Prerequisites: |
Linear algebra at the level of Math 2142 or 2243,
and either Math 2283 or 3283 (or their equivalent). Students will be expected to know calculus and linear algebra (e.g. familiarity with determinants and eigenvalues is expected), and be ready to read, understand and write proofs. |
Class location, time: | Mon-Wed 11:15 AM - 1:10 PM in Akerman Hall 211 |
Instructor: | Victor Reiner (You can call me "Vic"). |
Office: Vincent Hall 256 Telephone (with voice mail): 625-6682 E-mail is better: reiner@math.umn.edu |
|
Office hours: | To be determined. |
Discord server: | We will create a Discord server for the class, and post the link here. We hope it facilitates forming any study groups for the classe, which are encouraged. |
Required text: |
This is our only required text, a free PDF: Graph theory with applications by J.A. Bondy and U.S.R. Murty |
Course content: |
Graphs are networks of vertices (nodes) connected by edges. They are interesting objects in mathematics, but also usefully model problems in computer science, optimization, and social science. This is a first course in graph theory, emphasizing classical topics, such as
|
Title | Author(s), Publ. info |
---|---|
Introduction to graph theory | D. West, Prentice Hall 1996 |
Modern Graph Theory | B. Bollobas, Springer Graduate Texts in Math |
Graph theory | R. Diestel, The author's download page |
Schaum's outlines: graph theory | V. K. Balakrishnan |
A course in combinatorial optimization | A. Schrijver, The author's download page |
Homework, exams, grading: |
There will be 5 homework assignments due usually every 2-3 weeks, but
I encourage collaboration on the homework, as long as each person understands the solutions, writes them up in their own words, and indicates on the homework page their collaborators. The take-home midterms and final exam are open-book, open-library, open-web, but in contrast to the homework on exams, no collaboration or consultation of human sources is allowed. We will only be using the course Canvas site for turning in the homeworks and exams as PDFs. If you write solutions by hand, then use a scanning app (e.g., Adobe Photo Scan) or a scanner to create the PDFs. Do not just take a photo and convert it to PDF, as those are harder to read. Late homework will not be accepted. Homework solutions should be well-explained-- the grader is told not to give credit for an unsupported answer. Complaints about the grading should be brought to me. |
Grading scheme : |
|
Assignment or Exam | Due date | Problems (from Bondy and Murty, unless specified otherwise) |
---|---|---|
Homework 1 | Wed, Feb 8 |
Section 1.2: #4,10,11 Section 1.4: #4 Section 1.5: 5,7(a),10 Section 1.6: #7,10 Section 1.7: #2,31 Section 4.1: #1,2 Section 4.2: #2,3 |
Homework 2 | Wed, Feb 22 | |
Midterm exam 1 | Wed, Mar 1 | The exam will appear here in PDF. |
Homework 3 | Wed, Mar 29 | |
Homework 4 | Wed, Apr 12 | |
Midterm exam 2 | Wed, Apr 19 | The exam will appear here in PDF. |
Homework 5 | Wed, May 3 | |
Final exam | Wed, May 10 | The exam will appear here in PDF. |
Topic | Author | Title/info |
---|---|---|
List of open problems and conjectures in graph theory |
Doug West's Bonato and Nowakowski's IRMACS |
problems page
Sketchy Tweets: 10 minute conjectures in graph theory Open Problem Garden for Graph Theory |
Probabilistic method | N. Alon and J. Spencer | The probabilistic method
Wiley-Interscience, 2000 |
Surfaces and graphs on them | W.S. Massey | (Chap. 1 of) Algebraic topology: an introduction Springer-Verlag Graduate Texts in Math 56 |
P. Giblin | Graphs, surfaces and homology
Cambridge Univ. Press 2010 |