Careful readers of my blog might have heard about plans to have a second edition of Napkin out by the end of February. As it turns out I was overly ambitious, and (seeing that I am spending the next week in Romania) I am not going to make my self-imposed goal. Nonetheless, since I did finish a decent chunk of what I hoped to do, I decided the perfect is the enemy of the good and that I should at least put up what I have so far.
So since this is someplace between version 1 and the (hopefully eventually) version 2, it seems appropriate to call it version 1.5. The biggest changes include a complete rewrite of the algebraic geometry chapters, new parts on real analysis and measure theory, and a reorganization of many of the earlier chapters like group theory and topology, with more examples and problems. There’s also a new chapter 0 entitled “sales pitches” which gives an advertisement for each of the parts later. The obvious gaps: the chapters on probability are yet to be written, as is some more algebraic geometry. The updated flowchart from the beginning of the book is pictured below.
You can download the latest version from the usual page, or directly from https://usamo.files.wordpress.com/2019/02/napkin-v15-20190220.pdf. The number of errors has doubtless increased, and corrections are comments are more than welcome.
Incidentally, this seems as good a time as any to mention two more things:
- My personal website has seen some updates and re-organization, including most notably the OTIS lecture notes that I promised last Christmas, as well as my personal USAMO/IMO solutions.
- Also, I now have a public Facebook page. Right now I mostly plan to use it as a mirror for this blog, but I might also find some other uses for it later. Please feel free to like me ;)
That’s all. Hope you all like it! Best wishes from the Zurich airport.
Power Overwhelming 
At least on my end, it seems like the section hyperlinks are broken? Trying to go to the nth sales pitch takes me to the nth section of “Advice for the reader”.
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Totally made my day. Any notes from you are gems – already looking forward to reading them all. Thank you for writing the napkin – am also already looking forward to version 2!
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Have you by the way also thought of writing about some functional analysis? I‘m quite interested in how you would motivate topics in that subject.
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I don’t currently have plans to incorporate functional analysis, mostly because I don’t know it myself! Maybe eventually.
Power Overwhelming 於 2019年2月23日 週六，21:28寫道：
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I find that there is not a lot of analysis represented in the book, comparing to algebra and geometry. For example, I would like to see the following either appearing as chapters or “topics not in napkin”:
– “several complex variables” seems to be missing under “complex analysis”
– the “differentiation” part of measure theory also seems to be missing
– in general, “hard” analysis
– theory of differential equations
– functional analysis/operator theory
Also, no combinatorics is covered in the book. Maybe the appendix should list it.
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