Reddit reviews Physics for Mathematicians, Mechanics I

Physics for mathematicians - Spivak (http://www.amazon.com/Physics-Mathematicians-Mechanics-Michael-Spivak/dp/0914098322)

> There's a book that I cannot find now (hopefully someone else can come along and provide the reference) which is also "physics for mathematician".

Spivak! I have a copy and it's really good.

You could try Spivak’s book, Physics for Mathematicians, https://amzn.com/0914098322

https://www.amazon.com/Physics-Mathematicians-Mechanics-Michael-Spivak/dp/0914098322

Those notes eventually became this beautiful book.

I have spent many hours with it since it came out a couple of years ago. I can highly recommend it to anyone who, like myself, picked a lot of modern physics here and there, but never bothered to go back to thinking about classical mechanics.

Yes. I remember reading one of michael spivak's books where he says something like what you said, he then said he was attempting to make books titled "* for mathematicians" (mathematician here). This is the only one i know he actually made: physics for mathematicians

I did hope he did the series, but have lost it since. It would be amazing if there was a similar thing for ML

Er, sorry, I'm conflating a few things.

1. What would be a good recommendation for the OP
   
2. My thoughts on mathematical pedagogy and curriculum
   
   WRT (1), Spivak is fastidiously rigorous. It's not as dry as the standard higher-level textbooks like Baby Rudin, Munkres, and so on, but it's every bit as rigorous. A high-school student who has read through Spivak on his own is a pretty unusual character.
   
   For example, although Spivak doesn't use the jargon, there are several examples and exercises that ask students to prove various facts about vector spaces (finite and infinite-dimensional), linear transformations, and so on. The last chapter of Spivak is identical to the first chapter of Baby Rudin, after all — the construction of the real numbers from the rational numbers using Dedekind cuts and proving that the real numbers are the unique Archimedian complete totally ordered field up to isomorphism.
   
   That's the situation the OP is coming from, so "linear algebra" might be fun, but as a recommendation I think the OP will enjoy a more foundational approach to what they study next. It's good that he can see all the choices in front of him, of course.
   
   And I have no opinion about your specific recommendation, either, since I've never heard of that book.
   
   WRT (2), well, I love linear algebra. I'm generally frustrated with how it's taught. I feel the same way about probability and statistics, too.
   
   I admit I'm a bit of an odd duck when it comes to a typical math undergrad. I found physics, especially Newtonian mechanics and classic E&M, incredibly frustrating. That is, until we got to relativity and QM — smooth sailing from there! Later, I bought and read Physics for Mathematicians: Mechanics by (wait for it!) Michael Spivak and was finally able to understand WTF was going on with mechanics.
   
   Most of (undergrad) physics, linear algebra, ODEs, and so on always felt like a grab bag of manipulations and techniques that were justified "because they worked." This is exactly what I hated about math in HS and it wasn't until I had Spivak's Calculus in my first-year calculus course that I realized that high-school math wasn't really "math."
   
   Like I said, this is unusual, although I suspect the OP is more like me than the folks shouting "linear algebra! ODEs! multi-variable calculus!" I believe that there's a way to teach these subjects without such a strong divide between what folks call "practice" and "theory." I love Axler's Linear Algebra Without Determinants, for example, and this PDF about the relationship between differential equations and linear algebra.
   
   So, I'm not sure we're disagreeing about anything, really, although it seems like you think we are? I'm not advocating for anything in particular so much as expressing my thoughts and experiences from my math undergrad and how they relate to the OP's current situation.

If you want to start with mechanics, Spivak of all people [wrote a mechanics text.] (http://www.amazon.com/gp/aw/d/0914098322) I've personally never read it, but I've suffered more than enough at his hands read enough of his other works to expect good things.

In more advanced physics, there's general relativity, which is built on manifold theory, and gauge theory, which has lots of interesting math happening behind the scenes (and sometimes very prevalently, as with the gauge groups, usually taken to be SU(n)). Most physics texts will treat the mathier topics as of secondary interest and importance, and focus on the actual physics, so you might have some trouble finding an appropriately rigorous text, but there certainly exist such entities.

Also, let's not forget about Michael Spivak's^1 Physics for Mathematicians: Mechanics 1.


^1 you may have heard about his books on Calculus and Differential Geometry

Maybe this will help

Haven't looked at it so can't speak to it's quality but:

Physics for Mathematicians provides an axiomatic introduction to classical mechanics: https://www.amazon.com/Physics-Mathematicians-Mechanics-Michael-Spivak/dp/0914098322

Axiomatizing physics is one of Hilbert's problems.