The funny thing about books is that authors in free societies are allowed to self-publish whatever they want. The norms are different and, frankly, more democratic and with less gatekeeping.
https://www.sscardapane.it/alice-book/
https://sscardapane.notion.site/Guided-lab-sessions-18c25bd1...
https://www.sscardapane.it/assets/alice/Alice_book_volume_1....
The corresponding row vector is denoted by x^T when we need to distinguish them. We can also ignore the transpose for readability, if the shape is clear from context.
All that being said, the writing style from the first chapter is very encouraging at how approachable this will be.
I am a practicing mathematician who felt the same way you did when I started, and who still writes their papers in a way that many of my colleagues feel is gallingly pedantic. With that as my credentials, I hope I may say that it can be much worse as a reader to read something where every detail is spelled out, because a bit of syntactic sugar begins to seem as important as the heart of an argument. Where the dividing line is between precision and obfuscation depends on the reader, and so inevitably will leave some readers on the wrong side, but a trade-off does have to be made somewhere.
I would certainly appreciate if math papers were more explicit and "hand-holding" but understand why trained mathematicians would find that tedious.
There's no reason except inertia why there couldn't be. Lamport actually proposed a system for this: https://lamport.azurewebsites.net/pubs/lamport-how-to-write.....
But I agree with your general point: understanding the recipe and general thrust of the approach is often more important, because even if the exact proof misses some technical detail, that can often be patched.
Indeed. Lamport says that this was part of what inspired his interest in formal proofs: https://mathoverflow.net/questions/35727/community-experienc....
Then my profs told me I was not “wrong”, but proofs or expositions are to most mathematicians not programs (ha! How did I not know. You teach me natural deduction and expect me not to program?), more like convincing arguments/prose. At some point one abstracts.
Of course, some mathematicians take it too far and use these abstractions to obfuscate and prove how smart they are. Like everything, it's a balance.
I personally wasn't a fan of this particular shorthand when I read this book but I got used to it quickly.
fossa1•7mo ago