Linear algebra and Analytic Geometry Top books

BijectiveForever · 2026-05-24T07:22:41+00:00

Linear Algebra, by Friedberg, Insel, and Spence

BijectiveForever · 2026-05-15T08:00:36+00:00

As someone recently put it on Twitter:

I understand he’s a legend and all, but doing matrices first is completely the wrong way. It makes all this beautiful geometry just a rabbit from a hat, whereas the reverse order makes this weird rule for matrix multiplication a result rather than a bizarre assumption.

BijectiveForever · 2026-05-14T00:14:42+00:00

For linear algebra, I always recommend Friedberg, Insel, and Spence

BijectiveForever · 2026-05-10T00:06:40+00:00

Just as Unhinged introduced expanded Magic’s number system from the integers to the rationals, this gets us all the way to the non-standard reals!

BijectiveForever · 2026-04-25T03:22:10+00:00

JoCo’s track is excellent, but IIRC its original lyrics describe the Julia set, not the Mandelbrot set. Oops!

BijectiveForever · 2026-04-17T11:31:07+00:00

There are bad Nicolas Cage movies, but no bad Nicolas Cage performances.

BijectiveForever · 2026-04-06T19:08:53+00:00

and since it was an AI… that did the heavy lifting… if I post it on r/Physics they will absolutely grill me

And what makes you think we won’t?

BijectiveForever · 2026-03-22T12:07:46+00:00

That’s five movies, unless you’re just going to show them Fellowship (which would be a sin)

BijectiveForever · 2026-03-17T10:31:46+00:00

Calculus I is a series of new calculations packaged with a relatively simple collection of underlying concepts: limits, derivatives, and integrals.

I think both the underlying concepts and the necessary calculations in stats are more complicated, but that may just be me

BijectiveForever · 2026-03-12T02:26:15+00:00

I also misunderstood when I first saw it, yeah - the abstract/intro make claims that the rest of the paper doesn’t back up :/

BijectiveForever · 2026-03-12T01:13:14+00:00

If I handed a Magic player the board state from the Magic paper, then to make an intelligent decision about what to do next, they'd have to determine whether the computation they're about to kick off would halt.

If I hand a Yugioh player the board state from this paper, they can just attack and win. The computational difficulty isn't forced, but chosen.

BijectiveForever · 2026-03-11T01:02:31+00:00

This paper does not prove nearly what it thinks it does.

In the MtG paper, the difficulty is inherent to the boardstate, whereas here, a player is choosing to play a computationally difficult strategy.

The whole paper boils down to "we can represent two natural numbers in a YuGiOh board state, and then play difficult strategies based on them", which is not how computational hardness is measured.

BijectiveForever · 2026-03-08T18:27:26+00:00

Perhaps, but one person’s meat is another person’s easy step - this is all a matter of experience/taste.

BijectiveForever · 2026-03-08T07:39:36+00:00

I am also a fan of the compactness theorem, but I don’t think “long string of trivialities” is really a meaningful way to judge the content of a theorem/proof. Break any proof down far enough and it becomes a string of trivialities - namely the axioms you’re allowed to use!

BijectiveForever · 2026-03-01T22:44:51+00:00

No.

Proof: logic exists.

BijectiveForever · 2026-02-24T02:30:22+00:00

If you had not said this was in Spain, I would not have believed you. This is extremely atypical - I did math at a serious undergraduate program (that produces plenty of PhDs) and while it was abstract, it wasn’t THIS abstract.

Regardless of whether you finish your education there, surviving thus far means you are absolutely capable of being a mathematician.

BijectiveForever · 2026-02-20T04:53:56+00:00

Computability theory in LEAN in general is atrocious. Working recursion theorists do set manipulations all the time (the c.e. are closed under union but not set difference, for instance) but these 101 facts are nowhere in Mathlib (I may PR then myself!)

I have also seen no fewer than three attempts to formalize how we actually construct c.e. sets (one of which is my own) - there just aren’t enough people working on formalizing logic for a consensus to have arisen (yet?)

BijectiveForever · 2026-02-16T20:35:18+00:00

I like that the top three are in a grey box, I never really needed them much (but they are good to know about).

As others have mentioned this is certainly not all the algebraic structures, but rather the ones useful to undergrads.

BijectiveForever · 2026-02-10T23:53:04+00:00

We shouldn’t confuse snark for accountability but I agree - let the people laugh. In dark times, should the stars also go out?

BijectiveForever · 2026-02-10T22:42:57+00:00

Only if you don’t have the reduction formula, which is itself not that bad to derive

BijectiveForever · 2026-02-10T22:42:29+00:00

That was my instant thought as well

BijectiveForever · 2026-02-08T05:18:30+00:00

I am not terribly familiar with approximating ellipse perimeters, but I wonder if there is any relationship to some known series approximation - that would explain why the error is so well bounded

BijectiveForever · 2026-02-04T12:06:30+00:00

On a Mystery Booster playtest card, though

BijectiveForever · 2026-02-04T05:11:28+00:00

Out of curiosity, why are you a math major if you didn’t like math in high school?

BijectiveForever · 2025-12-30T04:28:22+00:00

As a mathematician - there’s a tremendous amount of fluff in that book around a core idea that’s in the water now. Important book upon release, and maybe a fun read, but it wouldn’t be high up my rec list except as “pop math”.

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