Graphs and Matrices
Ravindra B. Bapat
***** electronic version available at the library *****Course website
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.
20% Homework + 20% Participation + 60% Presentation
You get 2 participation points whenever you ask a question, or share your thoughts during the class. The maximum participation point is 20 points for each person. Record your activities using the link above.
There are 10 homework assignments. The deadline of each assignment is on Thursday 10:00 am one week after it was assigned. Starting from HW3, you have to use \(\LaTeX\) to type your homework. [ template tex ]
Each student needs to give two 50-minute presentations. The goal is to convey the ideas clearly in a steady pace. It is not necessary to make slides; in fact, you are not encourage to do so since the speakers often rely on the slides too much and did not explain the content in detail. See TWAG Study Group for the schedule.
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%.