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I haven't read Lax's linear algebra book, but I fell in love with his functional analysis book in the summer before I began grad school. His notes on hyperbolic

I haven't read Lax's linear algebra book, but I fell in love with his functional analysis book in the summer before I began grad school. His notes on hyperbolic pde are also great. Lax is of course a great mathematician, but he is also an incredibly lucid writer. He doesn't make anything more difficult than it needs to be. I would recommend reading anything written by him that you can get your hands on.

tanderson92 9y ago
There are three problems with Lax's book, from my experience (I used Lax in undergrad and Axler later and I would have gotten more from each if the order were reversed). 1) Lax leaves significant results to the problems, and the result is that there is little explanation of their importance. 2) Lax prefers short, mathematically impressive proofs which leverage the mathematics he has developed in the book to that point. But the proofs do not help in understanding. 3) Lax relies heavily on determinants and characteristic polynomials to prove major results. Axler deliberately avoids them, and he says why in the introduction too! Axler and Lax have two diametrically opposed approaches to linear algebra pedagogy. Neither is "wrong" but in my experience Axler's is much better for learning and Lax's is better for a deeper understanding (and for a different approach).
gajjanag 9y ago
Thanks a lot for this endorsement of his functional analysis book. I never got around to understanding functional analysis properly; mainly because I don't work on PDE's/control theory that would have used the ideas more heavily. Added to my todo list. Not really on topic, but I would like to use this opportunity to express gratitude to the HN community - although this forum is mostly tech-centric, it is wonderful to see things like this post get interest and discussion.
- tanderson92 9y ago
  Thank you for saying so! It's good to not feel left out. There are plenty of mathematicians and applied mathematicians here, too. We just do not comment on the JS/Rust discussions :)

tanderson92 9y ago

There are three problems with Lax's book, from my experience (I used Lax in undergrad and Axler later and I would have gotten more from each if the order were reversed). 1) Lax leaves significant results to the problems, and the result is that there is little explanation of their importance. 2) Lax prefers short, mathematically impressive proofs which leverage the mathematics he has developed in the book to that point. But the proofs do not help in understanding. 3) Lax relies heavily on determinants and characteristic polynomials to prove major results. Axler deliberately avoids them, and he says why in the introduction too! Axler and Lax have two diametrically opposed approaches to linear algebra pedagogy. Neither is "wrong" but in my experience Axler's is much better for learning and Lax's is better for a deeper understanding (and for a different approach).

gajjanag 9y ago

Thanks a lot for this endorsement of his functional analysis book. I never got around to understanding functional analysis properly; mainly because I don't work on PDE's/control theory that would have used the ideas more heavily. Added to my todo list. Not really on topic, but I would like to use this opportunity to express gratitude to the HN community - although this forum is mostly tech-centric, it is wonderful to see things like this post get interest and discussion.

tanderson92 9y ago
Thank you for saying so! It's good to not feel left out. There are plenty of mathematicians and applied mathematicians here, too. We just do not comment on the JS/Rust discussions :)