This one is not just in Dummit and Foote; it's just too easy to miss. I'd guess it appears in half the places that state this result. Fixed it in my own lecture notes a few months ago.
I ran into this same thing formalizing some of my old notes in Lean a few days ago. The tricky thing I suppose is that 0. Injectivity and A non-empty or B empty implies left invertibility, 1. Left invertibility implies injectivity. 2. Surjectivity iff right invertibility, and 3. Surjectivity rules out this corner case, so bijectivity iff invertibility. So this one vacuous case just throws a wrench in what is "supposed" to be true.
Those habitual mitigations go a long way. Just like there is defensive programming, there is defensive usage.
Under Windows: Don't put your files into "My Documents" or similar folder hierarchies; you never know if old software will correctly deal with the abstraction.
Working with files in general: Avoid nonstandard unicode names or long paths so your external hard drive doesn't choke on them. Avoid case sensitivity even when it is allowed on Unix systems, since you can't assume Windows won't ever touch them. Avoid whitespaces in names because sooner or later, some script won't escape them.
On the internet: Never draft long comments in the browser; always use a local text file. Anything can happen in the browser.
In games: Never save your game during what looks like a complex scripted scene even if the game does allow saving.
Using search engines: Avoid keywords that are likely to confuse/distract the search.
With dropbox-likes: Give it some time to sync even after the icon is green; god knows what is being predictively shortcutted under the hood.
Everywhere: Restart the program or system if certain signs of corruption appear. You don't know what's going wrong, but you know something is, and barring some unusually careful compartmentalization, a piece of software is still a state machine which, once it has strayed from the right path, cannot be trusted at all. OSes nowadays are adapted to this, but much of software is not, and you do not want to have it corrupt your file.
I feel like this question is typed wrong but the same reason someone wants copyright on human work to make money by prevent other people from stealing your work
Given the cost of generating images/text/etc. is much lower when using an AI system, as compared to a human, this seems appropriate. The purpose of intellectual property is to encourage people to invest that time into creating works that benefit others. Perhaps there’s an argument for a shorter copyright period to cover the cost of the compute spent, but certainly one wouldn’t expect AI intellectual property to require a similar level of incentive to produce.
- pre GPT-5.4: very limited use; some smart people got some mileage out of the models, but it always required serious work and a very suitable problem. Of course the models could solve homework problems, but that felt more like a downside to us who teach.
- since GPT-5.4 (Mar 2026): the "wow" release; suddenly answering MathOverflow-level problems that have previously been stumping experts. Still prone to hallucinations, but smart enough to use the built-in Python skill to verify its claims on small examples when possible. Probably a lot better at formula-heavy math than at the abstract "philosophical" kind.
- GPT-5.5: gave me a fascinating, significantly nontrivial and highly instructive "proof from the book" on an MO-hard problem that I'm in the process of writing up. Might have been luck and good prompting, though. Didn't really feel like a qualitative leap from 5.4, but I take quantitative any time. Still requires suitable problems, but it's much harder to rule out suitability from the get-go.
Claude and Gemini have been also-rans the whole time and still are. I use Claude for secretary-like tasks; occasionally it finds an easy proof too, but usually because I've missed something obvious.
Oh, and GPT, and to a lesser extent Claude, are great at hunting errors in maths. Probably 90% of my prompts so far have been for proofreading my writings.
Graham/Knuth/Patashnik is a lot less "basic discrete maths you're most likely to need" and a lot more "number sequences we've known and loved". Almost more useful for physicists due to the amount of summation fu you'll learn there.
The book Concrete Mathematics started as course notes for a class whose textbook initially was the (dense) "Mathematical Preliminaries" chapter of The Art of Computer Programming (Chapter 1 and roughly the first half of Volume 1), so it can be seen as an expanded and leisurely (and even more delightful, because of all the student jokes and other marginalia) version of that chapter. This is mathematics that Knuth needed for the rest of TAOCP.
So it's more "mathematics for the analysis of algorithms" (incidentally the title of another book by Greene and co-authored by Knuth), and so probably most applicable to the field of "AofA" rather than physics or computer science in general.
Lovely book, very few math books fill one with as much joy as this one.
This looks like an index of Mir books, without any additional sorting or curation. You probably can get a good education on many topics out of these, but also waste significant time on reading out-of-date and out-of-order texts. Someone experienced could make this a lot more useful by proposing a reading order and giving some sort of evaluations of importance and quality.
And keep in mind that these are from the pre-1990 USSR, so don't expect any modern maths or CS.
on the other hand, one could argue, for basic stuff it would be ok, but I agree, it is not really well curated, there are some books, which are duplicate
I have a hunch that most of the slop is not just on CS but specifically about AI. For some reason, a lot of people's first idea when they encounter an LLM is "let's have this LLM write an opinion piece about LLMs", as if they want to test its self-awareness or hack it by self-recursion. And then they get a medley of the learning data, which if they are lucky contains some technical explanations sprinkled in.
That said, AI-generated papers have already been spotted in other disciplines besides cs, and some of them are really obvious (arXiv:2508.11634v1 starts with a review of a non-existing paper). I really hope arXiv won't react by narrowing its scope to "novel research only"; in fact there is already AI slop in that category and it is harder to spot for a moderator.
("Peer-reviewed papers only" is mostly equivalent to "go away". Authors post on the arXiv in order to get early feedback, not just to have their paper openly accessible. And most journals at least formally discourage authors from posting their papers on the arXiv.)
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