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One example I'm aware of is Lawvere's fixed point theorem, of which Gödel's (first) incompleteness theorem, the undecidability of the Halting problem, and Cantor's theorem are all special cases.

Not really related to "group theory, linear algebra, real analysis, etc.", but interesting nevertheless.

It's quite a wide generalisation which really just captures the nature of diagonalisaion arguments, but it does formally tie together various proofs/theorems which "smell the same".

> Couldn't tell an average from a median

Without meaning to attack you personally (especially in the context of the rest of your comment), a comment like this annoys me a bit.

I presume by "average" you mean arithmetic mean, but the median is also an average, and depending on the context the median might be a far more useful statistic than the mean. Confusing the mean and the median is one thing, and perhaps you actually used this terminology in the interview; "confusing" "the average" and the median isn't really worthy of comment, and sounds more like a breakdown in communication between interviewer and candidate rather than a lack of technical knowledge. It just seems vaguely hypocritical to me to be expecting a certain level of ability from the candidate and then using imprecise/informal terminology.

This seems pretty good from a brief flick through; the author. Graham Hutton, is pretty well known in the CS community.

Some other resources for people who find that this piques their interest and that they want to go deeper:

* Formal Reasoning About Programs ("FRAP") by Adam Chlipala - available for free here: http://adam.chlipala.net/frap/. Forms the basis for 6.822 at MIT, and comes with an accompanying Coq formalisation (as well as psets in Coq).

* The Formal Semantics of Programming Languages: An Introduction by Glynn Winskel.

Nigel Smart's Cryptography Made Simple is a great book which covers elliptic curve cryptography amougst many other topics; despite its name it's a very technical book, but it's easily accessible to anyone with a CS/EE/Maths/Physics degree.

You can grab a copy from SpringerLink for free at the moment here: https://link.springer.com/book/10.1007%2F978-3-319-21936-3

You mean a piecewise definition of a function? I don't think this is unidiomatic or discouraged in Haskell at all.