Graphs and Matrices
Ravindra B. Bapat
***** electronic version available at the library *****Course website
Spectra of Graphs
Andries E. Brouwer and Willem H. Haemers
***** electronic version available at the library *****
A Combinatorial Approach to Matrix Theory and Its Applications
Richard A. Brualdi and Dragoš Cvetković
***** electronic version available at the library *****
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 partition, graph drawing, etc. Throughout the course, you will experience various beautiful relations between graphs and matrices.
30% Homework + 10% Active Learning + 20% Midterm1 + 20% Midterm2 + 20% Survey
Homework will be assigned during the class, and you have to present your work to get a full credit, usually on next Wednesday.
Active learning: Learn actively and regularly. Reflect on what you have learned. Post a photo on Padlet, write a few sentences about what you have learned, and leave your student IDs. Names are optional. Each post counted as 0.25 point.
Exams: After each exam, the questions and the sample answers will be uploaded below.
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.
Percentage scores will be converted to letter grades according to the university-wide standard table.
You are expected to attend the classes.
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%.
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.