Combinational Design

本課程是由 國立陽明交通大學應用數學系提供。

This is an introductory course of Combinatorial Designs.
Mainly, basic designs are introduced: Latin Squares, t-designs, Pooling designs and experimental designs.
We are aiming to learn also their applications.

Textbook:

Lecture Notes by Hung-Lin Fu.

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Instructor(s) Department of Applied Mathematics Hung-Lin Fu
Course Credits 3 Credits
Academic Year 109 Academic Year
Level Master student
Prior Knowledge Linear Algebra (I) and (II), Undergraduate Algebra (I), Discrete Mathematics
Related Resources Course Video   Course Syllabus   Course Handout

WeekCourse ContentCourse Video
Introduction to combinatorial design 1Watch Online
Introduction to combinatorial design 2Watch Online
Introduction of background knowledge: AlgebraWatch Online
Latin square 1Watch Online
Latin square 2Watch Online
Partial Latin squares 1Watch Online
Partial Latin squares 2Watch Online
Critical sets of Latin squaresWatch Online
Orthogonal Latin squares 1Watch Online
Orthogonal Latin squares 2Watch Online
Orthogonal Latin squares 3Watch Online
Transversals of Latin squares 1Watch Online
Transversals of Latin squares 2Watch Online
Extremal set theory 1Watch Online
Extremal set theory 2Watch Online
Block design 1Watch Online
Block design 2Watch Online
Steiner triple system 1Watch Online
Steiner triple system 2Watch Online
Steiner triple system 3Watch Online
Steiner triple system 4Watch Online
Steiner triple system 5Watch Online
Constructing designs using Latin squares 1Watch Online
Constructing designs using Latin squares 2Watch Online
Disproof of Euler’s conjecture 1Watch Online
Disproof of Euler’s conjecture 2Watch Online
On the construction of 2-(v, 4, 1) designsWatch Online
Packing and coveringWatch Online
t-design 1Watch Online
t-design 2Watch Online
Hadamard matrices 1Watch Online
Hadamard matrices 2Watch Online
Hadamard matrices 3Watch Online

課程目標

This is an introductory course of Combinatorial Designs.
Mainly, basic designs are introduced: Latin Squares, t-designs, Pooling designs and experimental designs.
We are aiming to learn also their applications.

 

課程章節

 

單元主題
組合設計簡介
拉丁方陣
正交拉丁方陣
極集合論
區集設計
Steiner triple system
反證歐拉猜想
Hadamard matrices

 

課程書目

Lecture Notes by Hung-Lin Fu.

 

評分標準

項目百分比
Homework100%

課程講義 Course Handout

章節 下載連結
Combinatorial Design Lecture 1-15PDF