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
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So far, this is identical to the Fall 2026 version below.
The book was last edited August 1, 2026.
Fall 2026
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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
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This is the first archived version of the textbook.
