Math589 Topological Methods in Graph Theory | 圖論中的拓樸方法


Announcements


Course Info top

Textbook

Graph Theory
   Reinhard Diestel
***** NSYSU has subscription to the electronic version of this book; visit Springer's website here through the school internet to access the book*****Course website

Learning objectives

This course focuses on graph structures — the connectivity, the planarity, and the minors. We will see how Menger's theorem characterizes the connectivity of a graph. On the other hand, Kuratowski's theorem shows that a graph is planar if and only if it does not contain \(K_5\) nor \(K_{3,3}\) as a minor. We will study the notion of minors and topological minors of a graph and see various families of graphs that are characterized by certain forbidden minors. In the end, we will go deeper into graph minors and study tree-width, tangle, the graph minor theorem, and so on.

Outlines

  • Connectivity
  • Planar graphs
  • Graph minors
  • Colin de Verdière parameter (optional)

Evaluation

30% Homework + 10% Active Learning + 20% Midterm1 + 20% Midterm2 + 20% Survey


Tentative Schedule top

Calendar


Homework/Quiz top

There are 30 homework assignments.

Homework: The homework will be assigned in each class. We will discuss how to solve the problems, but you have to type your answers in detail afterward. We will review your writing on Wednesdays. See NSYS Cyber University > Announcements for more details.

Active Learning: It is critical that you cultivate your active learning skills, which are not just for this course. You have to learn how to make a learning plan for yourself and how to stick with your plan. In this course, we introduce two things that you can do on a daily basis: One is for English learning, and the other is for mathematics learning.

  1. VoiceTube Pronunciation Challenge: Listen to the sentence and record your voice. That's it! You will learn new vocabularies day by day and build your listening/speaking skills at the same time.
  2. Play with a mathematics concept: Memorizing something is the very basic level of understanding. To understand a concept, you have to keep playing with it in your brain. Try to throw a question to yourself every once in a while, and try to catch it by answering the question. You will gain deeper understand of the concept. And more importantly, it's fun!

See NSYS Cyber University > 課程公告板 for more details.

Exams: After each exam, the questions and the sample answers will be uploaded below.


Policies/Ethics top

Accessibility

Students with diverse learning styles and needs are welcome in this course. In particular, if you have a disability/health consideration that may require accommodations, please feel free to approach me.

Grading

Percentage scores will be converted to letter grades according to the university-wide standard table.

Attendance

You are expected to attend the classes.

Missing work

If you miss some course components due to illness, accident, family affliction, or religious observances, please talk to me and provide the documentation. In such cases, the course component is excused, and your course score will be calculated by distributing the weight of the missed item(s) across the other course components. Missing components are limited to at most 20%.

Academic integrity

Do not copy others' work, including others' homework, the textbook, online materials, and others' answers in an exam; if it is really necessary, add proper citations to your references. It makes no point (and gives you no point) if the work is not yours since you learned nothing.