching Aids & Teacher's Website
Supplementary web resources
Office Hours
2:00-3:00 PM Friday

Sustainable Development Goals, SDGs(Link URL)
04.Quality Educationinclude experience courses:N
Please respect the intellectual property rights and use the materials legally.Please respect gender equality.
Update Date, year/month/day:None Printed Date, year/month/day:2025 / 7 / 02
The second-hand book website:http://www.myub.com.tw/