When I first caught a typo in this book which had mathematical implications, I knew I had to start keeping track of any edits I make, so that readers are not confused.
Here is the policy I intend to pursue with any corrections:
- The web version of the book, as well as the PDF that can be downloaded from the front page of the website, will be edited as soon as I have edits to make. The first page of the PDF shows the date it was last updated.
- From this page, you can download archived versions of the PDF which I will not edit further. I will post a new version at the beginning of every semester (on January 1st and August 1st) if there are any new edits to incorporate. If you are teaching from this book, you may want to give your students a link to one specific archived version, to avoid any confusion.
- Regardless, you can check this page to see all the changes I have made.
Current version
Download PDF
The following changes have been made since the previous version:
- I corrected problem 1 in Chapter 24; the previous statement of 1(b) was false.
- I corrected problem 5 in Chapter 26 to eliminate the trivial case of \(K_2\).
- I corrected problem 2 in Chapter 27 to skip an unnecessary case.
- I corrected an off-by-one error in the statement of Theorem 28.7.
- I made minor edits for clarity in Chapters 19, 24, 25, and 28.
- I added a practice problem to Chapter 14; some problem numbers in this chapter have changed.
- In the proof of Lemma 28.6, I added a sentence to address what happens if there is no \(s-x\) path in \(R'\).
- Problem 6 in Chapter 28 asked to prove too much and was false as stated; I replaced it by an easier but correct version, and added a new problem with some of the ideas from what the harder version would be.
The book was last edited October 19, 2026.
Fall 2026
Download PDF
The following changes have been made since the previous version:
- I replaced problem 4 in Chapter 4 by a shorter version, removing a suggested approach for solving it which was incorrect.
- I corrected problem 8 in Chapter 8 by adding the word “connected”.
- I added a second proof of Lemma 10.5 to Chapter 10.
- I corrected problems 6 and 8 in Chapter 12.
- I edited problem 2 in Chapter 13 to make it less computationally tedious and more mathematically interesting.
- I added problem 10 in Chapter 13 (from the most recent Putnam competition).
- I corrected the statement of Kuratowski’s theorem in Chapter 22, which was missing a “not”.
- I corrected the attribution of the short proof of the five-color theorem in Chapter 24; I discovered this summer that it already appeared in Birkhoff’s 1913 paper “The reducibility of maps”.
- I made minor edits for clarity in Chapters 5, 13, 14, and 15.
Spring 2026
Download PDF
This is the first archived version of the textbook.
