Mastodawn

Oh, but Linear Algebra is love! The purest human reflection on the exercise of simplicity in the apparent chaos of the world.

I am only half joking! :-) I appreciate your post is about LLMs. They are an obscene misuse of a sacred practice.

My worn-out copies of Paul Halmos's Finite Dimensional Vector Spaces and Emil Artin's Geometric Agebra --- these are the most treasured books in my personal library. (After The Magic Mountain, of course, but _that_ battered volume sits on a different shelf.)

#LinearAlgebra #PaulHalmos #EmilArtin #SimplicityIsLove #LLMsAreBlaphemous

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the roamer Apr 12

@ZachWeinersmith

I'm not up to date on recent Linear Algebra textbooks, but hey! Strang's book is uniquely beautiful, and uniquely effective in conveying deep structural insights elegantly and with concrete examples that stay with the reader. Perfect for a class setting, but also eminently suitable for self study. The right choice for your project! (imho)

Each field has a textbook that is accessible to inexperienced readers yet true to the deeper structures of the subject. That book ought to be written in every field, but in most fields it never is written. It requires a gifted author to come along and do the deed. Gilbert Strang's writing of his book was one of these special and rare events.

As it happens, linear algebra had another such event, a generation before Strang, in the shape of Paul Halmos's Finite-Dimensional Vector Spaces. Another beauty, on the abstract side of the spectrum, and perhaps the perfect complement to Strang.

#LinearAlgebra #GilbertStrang #PaulHalmos

the roamer Dec 27

A two-part lecture course on Topology, by Professor N. The first part is in the spring semester, the second part in the following autumn semester; between them is the long summer break.

First week of the autumn semester, first lecture. Professor N comes into the room. He walks to the blackboard and picks up the chalk. He turns to the class and starts:

"Hence, ... "

---
[Anectdote told by Paul Halmos in his autobiography. I quote from memory, so the details will vary.]

#lectures #HigherEducation #pedagogy #PaulHalmos

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the roamer Jul 27, 2025

@darkling

Indeed. And another re-arrangement of the axioms.

Paul Halmos in his autobiography reports on one of his colleagues who taught a course in measure theory (I quote from memory). He set out the axioms in lecture 1. Come lecture 2, and he explains that actually, the right axioms should be such and such. And so the semester progresses, each week a new, better axiom system, with no time left for any derivations.

I love that story, on so many levels.

#PaulHalmos #axiomatics #teaching #procrastination #TakeYourTime #yesthestudentswillhavelearntmoreinthislecturethaninanyother