We will learn ...
Graph theory is a universal tool to model many objects, including computer networks, social networks, relationships, and so on. On the other sides, matrices provide an intuitive way to record the data on graphs (weight, flow, capacity, and so on), while the eigenvalues and eigenvectors are holding the essential information of the data. In this course, we will focus on the adjacency matrix and the Laplacian matrix of a graph and introduce their applications, for example, counting the number of walks, modeling random walks, characterization of regular graphs, counting the number of spanning trees, graph partitioning, graph drawing, etc. Throughout the course, you will experience various beautiful relations between graphs and matrices.
Matrix theory
reviewing matrix properties from a graph theory point of view
Adjacency matrices
counting the number of walks, modeling random walks, characterization of regular graphs
Laplacian matrices
counting the number of spanning trees, graph partitioning, graph drawing
You need to do ...
HW0: Tell me your email before September 12 to get extra 2pt — this is a required work. Important information will be announced through email.
Matrix theory
Midterm 1 (20%):
Adjacency matrices
Midterm 2 (20%):
Laplacian matrices
Survey (20%):
Homework (40%):
A few tips for learning mathematics ...
Mistakes Make You Smarter: Everyone learns through experiences and mistakes. For each new concept you learn, generate as many examples as possible to train your brain to distinguish between right and wrong.
Ask Questions: Beyond knowledge, mathematics is fundamentally about logic. Question everything you encounter—why it is defined this way, why an assumption is required, why a proof needs a particular step, and so on.
Think Carefully: Sound arguments should hold true in any circumstance. Verify the examples you generate to ensure they align with your argument.
Help Each Other: Learning together can make the process easier. Teaching others is also an effective way to reinforce your own understanding.
Course Info
- Term: Sep 8, 2025 – Dec 26, 2025
- Meeting time: Tuesday, 9:10 am – 12:00 noon @ SC4013
- Instructor: Jephian Lin | 林晉宏
- Email: chlin [at] math.nsysu.edu.tw
- Office: SC2002-5
- Office Hours: Tuesday, 3:10 pm – 5:00 pm
- Office Hours: Thursday, 3:10 pm – 5:00 pm
Textbook
Graphs and Matrices
Ravindra B. Bapat
Further Resources
Spectra of Graphs
Andries E. Brouwer and Willem H. Haemers
A Combinatorial Approach to Matrix Theory and Its Applications
Richard A. Brualdi and Dragoš Cvetković
Tentative Schedule
Policies/Ethics
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.